492. Construct the Rectangle

#### QUESTION:

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.

#### SOLUTION:

``````public class Solution {
public int[] constructRectangle(int area) {
int[] result = new int[]{area,1};
for(int i = area ;i > 0;i--){
if(area%i!=0) continue;
int y = area/i;
if(i<y) continue;
result = result-result < i-y ? result: new int[]{i,y};
}
return result;
}
}

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