leetcode解题: Construct the rectangle (492)

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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:

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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:

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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.

解法1：O(Sqrt(area))

按照提议，如果area是一个完全平方数的话正方形的边长就是最佳答案。那么可以从平方根出发，找出 1 <= x <= sqrt(area)当中最大的能被area整除的数就是所要求的。
Java

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