Find a K-length subarray having Bitwise XOR equal to that of remaining array elements

Given an array arr[] of size N, the task is to check if any subarray of size K exists in the array or not, whose Bitwise XOR is equal to the Bitwise XOR of the remaining array elements. If found to be true, then print “YES”. Otherwise, print “NO”.

Examples:

Input: arr[] = { 2, 3, 3, 5, 7, 7, 3, 4 }, K = 5 
Output: YES 
Explanation:
Bitwise XOR of the subarray { 3, 3, 5, 7, 7 } is equal to 5 
Bitwise XOR of { 2, 3, 4 } is equal to 5. 
Therefore, the required output is YES.

Input: arr[] = { 2, 3, 4, 5, 6, 7, 4 }, K = 2 
Output: NO

Naive Approach: The simplest approach to solve this problem is to generate all subarrays of size K. For each subarray, check if the bitwise XOR of the subarray is equal to bitwise XOR of remaining elements or not. If found to be true, then print “YES”. Otherwise, print “NO”. 

Time Complexity: O(N²)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized using Sliding Window Technique Following are the observations:

If X ^ Y = Z, then X ^ Z = Y 
SubarrayXOR = arr[i] ^ arr[i + 1] ^ … ^ arr[j] 
totalXOR = arr[0] ^ arr[1] ^ arr[2] ….. ^ arr[N – 1] 
Bitwise XOR of the remaining array elements = totalXOR ^ SubarrayXOR 

• Calculate the Bitwise XOR of all array elements, say totalXOR.
• Calculate the Bitwise XOR of first K elements of the array, say SubarrayXOR.
• Use sliding window technique, traverse each subarray of size K and check if Bitwise XOR of the subarray is equal to the Bitwise XOR of the remaining array elements or not. If found to be true, then print “YES”.
• Otherwise, print “NO”.

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach

#include <bits/stdc++.h>
using namespace std;

// Utility function to check if subarray
// of size K exits whose XOR of elements
// equal to XOR ofremaning array elements
bool isSubarrayExistUtil(int arr[], int K, int N)
{

    int totalXOR = 0;
    int SubarrayXOR = 0;

    // Find XOR of whole array
    for (int i = 0; i < N; i++)
        totalXOR ^= arr[i];

    // Find XOR of first K elements
    for (int i = 0; i < K; i++)
        SubarrayXOR ^= arr[i];
    if (SubarrayXOR == (totalXOR ^ SubarrayXOR))
        return true;

    for (int i = K; i < N; i++) {

        // Adding XOR of next element
        SubarrayXOR ^= arr[i];

        // Removing XOR of previous element
        SubarrayXOR ^= arr[i - 1];

        // Check if XOR of current subarray matches
        // with the XOR of remaining elements or not
        if (SubarrayXOR == (totalXOR ^ SubarrayXOR))
            return true;
    }
    return false;
}

// Function to check if subarray of size
// K exits whose XOR of elements equal
// to XOR ofremaning array elements
void isSubarrayExist(int arr[], int K, int N)
{
    if (isSubarrayExistUtil(arr, K, N))
        cout << "YES\n";
    else
        cout << "NO\n";
}

// Driver Code
int32_t main()
{
    // Given array
    int arr[] = { 2, 3, 3, 5, 7, 7, 3, 4 };

    // Size of the array
    int N = sizeof(arr) / sizeof(arr[0]);

    // Given K
    int K = 5;

    // Function Call
    isSubarrayExist(arr, K, N);
}

C

// C program to implement
// the above approach

#include <stdbool.h> //to use true, false keywords
#include <stdint.h> //to use int_32
#include <stdio.h>

// Utility function to check if subarray
// of size K exits whose XOR of elements
// equal to XOR ofremaning array elements
bool isSubarrayExistUtil(int arr[], int K, int N)
{

  int totalXOR = 0;
  int SubarrayXOR = 0;

