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:
- Generate all Prime Numbers using Sieve of Eratosthenes.
- For all possible pairs from the given array, check if the XOR of that pair is prime or not.
- 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
// 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 Eratosthenesvoid 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 primevoid 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 Codeint 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;} |
Java
// Java implementation of the above approachclass GFG{static int sz = (int) 1e5;static boolean []isPrime = new boolean[sz + 1]; // Function for Sieve of Eratosthenesstatic 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 primestatic 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 Codepublic 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 |
Python
# Python implementation of the above approachsz = 10**5isPrime = [True]*(sz + 1)# Function for Sieve of Eratosthenesdef 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 print all Pairs whose# XOR is primedef 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 print this pair if (isPrime[(A[i] ^ A[j])]): print("(",A[i],",",A[j],")",end=" ")# Driver Codeif __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 |
C#
// C# implementation of the above approachusing System;class GFG{static int sz = (int) 1e5;static bool []isPrime = new bool[sz + 1]; // Function for Sieve of Eratosthenesstatic 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 primestatic 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 Codepublic 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 |
Javascript
<script>// Javascript implementation of // the above approachconst sz = 100000;let isPrime = new Array(sz + 1).fill(true);// Function for Sieve of Eratosthenesfunction generatePrime(){ let i, j; 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 primefunction Pair_of_PrimeXor(A, n){ for (let i = 0; i < n; i++) { for (let j = i + 1; j < n; j++) { // if A[i]^A[j] is prime, // then print this pair if (isPrime[(A[i] ^ A[j])]) { document.write("(" + A[i] + ", " + A[j] + ") "); } } }}// Driver Code let A = [ 1, 3, 6, 11 ]; let n = A.length; // Generate all the prime number generatePrime(); // Function Call Pair_of_PrimeXor(A, n);</script> |
Output:
(1, 3) (1, 6) (3, 6) (6, 11)
Time Complexity: O(N2), where N is the length of the given array.
Auxiliary Space: O(sz)
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