492. Construct the Rectangle

Problem

A web developer needs 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:

• The area of the rectangular web page you designed must equal to the given target area.

• The width W should not be larger than the length L, which means L >= W.

• The difference between length L and width W should be as small as possible.

Return an array [L, W] where L and W are the length and width of the web page you designed in sequence.

  Example 1:

Input: area = 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.

Example 2:

Input: area = 37
Output: [37,1]

Example 3:

Input: area = 122122
Output: [427,286]

  Constraints:

• 1 <= area <= 10^7

Solution (Java)

class Solution {
    /*
      Algorithm:
     - start with an index i from the square root all the way to 1;
     - if at any time, area % i == 0 (so i is a divisor of area), then it's the closest solution.
    */
    public int[] constructRectangle(int area) {
        int low = (int) Math.sqrt(area);
        while (low > 0) {
            if (area % low == 0) {
                return new int[] {area / low, low};
            }
            low--;
        }
        return new int[] {0, 0};
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).