  // Find XOR of whole array
  for (int i = 0; i < N; i++)
    totalXOR ^= arr[i];

  // Find XOR of first K elements
  for (int i = 0; i < K; i++)
    SubarrayXOR ^= arr[i];
  if (SubarrayXOR == (totalXOR ^ SubarrayXOR))
    return true;

  for (int i = K; i < N; i++) {

    // Adding XOR of next element
    SubarrayXOR ^= arr[i];

    // Removing XOR of previous element
    SubarrayXOR ^= arr[i - 1];

    // Check if XOR of current subarray matches
    // with the XOR of remaining elements or not
    if (SubarrayXOR == (totalXOR ^ SubarrayXOR))
      return true;
  }
  return false;
}

// Function to check if subarray of size
// K exits whose XOR of elements equal
// to XOR ofremaning array elements
void isSubarrayExist(int arr[], int K, int N)
{
  if (isSubarrayExistUtil(arr, K, N))
    printf("YES\n");
  else
    printf("NO\n");
}

// Driver Code
int32_t main()
{
  // Given array
  int arr[] = { 2, 3, 3, 5, 7, 7, 3, 4 };

  // Size of the array
  int N = sizeof(arr) / sizeof(arr[0]);

  // Given K
  int K = 5;

  // Function Call
  isSubarrayExist(arr, K, N);
}

// This code is contributed by phalashi.

Java

// Java program to implement
// the above approach
import java.util.*;

class GFG{

// Utility function to check if subarray
// of size K exits whose XOR of elements
// equal to XOR ofremaning array elements
static boolean isSubarrayExistUtil(int arr[],
                                   int K, int N)
{
    int totalXOR = 0;
    int SubarrayXOR = 0;

    // Find XOR of whole array
    for(int i = 0; i < N; i++)
        totalXOR ^= arr[i];

    // Find XOR of first K elements
    for(int i = 0; i < K; i++)
        SubarrayXOR ^= arr[i];
    if (SubarrayXOR == (totalXOR ^ SubarrayXOR))
        return true;

    for(int i = K; i < N; i++)
    {

        // Adding XOR of next element
        SubarrayXOR ^= arr[i];

        // Removing XOR of previous element
        SubarrayXOR ^= arr[i - 1];

        // Check if XOR of current subarray matches
        // with the XOR of remaining elements or not
        if (SubarrayXOR == (totalXOR ^ SubarrayXOR))
            return true;
    }
    return false;
}

// Function to check if subarray of size
// K exits whose XOR of elements equal
// to XOR ofremaning array elements
static void isSubarrayExist(int arr[],
                            int K, int N)
{
    if (isSubarrayExistUtil(arr, K, N))
        System.out.print("YES\n");
    else
        System.out.print("NO\n");
}

// Driver Code
public static void main(String[] args)
{

    // Given array
    int arr[] = { 2, 3, 3, 5, 7, 7, 3, 4 };

    // Size of the array
    int N = arr.length;

    // Given K
    int K = 5;

    // Function Call
    isSubarrayExist(arr, K, N);
}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program to implement
# the above approach

# Utility function to check if subarray
# of size K exits whose XOR of elements
# equal to XOR ofremaning array elements
def isSubarrayExistUtil(arr, K, N):
    totalXOR = 0
    SubarrayXOR = 0

    # Find XOR of whole array
    for i in range(N):
        totalXOR ^= arr[i]

    # Find XOR of first K elements
    for i in range(K):
        SubarrayXOR ^= arr[i]
    if (SubarrayXOR == (totalXOR ^ SubarrayXOR)):
        return True

    for i in range(K, N):

        # Adding XOR of next element
        SubarrayXOR ^= arr[i]

        # Removing XOR of previous element
        SubarrayXOR ^= arr[i - 1]

        # Check if XOR of current subarray matches
        # with the XOR of remaining elements or not
        if (SubarrayXOR == (totalXOR ^ SubarrayXOR)):
            return True
    return False

