Count of triplets that satisfy the given equation
Last Updated :
15 Apr, 2023
Given an array arr[] of N non-negative integers. The task is to count the number of triplets (i, j, k) where 0 ? i < j ? k < N such that A[i] ^ A[i + 1] ^ … ^ A[j – 1] = A[j] ^ A[j + 1] ^ … ^ A[k] where ^ is the bitwise XOR.
Examples:
Input: arr[] = {2, 5, 6, 4, 2}
Output: 2
The valid triplets are (2, 3, 4) and (2, 4, 4).
Input: arr[] = {5, 2, 7}
Output: 2
Naive approach: Consider each and every triplet and check whether the xor of the required elements is equal or not.
Efficient approach: If arr[i] ^ arr[i + 1] ^ … ^ arr[j – 1] = arr[j] ^ arr[j + 1] ^ … ^ arr[k] then arr[i] ^ arr[i + 1] ^ … ^ arr[k] = 0 since X ^ X = 0. Now the problem gets reduced to finding the sub-arrays with XOR 0. But every such sub-array can have multiple such triplets i.e.
If arr[i] ^ arr[i + 1] ^ … ^ arr[k] = 0
then, (arr[i]) ^ (arr[i + 1] ^ … ^ arr[k]) = 0
and, arr[i] ^ (arr[i + 1]) ^ … ^ arr[k] = 0
arr[i] ^ arr[i + 1] ^ (arr[i + 2]) ^ … ^ arr[k] = 0
…
j can have any value from i + 1 to k without violating the required property.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int CountTriplets( int * arr, int n)
{
int ans = 0;
for ( int i = 0; i < n - 1; i++) {
int first = arr[i];
for ( int j = i + 1; j < n; j++) {
first ^= arr[j];
if (first == 0)
ans += (j - i);
}
}
return ans;
}
int main()
{
int arr[] = { 2, 5, 6, 4, 2 };
int n = sizeof (arr) / sizeof (arr[0]);
cout << CountTriplets(arr, n);
return 0;
}
|
Java
class GFG
{
static int CountTriplets( int [] arr, int n)
{
int ans = 0 ;
for ( int i = 0 ; i < n - 1 ; i++)
{
int first = arr[i];
for ( int j = i + 1 ; j < n; j++)
{
first ^= arr[j];
if (first == 0 )
ans += (j - i);
}
}
return ans;
}
public static void main(String[] args)
{
int arr[] = { 2 , 5 , 6 , 4 , 2 };
int n = arr.length;
System.out.println(CountTriplets(arr, n));
}
}
|
Python3
def CountTriplets(arr, n):
ans = 0
for i in range (n - 1 ):
first = arr[i]
for j in range (i + 1 , n):
first ^ = arr[j]
if (first = = 0 ):
ans + = (j - i)
return ans
arr = [ 2 , 5 , 6 , 4 , 2 ]
n = len (arr)
print (CountTriplets(arr, n))
|
C#
using System;
class GFG
{
static int CountTriplets( int [] arr, int n)
{
int ans = 0;
for ( int i = 0; i < n - 1; i++)
{
int first = arr[i];
for ( int j = i + 1; j < n; j++)
{
first ^= arr[j];
if (first == 0)
ans += (j - i);
}
}
return ans;
}
public static void Main()
{
int []arr = {2, 5, 6, 4, 2};
int n = arr.Length;
Console.WriteLine(CountTriplets(arr, n));
}
}
|
Javascript
function CountTriplets(arr, n) {
let ans = 0;
for (let i = 0; i < n - 1; i++) {
let first = arr[i];
for (let j = i + 1; j < n; j++) {
first ^= arr[j];
if (first == 0) ans += j - i;
}
}
return ans;
}
const arr = [2, 5, 6, 4, 2];
const n = arr.length;
console.log(CountTriplets(arr, n));
|
Time Complexity: O(n2).
Auxiliary Space: O(1).
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