# XOR of elements in an array having prime frequency

Given an array arr[] of N elements, the task is to find the xor of the elements which have prime frequencies in the array. Note that 1 is neither prime nor composite.

Examples:

Input: arr[] = {5, 4, 6, 5, 4, 6}
Output: 7
All the elements appear 2 times which is a prime
So, 5 ^ 4 ^ 6 = 7

Input: arr[] = {1, 2, 3, 3, 2, 3, 2, 3, 3}
Output: 1
Only 2 and 3 appears prime number of times i.e. 3 and 5 respectively.
So, 2 ^ 3 = 1

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Traverse the array and store the frequencies of all the elements in a map.
• Build Sieve of Eratosthenes which will be used to test the primality of a number in O(1) time.
• Calculate the xor of elements having prime frequency using the Sieve array calculated in the previous step.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to create Sieve to check primes ` `void` `SieveOfEratosthenes(``bool` `prime[], ``int` `p_size) ` `{ ` `    ``// False here indicates ` `    ``// that it is not prime ` `    ``prime = ``false``; ` `    ``prime = ``false``; ` ` `  `    ``for` `(``int` `p = 2; p * p <= p_size; p++) { ` ` `  `        ``// If prime[p] is not changed, ` `        ``// then it is a prime ` `        ``if` `(prime[p]) { ` ` `  `            ``// Update all multiples of p, ` `            ``// set them to non-prime ` `            ``for` `(``int` `i = p * 2; i <= p_size; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to return the xor of elements ` `// in an array having prime frequency ` `int` `xorPrimeFreq(``int` `arr[], ``int` `n) ` `{ ` `    ``bool` `prime[n + 1]; ` `    ``memset``(prime, ``true``, ``sizeof``(prime)); ` ` `  `    ``SieveOfEratosthenes(prime, n + 1); ` ` `  `    ``int` `i, j; ` ` `  `    ``// Map is used to store ` `    ``// element frequencies ` `    ``unordered_map<``int``, ``int``> m; ` `    ``for` `(i = 0; i < n; i++) ` `        ``m[arr[i]]++; ` ` `  `    ``long` `xorVal = 0; ` ` `  `    ``// Traverse the map using iterators ` `    ``for` `(``auto` `it = m.begin(); it != m.end(); it++) { ` ` `  `        ``// Count the number of elements ` `        ``// having prime frequencies ` `        ``if` `(prime[it->second]) { ` `            ``xorVal ^= it->first; ` `        ``} ` `    ``} ` ` `  `    ``return` `xorVal; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 5, 4, 6, 5, 4, 6 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``cout << xorPrimeFreq(arr, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find xor of elements  ` `// in an array having prime frequency  ` `import` `java.util.*;  ` ` `  `class` `GFG  ` `{  ` ` `  `    ``// Function to create Sieve to check primes  ` `    ``static` `void` `SieveOfEratosthenes(``boolean` `prime[],  ` `                                        ``int` `p_size)  ` `    ``{  ` `        ``// False here indicates  ` `        ``// that it is not prime  ` `        ``prime[``0``] = ``false``;  ` `        ``prime[``1``] = ``false``;  ` `     `  `        ``for` `(``int` `p = ``2``; p * p <= p_size; p++)  ` `        ``{  ` `     `  `            ``// If prime[p] is not changed,  ` `            ``// then it is a prime  ` `            ``if` `(prime[p])  ` `            ``{  ` `     `  `                ``// Update all multiples of p,  ` `                ``// set them to non-prime  ` `                ``for` `(``int` `i = p * ``2``;  ` `                         ``i <= p_size; i += p)  ` `                    ``prime[i] = ``false``;  ` `            ``}  ` `        ``}  ` `    ``}  ` `     `  `    ``// Function to return the xor of elements  ` `    ``// in an array having prime frequency  ` `    ``static` `int` `xorOfElements(``int` `arr[], ``int` `n)  ` `    ``{  ` `        ``boolean` `prime[] = ``new` `boolean``[n + ``1``];  ` `        ``Arrays.fill(prime, ``true``);  ` `     `  `        ``SieveOfEratosthenes(prime, n + ``1``);  ` `     `  `        ``int` `i, j;  ` `     `  `        ``// Map is used to store  ` `        ``// element frequencies  ` `        ``HashMap m = ``new` `HashMap<>();  ` `        ``for` `(i = ``0``; i < n; i++)  ` `        ``{  ` `            ``if``(m.containsKey(arr[i]))  ` `                ``m.put(arr[i], m.get(arr[i]) + ``1``);  ` `            ``else` `                ``m.put(arr[i], ``1``);  ` `        ``}  ` `     `  `        ``int` `xor = ``0``;  ` `     `  `        ``// Traverse the map  ` `        ``for` `(Map.Entry entry : m.entrySet())  ` `        ``{  ` `            ``int` `key = entry.getKey();  ` `            ``int` `value = entry.getValue();  ` `             `  `            ``// xor the elements  ` `            ``// having prime frequencies  ` `            ``if` `(prime[value])  ` `            ``{  ` `                ``xor ^= (key);  ` `            ``}  ` `        ``}  ` `     `  `        ``return` `xor;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main(String args[])  ` `    ``{  ` `        ``int` `arr[] = { ``5``, ``4``, ``6``, ``5``, ``4``, ``6` `};  ` `        ``int` `n = arr.length;  ` `     `  `        ``System.out.println(xorOfElements(arr, n));  ` `    ``}  ` `}  ` ` `  `// This code is contributed by NikhilRathor `

