题目描述：

LeetCode 492. Construct the rectangle

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.

题目大意：

给定矩形的面积area，返回矩形的长度L和宽度W，使得L和W的差值最小。

注意：

1. 给定面积是正整数并且不超过10,000,000
2. 长度和宽度必须是正整数

解题思路：

枚举法

记area的平方根为sqrt

从int(sqrt) 向 1 递减枚举宽度W，若area % W == 0，则L = area / W

Python代码：

class Solution(object):
    def constructRectangle(self, area):
        """
        :type area: int
        :rtype: List[int]
        """
        sqrt = int(math.sqrt(area))
        L, W = area, 1
        for x in range(sqrt, 0, -1):
            if area % x == 0:
                L, W = area / x, x
                break
        return [L, W]

 

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