492. Construct the Rectangle

1. 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.

2. Example

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]

3. Constraints

• 1 <= area <= $10^7$

4. Solutions

My Accepted Solution

n = area
Time complexity: O($\sqrt{n}$)
Space complexity: O(1)

class Solution 
{
public:
    // vector<int> constructRectangle(int area)
    vector<int> constructRectangle(int area) 
    {    
        int width = sqrt(area);
        for ( ; width >= 1; width--)
        {
            if (area % width == 0) 
                break;
        }
        
        return vector<int>{area / width, width};
    }
};