GCD of elements which occur prime number of times

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

Examples:

Input: arr[] = {5, 4, 6, 5, 4, 6} 
Output: 1 
All the elements appear 2 times which is a prime 
So, gcd(5, 4, 6) = 1

Input: arr[] = {4, 8, 8, 1, 4, 3, 0} 
Output: 4 

Brute Force Approach:

• Initialize two arrays – one to store the frequency of each element in the array and another to store the count of elements that have prime frequencies.
• Traverse the frequency array and count the number of elements with prime frequencies.
• Find the GCD of the elements that have prime frequencies by iterating over the frequency array and checking the value of the count of prime frequency elements.
• Calculate the GCD of the elements that have prime frequencies by iterating over the array again and finding the GCD of elements that have a frequency equal to the GCD found in the previous step.
• Finally, return the GCD as the output.

Below is the implementation of the above approach: 

C++

#include <bits/stdc++.h>
using namespace std;

// Function to check if a number is prime or not
bool isPrime(int n) {
    if (n <= 1) return false;
    for (int i = 2; i * i <= n; i++)
        if (n % i == 0) return false;
    return true;
}

// Function to find the GCD of elements that have prime frequencies in the array
int gcdPrimeFreq(int arr[], int n) {
      // array to store the frequency of each element in the array, initialized to 0
    int freq[10001] = {0};

      // count the frequency of each element in the array
    for (int i = 0; i < n; i++) freq[arr[i]]++;

      // array to store the count of elements that have prime frequencies, initialized to 0
    int prime_freq[10001] = {0};


    for (int i = 0; i < 10001; i++) {
          // count the number of elements that have prime frequencies
        if (isPrime(freq[i])) prime_freq[freq[i]]++;
    }
      // initialize the GCD to 1
    int gcd = 1;
    for (int i = 0; i < 10001; i++) {
          // if there are more than 1 elements with a prime frequency, update the GCD to the prime frequency
        if (prime_freq[i] > 1) {
            gcd = i;
            break;
        }
    }
    for (int i = 0; i < n; i++) {
          // if the frequency of the element is equal to the GCD found above, update the GCD to the GCD of the current element and the current GCD
        if (freq[arr[i]] == gcd) gcd = __gcd(gcd, arr[i]);
    }
      // return the GCD of the elements that have prime frequencies
    return gcd;
}

int main() {
    int arr[] = { 5, 4, 6, 5, 4, 6 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << gcdPrimeFreq(arr, n);
    return 0;
}

Java

import java.util.Arrays;

class GFG {

  // Function to check if a number is prime or not
  public static boolean isPrime(int n) {
    if (n <= 1) return false;
    for (int i = 2; i * i <= n; i++)
      if (n % i == 0) return false;
    return true;
  }

  // gcd method returns the GCD of a and b
  public static int gcd(int a, int b)
  {
    // if b=0, a is the GCD
    if (b == 0)
      return a;

    // call the gcd() method recursively by
    // replacing a with b and b with
    // modulus(a,b) as long as b != 0
    else
      return gcd(b, a % b);
  }

  // Function to find the GCD of elements that have prime frequencies in the array
  public static int gcdPrimeFreq(int arr[], int n) {
    // array to store the frequency of each element in the array, initialized to 0
    int freq[] = new int[10001];
    Arrays.fill(freq, 0);

    // count the frequency of each element in the array
    for (int i = 0; i < n; i++) freq[arr[i]]++;

    // array to store the count of elements that have prime frequencies, initialized to 0
    int prime_freq[] = new int[10001];
    Arrays.fill(prime_freq, 0);

    for (int i = 0; i < 10001; i++) {
      // count the number of elements that have prime frequencies
      if (isPrime(freq[i])) prime_freq[freq[i]]++;
    }

