Print all possible pair with prime XOR in the Array

• Last Updated : 28 Jan, 2022

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

 `// C++ implementation of the above approach``#include ``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;``}`

Java

 `// 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`

Python

 `# 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 print all 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 print this 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`

C#

 `// 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`

Javascript

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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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