## Python3

 `# Python3 implementation of the approach  ` `from` `math ``import` `sqrt ` ` `  `# Function to create Sieve to check primes  ` `def` `SieveOfEratosthenes(prime, p_size) : ` ` `  `    ``# False here indicates  ` `    ``# that it is not prime  ` `    ``prime[``0``] ``=` `False``;  ` `    ``prime[``1``] ``=` `False``;  ` ` `  `    ``for` `p ``in` `range``(``2``, ``int``(sqrt(p_size)) ``+` `1``) : ` ` `  `        ``# If prime[p] is not changed,  ` `        ``# then it is a prime  ` `        ``if` `(prime[p]) : ` ` `  `            ``# Update all multiples of p,  ` `            ``# set them to non-prime  ` `            ``for` `i ``in` `range``(p ``*` `2``, p_size ``+` `1``, p) :  ` `                ``prime[i] ``=` `False``;  ` `                 `  `    ``return` `prime ` `     `  `# Function to return the xor of elements  ` `# in an array having prime frequency  ` `def` `xorPrimeFreq( arr, n) :  ` `    ``prime ``=` `[``True``] ``*` `(n ``+` `1``);  ` ` `  `    ``prime ``=` `SieveOfEratosthenes(prime, n ``+` `1``);  ` ` `  `    ``# Map is used to store  ` `    ``# element frequencies  ` `    ``m ``=` `dict``.fromkeys(arr, ``0``); ` `     `  `    ``for` `i ``in` `range``(n) : ` `        ``m[arr[i]] ``+``=` `1``;  ` ` `  `    ``xorVal ``=` `0``;  ` ` `  `    ``# Traverse the map using iterators  ` `    ``for` `key,value ``in` `m.items() : ` ` `  `        ``# Count the number of elements  ` `        ``# having prime frequencies  ` `        ``if` `(prime[value]) : ` `            ``xorVal ^``=` `key;  ` ` `  `    ``return` `xorVal;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``arr ``=` `[ ``5``, ``4``, ``6``, ``5``, ``4``, ``6` `];  ` `     `  `    ``n ``=` `len``(arr);  ` ` `  `    ``print``(xorPrimeFreq(arr, n));  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# program to find xor of elements  ` `// in an array having prime frequency  ` `using` `System; ` `using` `System.Collections.Generic;     ` ` `  `class` `GFG  ` `{  ` ` `  `    ``// Function to create Sieve to check primes  ` `    ``static` `void` `SieveOfEratosthenes(``bool` `[]prime,  ` `                                    ``int` `p_size)  ` `    ``{  ` `        ``// False here indicates  ` `        ``// that it is not prime  ` `        ``prime = ``false``;  ` `        ``prime = ``false``;  ` `     `  `        ``for` `(``int` `p = 2; p * p <= p_size; p++)  ` `        ``{  ` `     `  `            ``// If prime[p] is not changed,  ` `            ``// then it is a prime  ` `            ``if` `(prime[p])  ` `            ``{  ` `     `  `                ``// Update all multiples of p,  ` `                ``// set them to non-prime  ` `                ``for` `(``int` `i = p * 2;  ` `                         ``i <= p_size; i += p)  ` `                    ``prime[i] = ``false``;  ` `            ``}  ` `        ``}  ` `    ``}  ` `     `  `    ``// Function to return the xor of elements  ` `    ``// in an array having prime frequency  ` `    ``static` `int` `xorOfElements(``int` `[]arr, ``int` `n)  ` `    ``{  ` `        ``int` `i, j;  ` `        ``bool` `[]prime = ``new` `bool``[n + 1]; ` `        ``for``(i = 0; i< n + 1; i++) ` `            ``prime[i] = ``true``; ` `     `  `        ``SieveOfEratosthenes(prime, n + 1);  ` `     `  `        ``// Map is used to store  ` `        ``// element frequencies  ` `        ``Dictionary<``int``,  ` `                   ``int``> m = ``new` `Dictionary<``int``, ` `                                           ``int``>();  ` `        ``for` `(i = 0; i < n; i++)  ` `        ``{  ` `            ``if``(m.ContainsKey(arr[i]))  ` `                ``m[arr[i]] = m[arr[i]] + 1;  ` `            ``else` `                ``m.Add(arr[i], 1);  ` `        ``}  ` `     `  `        ``int` `xor = 0;  ` `     `  `        ``// Traverse the map  ` `        ``foreach``(KeyValuePair<``int``, ``int``> entry ``in` `m) ` `        ``{  ` `            ``int` `key = entry.Key;  ` `            ``int` `value = entry.Value;  ` `             `  `            ``// xor the elements  ` `            ``// having prime frequencies  ` `            ``if` `(prime[value])  ` `            ``{  ` `                ``xor ^= (key);  ` `            ``}  ` `        ``}  ` `        ``return` `xor;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main(String []args)  ` `    ``{  ` `        ``int` `[]arr = { 5, 4, 6, 5, 4, 6 };  ` `        ``int` `n = arr.Length;  ` `     `  `        ``Console.WriteLine(xorOfElements(arr, n));  ` `    ``}  ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```7
```

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