    // initialize the GCD to 1
    int gcd_ = 1;
    for (int i = 0; i < 10001; i++) {
      // if there are more than 1 elements with a prime frequency, update the GCD to the prime frequency
      if (prime_freq[i] > 1) {
        gcd_ = i;
        break;
      }
    }

    for (int i = 0; i < n; i++) {
      // if the frequency of the element is equal to the GCD found above, update the GCD to the GCD of the current element and the current GCD
      if (freq[arr[i]] == gcd_) gcd_ = gcd(gcd_, arr[i]);
    }

    // return the GCD of the elements that have prime frequencies
    return gcd_;
  }

  public static void main(String[] args) {
    int arr[] = { 5, 4, 6, 5, 4, 6 };
    int n = arr.length;
    System.out.println(gcdPrimeFreq(arr, n));
  }
}

// This code is contributed by prasad264

Python3

import math

# Function to check if a number is prime or not
def isPrime(n):
    if n <= 1:
        return False
    for i in range(2, int(math.sqrt(n))+1):
        if n % i == 0:
            return False
    return True

# Function to find the GCD of elements
# that have prime frequencies in the array
def gcdPrimeFreq(arr, n):

    # array to store the frequency of each element
    # in the array, initialized to 0
    freq = [0] * 10001

    # count the frequency of each element in the array
    for i in range(n):
        freq[arr[i]] += 1

    # array to store the count of elements
    # that have prime frequencies, initialized to 0
    prime_freq = [0] * 10001

    for i in range(10001):
        # count the number of elements that have prime frequencies
        if isPrime(freq[i]):
            prime_freq[freq[i]] += 1

    # initialize the GCD to 1
    gcd = 1

    for i in range(10001):
        # if there are more than 1 elements with
        # a prime frequency, update the GCD to the prime frequency
        if prime_freq[i] > 1:
            gcd = i
            break

    for i in range(n):
        # if the frequency of the element is equal
        # to the GCD found above, update the GCD to
        # the GCD of the current element and the current GCD
        if freq[arr[i]] == gcd:
            gcd = math.gcd(gcd, arr[i])

    # return the GCD of the elements that have prime frequencies
    return gcd

arr = [5, 4, 6, 5, 4, 6]
n = len(arr)
print(gcdPrimeFreq(arr, n))

C#

using System;
using System.Linq;

class GFG {
    // Function to check if a number is prime or not
    public static bool IsPrime(int n)
    {
        if (n <= 1)
            return false;
        for (int i = 2; i * i <= n; i++)
            if (n % i == 0)
                return false;
        return true;
    }

    // gcd method returns the GCD of a and b
    public static int Gcd(int a, int b)
    {
        // if b=0, a is the GCD
        if (b == 0)
            return a;

        // call the gcd() method recursively by
        // replacing a with b and b with
        // modulus(a,b) as long as b != 0
        else
            return Gcd(b, a % b);
    }

    // Function to find the GCD of elements that have prime
    // frequencies in the array
    public static int GcdPrimeFreq(int[] arr, int n)
    {
        // array to store the frequency of each element in
        // the array, initialized to 0
        int[] freq = new int[10001];
        Array.Fill(freq, 0);

        // count the frequency of each element in the array
        for (int i = 0; i < n; i++)
            freq[arr[i]]++;

        // array to store the count of elements that have
        // prime frequencies, initialized to 0
        int[] prime_freq = new int[10001];
        Array.Fill(prime_freq, 0);

        for (int i = 0; i < 10001; i++) {
            // count the number of elements that have prime
            // frequencies
            if (IsPrime(freq[i]))
                prime_freq[freq[i]]++;
        }

        // initialize the GCD to 1
        int gcd_ = 1;

        for (int i = 0; i < 10001; i++) {
            // if there are more than 1 elements with a
            // prime frequency, update the GCD to the prime
            // frequency
            if (prime_freq[i] > 1) {
                gcd_ = i;
                break;
            }
        }

        for (int i = 0; i < n; i++) {
            // if the frequency of the element is equal to
            // the GCD found above, update the GCD to the
            // GCD of the current element and the current
            // GCD
            if (freq[arr[i]] == gcd_)
                gcd_ = Gcd(gcd_, arr[i]);
        }

