Construct The Rectangle

Problem Statement

A web developer needs to know how to design a web page's size. Given a specific rectangular web page’s area, your task is to design a rectangular web page with length L and width W that satisfy the following requirements:

1. The area of the rectangular web page must equal 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.

Examples

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

• $1 <= area <= 107$

Algorithm

1. Start by initializing the width W as the integer square root of the given area.
2. Decrement the width W until you find a divisor of the area.
3. The corresponding length L is the quotient of the area divided by the width.
4. Return [L, W].

Code

Python

import math

class Solution:
    def constructRectangle(self, area: int) -> List[int]:
        width = int(math.sqrt(area))
        while area % width != 0:
            width -= 1
        length = area // width
        return [length, width]

C++

class Solution {
public:
    vector<int> constructRectangle(int area) {
       int width = sqrt(area);
       while (area % width != 0) {
           width--;
       }
       int length = area / width;
       return {length, width};
    }
};

Java

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

JavaScript

var constructRectangle = function (area) {
  let width = Math.floor(Math.sqrt(area));
  while (area % width !== 0) {
    width--;
  }
  let length = Math.floor(area / width);
  return [length, width];
};