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 that 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

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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

1


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