        // return the GCD of the elements that have prime
        // frequencies
        return gcd_;
    }

    public static void Main(string[] args)
    {
        int[] arr = { 5, 4, 6, 5, 4, 6 };
        int n = arr.Length;

        Console.WriteLine(GcdPrimeFreq(arr, n));
    }
}

Javascript

// Function to check if a number is prime or not
function isPrime(n) {
    if (n <= 1) return false;
    for (let i = 2; i * i <= n; i++)
        if (n % i == 0) return false;
    return true;
}

// Function to find the GCD of elements that have prime frequencies in the array
function gcdPrimeFreq(arr, n) {
    // array to store the frequency of each element in the array, initialized to 0
    const freq = new Array(10001).fill(0);

    // count the frequency of each element in the array
    for (let i = 0; i < n; i++) freq[arr[i]]++;

    // array to store the count of elements that have prime frequencies, initialized to 0
    const prime_freq = new Array(10001).fill(0);

    for (let i = 0; i < 10001; i++) {
        // count the number of elements that have prime frequencies
        if (isPrime(freq[i])) prime_freq[freq[i]]++;
    }

    // initialize the GCD to 1
    let gcd = 1;
    for (let i = 0; i < 10001; i++) {
        // if there are more than 1 elements with a prime frequency, update the GCD to the prime frequency
        if (prime_freq[i] > 1) {
            gcd = i;
            break;
        }
    }

    for (let i = 0; i < n; i++) {
        // if the frequency of the element is equal to the GCD found above, update the GCD to the GCD of the current element and the current GCD
        if (freq[arr[i]] == gcd) gcd = gcdFunction(gcd, arr[i]);
    }

    // return the GCD of the elements that have prime frequencies
    return gcd;
}

// Function to find the GCD of two numbers
function gcdFunction(a, b) {
    if (a == 0) return b;
    return gcdFunction(b % a, a);
}

const arr = [5, 4, 6, 5, 4, 6];
const n = arr.length;
console.log(gcdPrimeFreq(arr, n));

Output

1

Time Complexity: O(n * sqrt(max_value))
Auxiliary Space:  O(max_value), as we need to store a boolean array of size max_value to mark the prime numbers.

Efficient 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 gcd 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 <bits/stdc++.h>
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[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 GCD of elements
// in an array having prime frequency
int gcdPrimeFreq(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]]++;

    int gcd = 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]) {
            gcd = __gcd(gcd, it->first);
        }
    }

    return gcd;
}

// Driver code
int main()
{
    int arr[] = { 5, 4, 6, 5, 4, 6 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << gcdPrimeFreq(arr, n);

    return 0;
}

Java

// Java implementation of the approach
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 GCD of elements
// in an array having prime frequency
static int gcdPrimeFreq(int arr[], int n)
{
    boolean []prime = new boolean[n + 1];
    for (int i = 0; i < n + 1; i++)
        prime[i] = true;

    SieveOfEratosthenes(prime, n + 1);

    int i, j;

    // Map is used to store
    // element frequencies
    HashMap<Integer,
            Integer> mp = new HashMap<Integer,
                                      Integer>();

    for (i = 0 ; i < n; i++)
    {
        if(mp.containsKey(arr[i]))
        {
            mp.put(arr[i], mp.get(arr[i]) + 1);
        }
        else
        {
            mp.put(arr[i], 1);
        }
    }
    int gcd = 0;

    // Traverse the map using iterators
    for (Map.Entry<Integer,
                   Integer> it : mp.entrySet())
    {

        // Count the number of elements
        // having prime frequencies
        if (prime[it.getValue()])
        {
            gcd = __gcd(gcd, it.getKey());
        }
    }
    return gcd;
}
static int __gcd(int a, int b)
{
    if (b == 0)
        return a;
    return __gcd(b, a % b);

