Related Articles

# Check if N rectangles of equal area can be formed from (4 * N) integers

• Last Updated : 25 Mar, 2021

Given an integer N and an array arr[] of size 4 * N, the task is to check whether N rectangles of equal area can be formed from this array if each element can be used only once.

Examples:

Input: arr[] = {1, 8, 2, 1, 2, 4, 4, 8}, N = 2
Output: Yes
Two rectangles with sides (1, 8, 1, 8) and (2, 4, 2, 4) can be formed.
Both of these rectangles have the same area.

Input: arr[] = {1, 3, 3, 5, 5, 7, 1, 6}, N = 2
Output: No

Approach:

• Four sides are needed to form a rectangle.
• Given 4 * N integers, utmost N rectangles can be formed using numbers only once.
• The task is to check if the areas of all the rectangles are same. To check this, the array is first sorted.
• The sides are considered as the first two elements and the last two elements.
• Area is calculated and checked if it has the same area as the initially calculated area.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to check whether we can make n``// rectangles of equal area``bool` `checkRectangles(``int``* arr, ``int` `n)``{``    ``bool` `ans = ``true``;` `    ``// Sort the array``    ``sort(arr, arr + 4 * n);` `    ``// Find the area of any one rectangle``    ``int` `area = arr * arr[4 * n - 1];` `    ``// Check whether we have two equal sides``    ``// for each rectangle and that area of``    ``// each rectangle formed is the same``    ``for` `(``int` `i = 0; i < 2 * n; i = i + 2) {``        ``if` `(arr[i] != arr[i + 1]``            ``|| arr[4 * n - i - 1] != arr[4 * n - i - 2]``            ``|| arr[i] * arr[4 * n - i - 1] != area) {` `            ``// Update the answer to false``            ``// if any condition fails``            ``ans = ``false``;``            ``break``;``        ``}``    ``}` `    ``// If possible``    ``if` `(ans)``        ``return` `true``;` `    ``return` `false``;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 1, 8, 2, 1, 2, 4, 4, 8 };``    ``int` `n = 2;` `    ``if` `(checkRectangles(arr, n))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.*;` `class` `GFG``{` `// Function to check whether we can make n``// rectangles of equal area``static` `boolean` `checkRectangles(``int``[] arr, ``int` `n)``{``    ``boolean` `ans = ``true``;` `    ``// Sort the array``    ``Arrays.sort(arr);` `    ``// Find the area of any one rectangle``    ``int` `area = arr[``0``] * arr[``4` `* n - ``1``];` `    ``// Check whether we have two equal sides``    ``// for each rectangle and that area of``    ``// each rectangle formed is the same``    ``for` `(``int` `i = ``0``; i < ``2` `* n; i = i + ``2``)``    ``{``        ``if` `(arr[i] != arr[i + ``1``] ||``            ``arr[``4` `* n - i - ``1``] != arr[``4` `* n - i - ``2``] ||``            ``arr[i] * arr[``4` `* n - i - ``1``] != area)``        ``{` `            ``// Update the answer to false``            ``// if any condition fails``            ``ans = ``false``;``            ``break``;``        ``}``    ``}` `    ``// If possible``    ``if` `(ans)``        ``return` `true``;` `    ``return` `false``;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``1``, ``8``, ``2``, ``1``, ``2``, ``4``, ``4``, ``8` `};``    ``int` `n = ``2``;` `    ``if` `(checkRectangles(arr, n))``        ``System.out.print(``"Yes"``);``    ``else``        ``System.out.print(``"No"``);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python implementation of the approach` `# Function to check whether we can make n``# rectangles of equal area``def` `checkRectangles(arr, n):``    ``ans ``=` `True` `    ``# Sort the array``    ``arr.sort()` `    ``# Find the area of any one rectangle``    ``area ``=` `arr[``0``] ``*` `arr[``4` `*` `n ``-` `1``]` `    ``# Check whether we have two equal sides``    ``# for each rectangle and that area of``    ``# each rectangle formed is the same``    ``for` `i ``in` `range``(``0``, ``2` `*` `n, ``2``):``        ``if` `(arr[i] !``=` `arr[i ``+` `1``]``            ``or` `arr[``4` `*` `n ``-` `i ``-` `1``] !``=` `arr[``4` `*` `n ``-` `i ``-` `2``]``            ``or` `arr[i] ``*` `arr[``4` `*` `n ``-` `i ``-` `1``] !``=` `area):` `            ``# Update the answer to false``            ``# if any condition fails``            ``ans ``=` `False``            ``break` `    ``# If possible``    ``if` `(ans):``        ``return` `True` `    ``return` `False` `# Driver code``arr ``=` `[ ``1``, ``8``, ``2``, ``1``, ``2``, ``4``, ``4``, ``8` `]``n ``=` `2` `if` `(checkRectangles(arr, n)):``    ``print``(``"Yes"``)``else``:``    ``print``(``"No"``)` `# This code is contributed by Sanjit_Prasad`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `// Function to check whether we can make n``// rectangles of equal area``static` `bool` `checkRectangles(``int``[] arr, ``int` `n)``{``    ``bool` `ans = ``true``;` `    ``// Sort the array``    ``Array.Sort(arr);` `    ``// Find the area of any one rectangle``    ``int` `area = arr * arr[4 * n - 1];` `    ``// Check whether we have two equal sides``    ``// for each rectangle and that area of``    ``// each rectangle formed is the same``    ``for` `(``int` `i = 0; i < 2 * n; i = i + 2)``    ``{``        ``if` `(arr[i] != arr[i + 1] ||``            ``arr[4 * n - i - 1] != arr[4 * n - i - 2] ||``            ``arr[i] * arr[4 * n - i - 1] != area)``        ``{` `            ``// Update the answer to false``            ``// if any condition fails``            ``ans = ``false``;``            ``break``;``        ``}``    ``}` `    ``// If possible``    ``if` `(ans)``        ``return` `true``;` `    ``return` `false``;``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 1, 8, 2, 1, 2, 4, 4, 8 };``    ``int` `n = 2;` `    ``if` `(checkRectangles(arr, n))``        ``Console.Write(``"Yes"``);``    ``else``        ``Console.Write(``"No"``);``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``
Output:
`Yes`

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up