Leetcode problem – 492. Construct the Rectangle

Description:

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:

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.

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 power of 7

Solution:

class Solution {
    public int[] constructRectangle(int area) {
        int width = 1;
        int length = area;
        int areaCount;
        int[] result = new int[2];
        int diff = Integer.MAX_VALUE;


        while(length>=width){
           areaCount = width*length;
           
           if(area==areaCount && diff>(length-width)){
             diff = length-width;
             result[0] = length;
             result[1] = width;
           }
           width++;
           length = area/width;
        }
        return result;
    }
}

Approach:
To find the dimensions of a rectangle (length and width) with a given area, loop through possible values of width and calculate the corresponding length as area / width. Continue this process as long as width <= length, since we only need to consider cases where the length is greater than or equal to the width.

For each pair (length, width) that satisfies length * width == area, check which one has the smallest difference between length and width. This ensures we find a pair with dimensions as close as possible.

Example #1:
Input: area = 4
Possible pairs:

(4, 1) → Difference = 3

(2, 2) → Difference = 0

Output: (2, 2) — because it has the minimum difference between length and width.