給定一個面積，求長寬差值最小的結果 Construct the Rectangle

問題：

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.

解決：

①  本質上是求一個整數（面積）差值最小的兩個因子，而且長大於寬。

class Solution { //551ms
    public int[] constructRectangle(int area) {
        int x = area;
        int y = 1;
        int diff = x - y;
        for (int i = x;i >= y;i --){
            if (area % i == 0){
                if (diff > Math.abs(i - area / i)){
                    diff = Math.abs(i - area / i);
                    x = i;
                    y = area / i;
                }
            }
        }
        return new int[]{x,y};
    }
}

② 

class Solution { //5ms
    public int[] constructRectangle(int area) {
        int w = (int)Math.sqrt(area);
        while(area % w != 0 ) w --;
        return new int[]{area / w, w };
    }
}