Add an element in Array to make the bitwise XOR as K

Given an array arr[] containing N positive integers, the task is to add an integer such that the bitwise Xor of the new array becomes K.

Examples:

Input: arr[] = 1, 4, 5, 6, K = 4
Output: 2
Explanation: Bit-wise XOR of the array is 6.
And bit-wise XOR of 6 and 2 is 4.

Input: arr[] = 2, 7, 9, 1, K = 5
Output: 8

Approach: The solution to the problem is based on the following idea of bitwise Xor:

If for two numbers X and Y, the bitwise Xor of X and Y is Z then the bitwise Xor of X and Z is Y.

Follow the steps to solve the problem:

Let the bitwise XOR of the array elements be X.
Say the required value to be added is Y such that X Xor Y = K.
From the above observation, it is clear that the value to be added (Y) is the same as X Xor K.

Below is the implementation of the above approach:

C++

// C++ code to implement the above approach
 
#include 
using namespace std;
 
// Function to find the required value
int find_K(int K, vector<int>& arr)
    int XOR = 0;
 
    // Find XOR of all the array elements
    for (int i = 0; i < arr.size(); i++)
        XOR ^= arr[i];
 
    // K = XOR^N, where N is size of array
    return XOR ^ K;
 
// Drivers code
int main()
    int K = 4;
    vector<int> arr =  1, 4, 5, 6 ;
 
    // Function call
    cout << find_K(K, arr);
    return 0;

Java

// Java code to implement the above approach
import java.io.*;
 
class GFG 
    // Function to find the required value
    public static int find_K(int K, int arr[])
    
        int XOR = 0;
 
        // Find XOR of all the array elements
        for (int i = 0; i < arr.length; i++)
            XOR ^= arr[i];
 
        // K = XOR^N, where N is size of array
        return XOR ^ K;
    
 
    // Driver Code
    public static void main(String[] args)
    
        int K = 4;
        int arr[] =  1, 4, 5, 6 ;
 
        // Function call
        System.out.print(find_K(K, arr));
    
 
// This code is contributed by Rohit Pradhan

Python3

# Python code to implement the above approach
 
# Function to find the required value
def find_K(K, arr):
    XOR = 0
 
    # Find XOR of all the array elements
    for i in range(len(arr)):
        XOR ^= arr[i]
 
    # K = XOR^N, where N is size of array
    return XOR ^ K
 
# Drivers code
K = 4
arr = [ 1, 4, 5, 6 ]
 
# Function call
print(find_K(K, arr))
 
# This code is contributed by shinjanpatra

C#

// C# code to implement the above approach
using System;
 
class GFG
 
  // Function to find the required value
  static int find_K(int K, int[] arr)
  
    int XOR = 0;
 
    // Find XOR of all the array elements
    for (int i = 0; i < arr.Length; i++)
      XOR ^= arr[i];
 
    // K = XOR^N, where N is size of array
    return XOR ^ K;
  
 
  // Driver Code
  public static int Main()
  
    int K = 4;
    int[] arr = new int[]  1, 4, 5, 6 ;
 
    // Function call
    Console.Write(find_K(K, arr));
    return 0;
  
 
// This code is contributed by Taranpreet

Javascript

Output

Time Complexity: O(N)
Auxiliary Space: O(1)

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