}

// Driver code
static public void main ( String []arg)
{
    int arr[] = { 5, 4, 6, 5, 4, 6 };
    int n = arr.length;

    System.out.println(gcdPrimeFreq(arr, n));
}
}

// This code is contributed by Rajput-Ji

Python3

# Python3 implementation of the approach
from math import sqrt, gcd

# 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(2 * p, p_size, p) :
                prime[i] = False;

# Function to return the GCD of elements
# in an array having prime frequency
def gcdPrimeFreq(arr, n) :

    prime = [True] * (n + 1);

    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;

    __gcd = 0;

    # Traverse the map using iterators
    for key,value in m.items() :

        # Count the number of elements
        # having prime frequencies
        if (prime[value]) :
            __gcd = gcd(__gcd, key);

    return __gcd;

# Driver code
if __name__ == "__main__" :

    arr = [ 5, 4, 6, 5, 4, 6 ];
    n = len(arr);

    print(gcdPrimeFreq(arr, n));

# This code is contributed by AnkitRai01

C#

// C# implementation of the approach
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[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 GCD of elements
// in an array having prime frequency
static int gcdPrimeFreq(int []arr, int n)
{
    int i;
    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> mp = new Dictionary<int, int>();
    for (i = 0 ; i < n; i++)
    {
        if(mp.ContainsKey(arr[i]))
        {
            var val = mp[arr[i]];
            mp.Remove(arr[i]);
            mp.Add(arr[i], val + 1);
        }
        else
        {
            mp.Add(arr[i], 1);
        }
    }
    int gcd = 0;

    // Traverse the map using iterators
    foreach(KeyValuePair<int, int> it in mp)
    {

        // Count the number of elements
        // having prime frequencies
        if (prime[it.Value])
        {
            gcd = __gcd(gcd, it.Key);
        }
    }
    return gcd;
}
static int __gcd(int a, int b)
{
    if (b == 0)
        return a;
    return __gcd(b, a % b);

}

// Driver code
static public void Main ( String []arg)
{
    int []arr = { 5, 4, 6, 5, 4, 6 };
    int n = arr.Length;

    Console.WriteLine(gcdPrimeFreq(arr, n));
}
}

// This code is contributed by Princi Singh

Javascript

<script>
// javascript implementation of the approach
function gcd_two_numbers(x, y) {
  x = Math.abs(x);
  y = Math.abs(y);
  while(y) {
    var t = y;
    y = x % y;
    x = t;
  }
  return x;
}

// Function to create Sieve to check primes
function SieveOfEratosthenes(prime, p_size){
    // False here indicates
    // that it is not prime
    prime[0] = false;
    prime[1] = false;

    for (let 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 (let i = p * 2; i <= p_size; i += p)
                prime[i] = false;
        }
    }
    return prime;
}

// Function to return the GCD of elements
// in an array having prime frequency
function gcdPrimeFreq( arr,  n){
    let prime = [];
    for(let i = 0;i<n+1;i++){
        prime.push(true);
    }
    prime = SieveOfEratosthenes(prime, n + 1);
    let i, j;
    // Map is used to store
    // element frequencies
    let m = new Map();
    for (i = 0; i < n; i++){
      if(m[arr[i]])
        m[arr[i]]++;
      else
        m[arr[i]] = 1;
    }
    let gcd = 0;

    // Traverse the map using iterators
    for (var it in m) {

        // Count the number of elements
        // having prime frequencies
        if (prime[m[it]]) {
            gcd = gcd_two_numbers(gcd, it);
        }
    }

    return gcd;
}

// Driver code
let a = [ 5, 4, 6, 5, 4, 6 ];

let len = a.length;

document.write( gcdPrimeFreq(a, len));
</script>

Output:

1

Time Complexity: O(n*log(log(n)))
Auxiliary Space: O(n), as extra space of size n is used