# Function to check if subarray of size
# K exits whose XOR of elements equal
# to XOR ofremaning array elements
def isSubarrayExist(arr, K, N):
    if (isSubarrayExistUtil(arr, K, N)):
        print("YES")
    else:
        print("NO")

# Driver Code
if __name__ == '__main__':

    # Given array
    arr = [2, 3, 3, 5, 7, 7, 3, 4]

    # Size of the array
    N = len(arr)

    # Given K
    K = 5

    # Function Call
    isSubarrayExist(arr, K, N)

    # This code is contributed by mohit kumar 29

C#

// C# program to implement
// the above approach
using System;
class GFG
{

// Utility function to check if subarray
// of size K exits whose XOR of elements
// equal to XOR ofremaning array elements
static bool isSubarrayExistUtil(int []arr,
                                   int K, int N)
{
    int totalXOR = 0;
    int SubarrayXOR = 0;

    // Find XOR of whole array
    for(int i = 0; i < N; i++)
        totalXOR ^= arr[i];

    // Find XOR of first K elements
    for(int i = 0; i < K; i++)
        SubarrayXOR ^= arr[i];
    if (SubarrayXOR == (totalXOR ^ SubarrayXOR))
        return true;
    for(int i = K; i < N; i++)
    {

        // Adding XOR of next element
        SubarrayXOR ^= arr[i];

        // Removing XOR of previous element
        SubarrayXOR ^= arr[i - 1];

        // Check if XOR of current subarray matches
        // with the XOR of remaining elements or not
        if (SubarrayXOR == (totalXOR ^ SubarrayXOR))
            return true;
    }
    return false;
}

// Function to check if subarray of size
// K exits whose XOR of elements equal
// to XOR ofremaning array elements
static void isSubarrayExist(int []arr,
                            int K, int N)
{
    if (isSubarrayExistUtil(arr, K, N))
        Console.Write("YES\n");
    else
        Console.Write("NO\n");
}

// Driver Code
public static void Main(String[] args)
{

    // Given array
    int []arr = { 2, 3, 3, 5, 7, 7, 3, 4 };

    // Size of the array
    int N = arr.Length;

    // Given K
    int K = 5;

    // Function Call
    isSubarrayExist(arr, K, N);
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// javascript program to implement
// the above approach

    // Utility function to check if subarray
    // of size K exits whose XOR of elements
    // equal to XOR ofremaning array elements
    function isSubarrayExistUtil(arr , K , N)
    {
        var totalXOR = 0;
        var SubarrayXOR = 0;

        // Find XOR of whole array
        for (i = 0; i < N; i++)
            totalXOR ^= arr[i];

        // Find XOR of first K elements
        for (i = 0; i < K; i++)
            SubarrayXOR ^= arr[i];
        if (SubarrayXOR == (totalXOR ^ SubarrayXOR))
            return true;

        for (i = K; i < N; i++) {

            // Adding XOR of next element
            SubarrayXOR ^= arr[i];

            // Removing XOR of previous element
            SubarrayXOR ^= arr[i - 1];

            // Check if XOR of current
            // subarray matches
            // with the XOR of remaining
            // elements or not
            if (SubarrayXOR ==
            (totalXOR ^ SubarrayXOR))
                return true;
        }
        return false;
    }

    // Function to check if subarray of size
    // K exits whose XOR of elements equal
    // to XOR ofremaning array elements
    function isSubarrayExist(arr , K , N) {
        if (isSubarrayExistUtil(arr, K, N))
            document.write("YES\n");
        else
            document.write("NO\n");
    }

    // Driver Code


        // Given array
        var arr = [ 2, 3, 3, 5, 7, 7, 3, 4 ];

        // Size of the array
        var N = arr.length;

        // Given K
        var K = 5;

        // Function Call
        isSubarrayExist(arr, K, N);

// This code contributed by Rajput-Ji

</script>

Output:

YES

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