Print all possible pair with prime XOR in the Array

Given an array arr[] of N positive integers. The task is to print all possible pairs such that their XOR is a Prime Number.

Examples:

Input: arr[] = {1, 3, 6, 11}
Output: (1, 3) (1, 6) (3, 6) (6, 11)
Explanation:
The XOR of the above pairs:
1^3 = 2
1^6 = 7
3^6 = 5
6^11 = 13



Input: arr[] = { 22, 58, 63, 0, 47 }
Output: (22, 63) (58, 63) (0, 47)
Explanation:
The XOR of the above pairs:
22^33 = 37
58^63 = 5
0^47 = 47

Approach:

  1. Generate all Prime Numbers using Sieve of Eratosthenes.
  2. For all possible pairs from the given array, check if the XOR of that pair is prime or not.
  3. If the XOR of a pair is prime then print that pair else check for the next pair.

Below is the implementation of the above approach:

CPP

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
const int sz = 1e5;
bool isPrime[sz + 1];
  
// Function for Sieve of Eratosthenes
void generatePrime()
{
    int i, j;
    memset(isPrime, true, sizeof(isPrime));
  
    isPrime[0] = isPrime[1] = false;
  
    for (i = 2; i * i <= sz; i++) {
  
        // If i is prime, then make all
        // multiples of i false
        if (isPrime[i]) {
            for (j = i * i; j < sz; j += i) {
                isPrime[j] = false;
            }
        }
    }
}
  
// Function to print all Pairs whose
// XOR is prime
void Pair_of_PrimeXor(int A[], int n)
{
  
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
  
            // if A[i]^A[j] is prime,
            // then print this pair
            if (isPrime[(A[i] ^ A[j])]) {
  
                cout << "(" << A[i]
                     << ", " << A[j] << ") ";
            }
        }
    }
}
  
// Driver Code
int main()
{
    int A[] = { 1, 3, 6, 11 };
    int n = sizeof(A) / sizeof(A[0]);
  
    // Generate all the prime number
    generatePrime();
  
    // Function Call
    Pair_of_PrimeXor(A, n);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java implementation of the above approach
class GFG
{
static int sz = (int) 1e5;
static boolean []isPrime = new boolean[sz + 1];
   
// Function for Sieve of Eratosthenes
static void generatePrime()
{
    int i, j;
    for (i = 2; i  <= sz; i++)
        isPrime[i] = true;
   
    for (i = 2; i * i <= sz; i++) {
   
        // If i is prime, then make all
        // multiples of i false
        if (isPrime[i]) {
            for (j = i * i; j < sz; j += i) {
                isPrime[j] = false;
            }
        }
    }
}
   
// Function to print all Pairs whose
// XOR is prime
static void Pair_of_PrimeXor(int A[], int n)
{
   
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
   
            // if A[i]^A[j] is prime,
            // then print this pair
            if (isPrime[(A[i] ^ A[j])]) {
   
                System.out.print("(" +  A[i]
                    + ", " +  A[j]+ ") ");
            }
        }
    }
}
   
// Driver Code
public static void main(String[] args)
{
    int A[] = { 1, 3, 6, 11 };
    int n = A.length;
   
    // Generate all the prime number
    generatePrime();
   
    // Function Call
    Pair_of_PrimeXor(A, n);
}
}
  
// This code is contributed by sapnasingh4991

chevron_right


Python

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python implementation of the above approach
sz = 10**5
isPrime = [True]*(sz + 1)
  
# Function for Sieve of Eratosthenes
def generatePrime():
    i, j = 0, 0
    isPrime[0] = isPrime[1] = False
  
    for i in range(2, sz + 1):
        if i * i > sz:
            break
  
        # If i is prime, then make all
        # multiples of i false
        if (isPrime[i]):
            for j in range(i*i, sz, i):
                isPrime[j] = False
  
# Function to prall Pairs whose
# XOR is prime
def Pair_of_PrimeXor(A, n):
  
    for i in range(n):
        for j in range(i + 1, n):
  
            # if A[i]^A[j] is prime,
            # then prthis pair
            if (isPrime[(A[i] ^ A[j])]):
  
                print("(",A[i],",",A[j],")",end=" ")
  
# Driver Code
if __name__ == '__main__':
    A = [1, 3, 6, 11]
    n =len(A)
  
    # Generate all the prime number
    generatePrime()
  
    # Function Call
    Pair_of_PrimeXor(A, n)
  
# This code is contributed by mohit kumar 29

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# implementation of the above approach
using System;
  
class GFG
{
static int sz = (int) 1e5;
static bool []isPrime = new bool[sz + 1];
    
// Function for Sieve of Eratosthenes
static void generatePrime()
{
    int i, j;
    for (i = 2; i  <= sz; i++)
        isPrime[i] = true;
    
    for (i = 2; i * i <= sz; i++) {
    
        // If i is prime, then make all
        // multiples of i false
        if (isPrime[i]) {
            for (j = i * i; j < sz; j += i) {
                isPrime[j] = false;
            }
        }
    }
}
    
// Function to print all Pairs whose
// XOR is prime
static void Pair_of_PrimeXor(int []A, int n)
{
    
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
    
            // if A[i]^A[j] is prime,
            // then print this pair
            if (isPrime[(A[i] ^ A[j])]) {
    
                Console.Write("(" +  A[i]
                    + ", " +  A[j]+ ") ");
            }
        }
    }
}
    
// Driver Code
public static void Main(String[] args)
{
    int []A = { 1, 3, 6, 11 };
    int n = A.Length;
    
    // Generate all the prime number
    generatePrime();
    
    // Function Call
    Pair_of_PrimeXor(A, n);
}
}
  
// This code is contributed by Rajput-Ji

chevron_right


Output:

(1, 3) (1, 6) (3, 6) (6, 11)

Time Complexity: O(N2), where N is the length of the given array.

competitive-programming-img




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.