Description： 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.

題意：給定一個網頁的矩形空間的面積target，計算最優的長L和寬W；需要滿足三個條件：

1. 滿足L x W = target
2. L >= W
3. dif = |l_i - w_i|= argmin_i|l_i - w_i|

解法：窮舉所有的可能，首先需要排除那些不符合條件1和2的，再來選擇最優的那個；

Java

class Solution {
    public int[] constructRectangle(int area) {
        int L = 0;
        int W = 0;
        int dif = Integer.MAX_VALUE;
        for (int l = 1; l <= area; l++) {
            int w = area / l;
            if (l * w != area || l < w) continue;
            if (l - w < dif) {
                L = l;
                W = w;
                dif = l - w;
            } 
        }
        return new int[] {L, W};
    }
}