Given ‘N’ number of sticks of length a1, a2, a3…an. The task is to count the number of squares and rectangles possible.
Note: One stick should be used only once i.e. either in any of the squares or rectangles.
Examples:
Input: arr[] = {1, 2, 1, 2}
Output: 1
Rectangle with sides 1 1 2 2
Input: arr[] = {1, 2, 3, 4, 5, 6, 7, 8, 9}
Output: 0
No square or rectangle is possible
Approach: Below is the step by step algorithm to solve this problem :
- Initialize the number of sticks.
- Initialize all the sticks with it’s lengths in an array.
- Sort the array in an increasing order.
- Calculate the number of pairs of sticks with the same length.
- Divide the total number of pairs by 2, which will be the total possible rectangle and square.
Below is the implementation of above approach:
C++
// C++ implementation of above approach#include <bits/stdc++.h>using namespace std;// Function to find the possible// rectangles and squaresint rectangleSquare(int arr[], int n){ // sort all the sticks sort(arr, arr + n); int count = 0; // calculate all the pair of // sticks with same length for (int i = 0; i < n - 1; i++) { if (arr[i] == arr[i + 1]) { count++; i++; } } // divide the total number of pair // which will be the number of possible // rectangle and square return count / 2;}// Driver codeint main(){ // initialize all the stick lengths int arr[] = { 2, 2, 4, 4, 4, 4, 6, 6, 6, 7, 7, 9, 9 }; int n = sizeof(arr) / sizeof(arr[0]); cout << rectangleSquare(arr, n); return 0;} |
Java
// Java implementation of above approachimport java.util.Arrays;class GFG{ // Function to find the possible // rectangles and squares static int rectangleSquare(int arr[], int n) { // sort all the sticks Arrays.sort(arr); int count = 0; // calculate all the pair of // sticks with same length for (int i = 0; i < n - 1; i++) { if (arr[i] == arr[i + 1]) { count++; i++; } } // divide the total number of pair // which will be the number of possible // rectangle and square return count / 2; } // Driver code public static void main(String[] args) { // initialize all the stick lengths int arr[] = {2, 2, 4, 4, 4, 4, 6, 6, 6, 7, 7, 9, 9}; int n = arr.length; System.out.println(rectangleSquare(arr, n)); }} // This code is contributed // by PrinciRaj1992 |
Python3
# Python3 implementation of above approach # Function to find the possible # rectangles and squares def rectangleSquare( arr, n): # sort all the sticks arr.sort() count = 0 #print(" xx",arr[6]) # calculate all the pair of # sticks with same length k=0 for i in range(n-1): if(k==1): k=0 continue if (arr[i] == arr[i + 1]): count=count+1 k=1 # divide the total number of pair # which will be the number of possible # rectangle and square return count/2# Driver codeif __name__=='__main__':# initialize all the stick lengths arr = [2, 2, 4, 4, 4, 4, 6, 6, 6, 7, 7, 9, 9] n = len(arr) print(rectangleSquare(arr, n))# this code is written by ash264 |
C#
// C# implementation of above approach using System;class GFG { // Function to find the possible // rectangles and squares static int rectangleSquare(int []arr, int n) { // sort all the sticks Array.Sort(arr); int count = 0; // calculate all the pair of // sticks with same length for (int i = 0; i < n - 1; i++) { if (arr[i] == arr[i + 1]) { count++; i++; } } // divide the total number of pair // which will be the number of possible // rectangle and square return count / 2; } // Driver code public static void Main(String[] args) { // initialize all the stick lengths int []arr = {2, 2, 4, 4, 4, 4, 6, 6, 6, 7, 7, 9, 9}; int n = arr.Length; Console.WriteLine(rectangleSquare(arr, n)); } } // This code has been contributed// by Rajput-Ji |
PHP
<?php// PHP implementation of above approach// Function to find the possible// rectangles and squaresfunction rectangleSquare($arr, $n){ // sort all the sticks sort($arr); $count = 0; // calculate all the pair of // sticks with same length for ($i = 0; $i < $n - 1; $i++) { if ($arr[$i] == $arr[$i + 1]) { $count++; $i++; } } // divide the total number of pair // which will be the number of possible // rectangle and square return ($count / 2);}// Driver code// initialize all the stick lengths$arr = array(2, 2, 4, 4, 4, 4, 6, 6, 6, 7, 7, 9, 9 );$n = sizeof($arr);echo rectangleSquare($arr, $n);// This code is contributed by Sachin.?> |
Javascript
<script>// javascript implementation of above approach // Function to find the possible // rectangles and squares function rectangleSquare(arr , n){ // sort all the sticks arr.sort(); var count = 0; // calculate all the pair of // sticks with same length for (i = 0; i < n - 1; i++) { if (arr[i] == arr[i + 1]) { count++; i++; } } // divide the total number of pair // which will be the number of possible // rectangle and square return count / 2;}// Driver code // initialize all the stick lengths var arr = [2, 2, 4, 4, 4, 4, 6, 6, 6, 7, 7, 9, 9];var n = arr.length;document.write(rectangleSquare(arr, n));// This code is contributed by 29AjayKumar </script> |
Output
3
Complexity Analysis:
- Time Complexity: O(n*log n) where n is the size of the array.
- Auxiliary Space: O(1)
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