Number whose XOR sum with given array is a given number k
Last Updated :
10 Nov, 2022
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 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.
# 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# 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 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.
?>
<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>
Output11 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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