Ways to split array into two groups of same XOR value

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Given an array A of n integers. The task is to count the number of ways to split given array elements into two disjoint groups, such that XOR of elements of each group is equal.

Examples:

Input : A[] = { 1, 2, 3 }
Output : 3
{(1), (2, 3)}, {(2), (1, 3)}, {(3), (1, 2)} are three ways with equal XOR value of two groups.

Input : A[] = { 5, 2, 3, 2 }
Output : 0

Let’s denote XOR between all elements in the first group as G₁ and XOR between all elements in the second group as G₂. Now, the following relation is always correct: G₁ ⊕ G₂ = A₁ ⊕ A₂ ⊕ …. ⊕ A_n.
So for G₁ = G₂, xor between all elements of array A is equal to 0. So, in that case, answer will be (2ⁿ – 2)/2 = (2^n-1 – 1). In second case, when XOR between all elements isn’t 0, we can not split array. Answer will be 0.

Implementation:

C++

// CPP Program to count number of ways to split 
// array into two groups such that each group 
// has equal XOR value 
#include<bits/stdc++.h>
using namespace std;
 
// Return the count number of ways to split 
// array into two  groups such that each group 
// has equal XOR value.
int countgroup(int a[], int n)
{
  int xs = 0;
  for (int i = 0; i < n; i++)
    xs = xs ^ a[i];
 
  // We can split only if XOR is 0. Since
  // XOR of all is 0, we can consider all
  // subsets as one group.
  if (xs == 0)
    return (1 << (n-1)) - 1;
 
  return 0;
}
 
// Driver Program
int main()
{
  int a[] = { 1, 2, 3 };
  int n = sizeof(a)/sizeof(a[0]);
  cout << countgroup(a, n) << endl;
  return 0;
} 

Java

// Java Program to count number of ways 
// to split array into two groups such 
// that each group has equal XOR value
import java.io.*;
import java.util.*;
 
class GFG {
 
// Return the count number of ways to split
// array into two groups such that each group
// has equal XOR value.
static int countgroup(int a[], int n) {
    int xs = 0;
    for (int i = 0; i < n; i++)
    xs = xs ^ a[i];
 
    // We can split only if XOR is 0. Since
    // XOR of all is 0, we can consider all
    // subsets as one group.
    if (xs == 0)
    return (1 << (n - 1)) - 1;
 
    return 0;
}
 
// Driver program
public static void main(String args[]) {
    int a[] = {1, 2, 3};
    int n = a.length;
    System.out.println(countgroup(a, n));
}
}
 
// This code is contributed by Nikita Tiwari.

Python3

# Python3 code to count number of ways 
# to split array into two groups such
# that each group has equal XOR value 
 
# Return the count of number of ways
# to split array into two groups such
# that each group has equal XOR value.
def countgroup(a, n):
    xs = 0
    for i in range(n):
        xs = xs ^ a[i]
     
    # We can split only if XOR is 0. 
    # Since XOR of all is 0, we can 
    # consider all subsets as one group.
    if xs == 0:
        return (1 << (n-1)) - 1
     
    return 0
     
# Driver Program
a = [1, 2, 3]
n = len(a)
print(countgroup(a, n)) 
 
# This code is contributed by "Sharad_Bhardwaj".

C#

// C# Program to count number of ways
// to split array into two groups such
// that each group has equal XOR value
using System;
 
class GFG {
 
    // Return the count number of ways to split
    // array into two groups such that each group
    // has equal XOR value.
    static int countgroup(int[] a, int n)
    {
        int xs = 0;
        for (int i = 0; i < n; i++)
            xs = xs ^ a[i];
 
        // We can split only if XOR is 0. Since
        // XOR of all is 0, we can consider all
        // subsets as one group.
        if (xs == 0)
            return (1 << (n - 1)) - 1;
 
        return 0;
    }
 
    // Driver program
    public static void Main()
    {
        int[] a = { 1, 2, 3 };
        int n = a.Length;
        Console.WriteLine(countgroup(a, n));
    }
}
 
// This code is contributed by vt_m.

PHP

<?php
// PHP Program to count number
// of ways to split array into 
// two groups such that each  
// group has equal XOR value 
 
// Return the count number of
// ways to split array into 
// two groups such that each  
// grouphas equal XOR value.
function countgroup($a, $n)
{
    $xs = 0;
    for ($i = 0; $i < $n; $i++)
        $xs = $xs ^ $a[$i];
     
    // We can split only if XOR is 0. Since
    // XOR of all is 0, we can consider all
    // subsets as one group.
    if ($xs == 0)
        return (1 << ($n - 1)) - 1;
     
    return 0;
}
 
// Driver Code
$a = array(1, 2, 3);
$n = count($a);
echo countgroup($a, $n);
 
// This code is contributed by anuj_67.
?>

Javascript

<script>
 
      // JavaScript Program to count number of ways to split
      // array into two groups such that each group
      // has equal XOR value
 
      // Return the count number of ways to split
      // array into two groups such that each group
      // has equal XOR value.
      function countgroup(a, n) {
        var xs = 0;
        for (var i = 0; i < n; i++) xs = xs ^ a[i];
 
        // We can split only if XOR is 0. Since
        // XOR of all is 0, we can consider all
        // subsets as one group.
        if (xs == 0) return (1 << (n - 1)) - 1;
      }
 
      // Driver Program
       
      var a = [1, 2, 3];
      var n = a.length;
      document.write(countgroup(a, n) + "<br>");
       
</script>

Output

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

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