Given a rectangle of length l and breadth b, we need to find the area of the smallest square which can be formed with the rectangles of these given dimensions.
Examples:
Input : 1 2 Output : 4 We can form a 2 x 2 square using two rectangles of size 1 x 2. Input : 7 10 Output :4900
Let’s say we want to make a square of side length a from rectangles of length l & b. This means that a is a multiple of both l & b. Since we want the smallest square, it has to be the lowest common multiple (LCM) of l & b.
Program 1:
C++
// C++ Program to find the area// of the smallest square which// can be formed with rectangles// of given dimensions#include <bits/stdc++.h>using namespace std;// Recursive function to return gcd of a and bint gcd(int a, int b){ // Everything divides 0 if (a == 0 || b == 0) return 0; // Base case if (a == b) return a; // a is greater if (a > b) return gcd(a - b, b); return gcd(a, b - a);}// Function to find the area// of the smallest squareint squarearea(int l, int b){ // the length or breadth or side // cannot be negative if (l < 0 || b < 0) return -1; // LCM of length and breadth int n = (l * b) / gcd(l, b); // squaring to get the area return n * n; }// Driver codeint main(){ int l = 6, b = 4; cout << squarearea(l, b) << endl; return 0;} |
Java
// JavaProgram to find the area// of the smallest square which// can be formed with rectangles// of given dimensionsclass GFG {// Recursive function to // return gcd of a and bstatic int gcd(int a, int b){// Everything divides 0if (a == 0 || b == 0) return 0;// Base caseif (a == b) return a;// a is greaterif (a > b) return gcd(a - b, b);return gcd(a, b - a);}// Function to find the area// of the smallest squarestatic int squarearea(int l, int b){// the length or breadth or side// cannot be negativeif (l < 0 || b < 0) return -1; // LCM of length and breadth int n = (l * b) / gcd(l, b); // squaring to get the area return n * n; }// Driver codepublic static void main(String[] args) { int l = 6, b = 4; System.out.println(squarearea(l, b));}}// This code is contributed // by ChitraNayal |
Python 3
# Python3 Program to find the area# of the smallest square which# can be formed with rectangles# of given dimensions# Recursive function to return gcd of a and bdef gcd( a, b): # Everything divides 0 if (a == 0 or b == 0): return 0 # Base case if (a == b): return a # a is greater if (a > b): return gcd(a - b, b) return gcd(a, b - a)# Function to find the area# of the smallest squaredef squarearea( l, b): # the length or breadth or side # cannot be negative if (l < 0 or b < 0): return -1 # LCM of length and breadth n = (l * b) / gcd(l, b) # squaring to get the area return n * n # Driver codeif __name__=='__main__': l = 6 b = 4 print(int(squarearea(l, b)))#This code is contributed by ash264 |
C#
// C# Program to find the area// of the smallest square which// can be formed with rectangles// of given dimensionsusing System;class GFG{// Recursive function to // return gcd of a and bstatic int gcd(int a, int b){// Everything divides 0if (a == 0 || b == 0) return 0;// Base caseif (a == b) return a;// a is greaterif (a > b) return gcd(a - b, b);return gcd(a, b - a);}// Function to find the area// of the smallest squarestatic int squarearea(int l, int b){// the length or breadth or side// cannot be negativeif (l < 0 || b < 0) return -1; // LCM of length and breadth int n = (l * b) / gcd(l, b); // squaring to get the area return n * n; }// Driver codepublic static void Main() { int l = 6, b = 4; Console.Write(squarearea(l, b));}}// This code is contributed // by ChitraNayal |
PHP
<?php // PHP Program to find the area// of the smallest square which// can be formed with rectangles// of given dimensions// Recursive function to// return gcd of a and bfunction gcd($a, $b){ // Everything divides 0 if ($a == 0 || $b == 0) return 0; // Base case if ($a == $b) return $a; // a is greater if ($a > $b) return gcd($a - $b, $b); return gcd($a, $b - $a);}// Function to find the area// of the smallest squarefunction squarearea($l, $b){ // the length or breadth or side // cannot be negative if ($l < 0 || $b < 0) return -1; // LCM of length and breadth $n = ($l * $b) / gcd($l, $b); // squaring to get the area return $n * $n; }// Driver code$l = 6;$b = 4;echo squarearea($l, $b)."\n";// This code is contributed // by ChitraNayal?> |
Javascript
<script>// Javascript Program to find the area// of the smallest square which// can be formed with rectangles// of given dimensions// Recursive function to // return gcd of a and bfunction gcd(a , b){ // Everything divides 0 if (a == 0 || b == 0) return 0; // Base case if (a == b) return a; // a is greater if (a > b) return gcd(a - b, b); return gcd(a, b - a);}// Function to find the area// of the smallest squarefunction squarearea(l , b){// the length or breadth or side// cannot be negativeif (l < 0 || b < 0) return -1; // LCM of length and breadth var n = (l * b) / gcd(l, b); // squaring to get the area return n * n; }// Driver code var l = 6, b = 4; document.write(squarearea(l, b));// This code is contributed by Amit Katiyar </script> |
Output:
144
Time Complexity: O(log(min(l,b)))
Auxiliary Space: O(log(min(l, b)))
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