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.

class Solution {
    public int[] constructRectangle(int area) {
        int sq = (int) Math.sqrt(area);
        for(int i = sq; i >=1; i--){
            if(! (area % i == 0)) continue;
                return new int[]{area / i, i};
        }
        return new int[]{};
    }
}

 Note:

To make two numbers multiply to get another number, we know both of them should less or equal to sqrt(area), so we start from that and check the answer.