[LeetCode] 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.

Thought process:
First get the square root of area.
  1. If area is a perfect square: square root is both the length and width.
  2. Otherwise: length is larger than sqrt and width is less. So treat it as length / width as increment / decrement until it's divisible by area.

Solution:

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

Time complexity: O(a - sqrt(a)) = O(a).
Location: Philadelphia, PA, USA

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