# 492. Construct the Rectangle

**<font color=red>难度: Easy</font>**

## 刷题内容

> 原题连接

* https://leetcode.com/problems/construct-the-rectangle/

> 内容描述

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

## 解题方案

> 思路 1
******- 时间复杂度: O(sqrt(N))******- 空间复杂度: O(1)******

sb题没什么好说的，beats 100%

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



