Given an array of N numbers and a number K. The task is to insert a number in the given array such that the bitwise XOR of all the elements in the new array equals the given input K.
Examples:
Input: a = {1, 2, 3, 4, 5}, k = 10
Output: 11
Explanation: 1 ^ 2 ^ 3 ^ 4 ^ 5 ^ 11 = 10Input: A[] = { 12, 23, 34, 56, 78 }, k = 6
Output: 73
Approach:
The basic idea is to use the simple XOR property, i.e. if X ^ Y = Z then X ^ Z = Y. Let’s suppose the number to be inserted in array be X such that (A[0] ^ A[1] ^ … ^ A[n – 1]) ^ X = k. Thus, to find X we can use the relation (A[0] ^ A[1] ^ … ^ A[n – 1]) ^ k = X.
Below is the implementation of above approach.
C++
// CPP Program to find the number// whose XOR sum with given array is// equal to a given number k#include <bits/stdc++.h>using namespace std;// This function returns the number to// be inserted in the given arrayint findEletobeInserted(int A[], int n, int k){ // initialise the answer with k int ans = k; for (int i = 0; i < n; i++) ans ^= A[i]; // XOR of all elements in the array return ans;}// Driver Code to test above functionint main(){ int A[] = { 1, 2, 3, 4, 5 }; int n = sizeof(A) / sizeof(A[0]); int k = 10; cout << findEletobeInserted(A, n, k) << " has to be inserted" " in the given array to make xor sum of " << k << endl; return 0;} |
Java
// Java Program to find the number// whose XOR sum with given array is// equal to a given number kimport java.io.*;class GFG { // This function returns the number to // be inserted in the given array static int findEletobeInserted(int A[], int n, int k) { // initialise the answer with k int ans = k; for (int i = 0; i < n; i++) // XOR of all elements in // the array ans ^= A[i]; return ans; } // Driver Code to test above function public static void main (String[] args) { int A[] = { 1, 2, 3, 4, 5 }; int n =A.length; int k = 10; System.out.println( findEletobeInserted(A, n, k) + " has to be inserted in " + "the given array to make" + " xor sum of " + k); }}// This code is contributed by anuj_67. |
Python3
# Python 3 Program to find the number# whose XOR sum with given array is# equal to a given number k# This function returns the number to# be inserted in the given arraydef findEletobeInserted(A, n, k): # initialise the answer with k ans = k for i in range(n): ans ^= A[i] # XOR of all elements # in the array return ans# Driver Codeif __name__ == '__main__': A = [1, 2, 3, 4, 5] n = len(A) k = 10 print(findEletobeInserted(A, n, k), "has to be inserted in the given", "array to make xor sum of", k)# This code is contributed by# Surendra_Gangwar |
C#
// C# Program to find the number// whose XOR sum with given array is// equal to a given number kusing System ;class GFG { // This function returns the number to // be inserted in the given array static int findEletobeInserted(int []A, int n, int k) { // initialise the answer with k int ans = k; for (int i = 0; i < n; i++) // XOR of all elements in // the array ans ^= A[i]; return ans; } // Driver Code to test above function public static void Main () { int []A = { 1, 2, 3, 4, 5 }; int n =A.Length; int k = 10; Console.WriteLine( findEletobeInserted(A, n, k) + " has to be inserted in " + "the given array to make" + " xor sum of " + k); }}// This code is contributed by anuj_67. |
PHP
<?php// PHP Program to find the number// whose XOR sum with given array is// equal to a given number k// This function returns the number to// be inserted in the given arrayfunction findEletobeInserted($A, $n, $k){ // initialise the answer with k $ans = $k; for ( $i = 0; $i < $n; $i++) // XOR of all elements // in the array $ans ^= $A[$i]; return $ans;} // Driver Code $A = array(1, 2, 3, 4, 5); $n = count($A); $k = 10; echo findEletobeInserted($A, $n, $k) ; echo " has to be inserted"; echo " in the given array to make xor sum of "; echo $k , "\n";// This code is contributed by anuj_67.?> |
Javascript
<script>// Javascript Program to find the number// whose XOR sum with given array is// equal to a given number k// This function returns the number to// be inserted in the given arrayfunction findEletobeInserted(A, n, k){ // initialise the answer with k var ans = k; for(var i = 0; i < n; i++) // XOR of all elements in // the array ans ^= A[i]; return ans;}// Driver Code var A = [ 1, 2, 3, 4, 5 ];var n = A.length;var k = 10;document.write(findEletobeInserted(A, n, k) + " has to be inserted in " + "the given array to make" + " xor sum of " + k);// This code is contributed by Khushboogoyal499</script> |
Output
11 has to be inserted in the given array to make xor sum of 10
Time Complexity: O(n)
Auxiliary Space: O(1)
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