Maximum value of XOR among all triplets of an array in C++

In this problem, we are given an array of integers. Our task is to create the maximum value of XOR among all triplets of an array.

Let’s take an example to understand the problem,

Input − array = {5, 6, 1, 2}

Output − 6

Explanation −

All triplets are:
5^6^1 = 2
5^6^2 = 1
5^1^2 = 6
6^1^2 = 5

To solve this problem, a direct approach will be to find the XOR of all possible triplets and print the maximum of all triplets. This will not be effective if we work with an array with a huge number of elements in the array.

To find the maximum XOR, we will first create a set that contains the XOR of all pairs of elements. Then we will find the XOR between all pairs and the element and find the maximum XOR’s.

Example

Program to illustrate the working of our solution,

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int MaxTripletXor(int n, int a[]){
   set<int> XORpair;
   for (int i = 0; i < n; i++) {
      for (int j = i; j < n; j++) {
         XORpair.insert(a[i] ^ a[j]);
      }
   }
   int maxXOR = 0;
   for (auto i : XORpair) {
      for (int j = 0; j < n; j++) {
         maxXOR = max(maxXOR, i ^ a[j]);
      }
   }
   return maxXOR;
}
int main(){
   int matrix[] = {1, 2, 3, 5, 7};
   int n = sizeof(matrix) / sizeof(matrix[0]);
   cout<<"The maximum XOR sum triplets is "<<MaxTripletXor(n, matrix);
   return 0;
}

Output

The maximum XOR sum triplets is 7