492. Construct the Rectangle

1. Question

A web developer needs 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.

Return an array [L, W] where L and W are the length and width of the web page you designed in sequence.

2. Examples

Example 1:

Input: area = 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.

Example 2:

Input: area = 37
Output: [37,1]

Example 3:

Input: area = 122122
Output: [427,286]

3. Constraints

• 1 <= area <= 10⁷

4. References

来源：力扣（LeetCode） 链接：https://leetcode-cn.com/problems/construct-the-rectangle 著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

5. Solutions

开根解决

class Solution {
  public int[] constructRectangle(int area) {
    int length = (int) Math.sqrt(area);

    while (area % length != 0) {
      length--;
    }
    return new int[] { area / length, length};
  }
}