Number whose XOR sum with given array is a given number k

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 = 10

Input: 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 array
int 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 function
int 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 k
import 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 array
def 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 Code
if __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 k
using 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 array
function 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 array
function 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)