Construct the Rectangle Problem & Solution

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.

See the construct the rectangle problem on LeetCode.

C++ Solution

#pragma GCC optimize("Ofast")
#pragma GCC optimization("unroll-loops")

static const int _=[](){ios::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);return 0;}();

class Solution {
  vector<int> constructRectangle(int area) {

    // Starts with the square root and keeps decrementing to find an exact match.
    for (int i = sqrt(area); i > 0; --i) {
      if (area % i == 0) {

        // The denominator keeps getting smaller, so `area / i` will be larger.
        return {area / i, i};

    // If the area is a prime number, return itself because it's the only way to decompose.
    return {area, 1};