Prefix Xor Array

Given an array arr[] of size N, find the Prefix Xor of the array. A prefix xor array is another array prefixXor[] of the same size, such that the value of prefixXor[i] is arr[0] ^ arr[1] ^ arr[2] . . . arr[i].

Examples:

Input: arr[] = {10, 20, 10, 5, 15}
Output: prefixXor[] = {10, 30, 20, 17, 30 }
Explanation: While traversing the array, update the element by xoring it with its previous element.
prefixXor[0] = 10, 
prefixXor[1] = prefixXor[0] ^ arr[1] = 30, 
prefixXor[2] = prefixXor[1] ^ arr[2] = 20 and so on.

Input: arr[]={1,2,1,2,5}
Output: prefixXor[] = {1, 3, 2, 0, 5 }

Approach: To solve the problem follow the given steps:

• Declare a new array prefixXor[] of the same size as the input array
• Run a for loop to traverse the input array
• For each index add the value of the current element and the previous value of the prefix sum array

Below is the implementation of the approach:

C++

// C++ program for Implementing prefix sum array
#include <bits/stdc++.h>
using namespace std;

// Fills prefix sum array
void PrefixXor(int arr[], int n, int preXor[])
{
    preXor[0] = arr[0];
    // Xoring present element with previous element
    for (int i = 1; i < n; i++)
        preXor[i] = preXor[i - 1] ^ arr[i];
}

// Driver Code
int main()
{
    int arr[] = { 10, 20, 10, 5, 15 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int preXor[n];

    // Function call
    PrefixXor(arr, n, preXor);
    cout << "Given Array: ";
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
    cout << endl;
    cout << "Prefix Xor: ";
    for (int i = 0; i < n; i++)
        cout << preXor[i] << " ";
}

Java

public class PrefixXor {
    // Fills prefix XOR array
    static void prefixXor(int[] arr, int n, int[] preXor)
    {
        preXor[0] = arr[0];
        // Xoring present element with the previous element
        for (int i = 1; i < n; i++) {
            preXor[i] = preXor[i - 1] ^ arr[i];
        }
    }

    public static void main(String[] args)
    {
        int[] arr = { 10, 20, 10, 5, 15 };
        int n = arr.length;
        int[] preXor = new int[n];

        // Function call
        prefixXor(arr, n, preXor);

        System.out.print("Given Array: ");
        for (int i = 0; i < n; i++) {
            System.out.print(arr[i] + " ");
        }
        System.out.println();

        System.out.print("Prefix XOR: ");
        for (int i = 0; i < n; i++) {
            System.out.print(preXor[i] + " ");
        }
    }
}

Python

def prefix_xor(arr, n, pre_xor):
    pre_xor[0] = arr[0]
    # Xoring present element with the previous element
    for i in range(1, n):
        pre_xor[i] = pre_xor[i - 1] ^ arr[i]


if __name__ == "__main__":
    arr = [10, 20, 10, 5, 15]
    n = len(arr)
    pre_xor = [0] * n

    # Function call
    prefix_xor(arr, n, pre_xor)

    print("Given Array:", end=" ")
    for i in range(n):
        print(arr[i], end=" ")
    print()

    print("Prefix XOR:", end=" ")
    for i in range(n):
        print(pre_xor[i], end=" ")

C#

using System;

class PrefixXorExample
{
    // Fills prefix sum array
    static void PrefixXor(int[] arr, int n, int[] preXor)
    {
        preXor[0] = arr[0];
        // Xoring present element with previous element
        for (int i = 1; i < n; i++)
            preXor[i] = preXor[i - 1] ^ arr[i];
    }

    // Driver Code
    static void Main()
    {
        int[] arr = { 10, 20, 10, 5, 15 };
        int n = arr.Length;
        int[] preXor = new int[n];

        // Function call
        PrefixXor(arr, n, preXor);
        Console.Write("Given Array: ");
        foreach (int item in arr)
        {
            Console.Write(item + " ");
        }
        Console.WriteLine();
        Console.Write("Prefix Xor: ");
        foreach (int item in preXor)
        {
            Console.Write(item + " ");
        }
    }
}

Javascript

// Fills prefix sum array 
function prefixXor(arr) {
    const n = arr.length;
    const preXor = Array(n);

    preXor[0] = arr[0];

    // Xoring present element with previous element 
    for (let i = 1; i < n; i++) {
        preXor[i] = preXor[i - 1] ^ arr[i];
    }

    return preXor;
}

// Driver Code 
function main() {
    const arr = [10, 20, 10, 5, 15];
    const n = arr.length;

    // Function call 
    const preXor = prefixXor(arr);

    console.log("Given Array:", arr.join(" "));
    console.log("Prefix Xor:", preXor.join(" "));
}

// Run the main function
main();

Output

Given Array: 10 20 10 5 15 
Prefix Xor: 10 30 20 17 30 

Time Complexity: O(N), where N is the size of input array
Auxiliary Space: O(N)

Practice Problems on Prefix Xor Array:

Problem	Practice Link
Find XOR of numbers from the range [L, R]	solve
XOR of a given range	solve
XOR of all elements	solve
XOR counts of 0s and 1s in binary representation	solve
Count number of subsets having a particular XOR value	solve
Find number of pairs in an array such that their XOR is 0	solve
Game of xor	solve
Maximum XOR of Two Numbers in an Array	solve
Find the maximum subset XOR of a given set	solve