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Sum of elements in an array having prime frequency
  • Last Updated : 01 Jul, 2019

Given an array arr, the task is to find the sum 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: 15
All the elements appear 2 times which is a prime
So, 5 + 4 + 6 = 15

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

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 sum of elements having prime frequency using the Sieve array calculated in the previous step.

Below is the implementation of the above approach:

C++




// C++ program to find sum of elements
// in an array having prime frequency
#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 sum of elements
// in an array having prime frequency
int sumOfElements(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 sum = 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]) {
            sum += (it->first);
        }
    }
  
    return sum;
}
  
// Driver code
int main()
{
    int arr[] = { 5, 4, 6, 5, 4, 6 };
    int n = sizeof(arr) / sizeof(arr[0]);
  
    cout << sumOfElements(arr, n);
    return 0;
}

Java




// Java program to find sum 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 sum of elements
    // in an array having prime frequency
    static int sumOfElements(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<Integer, Integer> 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 sum = 0;
      
        // Traverse the map
        for (Map.Entry<Integer, Integer> entry : m.entrySet()) 
        {
            int key = entry.getKey();
            int value = entry.getValue();
              
            // Count the number of elements
            // having prime frequencies
            if (prime[value]) 
            {
                sum += (key);
            }
        }
      
        return sum;
    }
      
    // Driver code
    public static void main(String args[])
    {
        int arr[] = { 5, 4, 6, 5, 4, 6 };
        int n = arr.length;
      
        System.out.println(sumOfElements(arr, n));
    }
}
  
// This code is contributed by ghanshyampandey

Python3




# Python3 program to find Sum of elements
# in an array having prime frequency
import math as mt
  
# 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, mt.ceil(mt.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
          
# Function to return the Sum of elements
# in an array having prime frequency
def SumOfElements(arr, n):
    prime = [True for i in range(n + 1)]
    SieveOfEratosthenes(prime, n + 1)
  
    i, j = 0, 0
  
    # Map is used to store
    # element frequencies
    m = dict()
    for i in range(n):
        if arr[i] in m.keys():
            m[arr[i]] += 1
        else:
            m[arr[i]] = 1
              
    Sum = 0
  
    # Traverse the map using iterators
    for i in m:
          
        # Count the number of elements
        # having prime frequencies
        if (prime[m[i]]):
            Sum += (i)
      
    return Sum
  
# Driver code
arr = [5, 4, 6, 5, 4, 6 ]
n = len(arr)
print(SumOfElements(arr, n))
  
# This code is contributed
# by Mohit kumar 29

C#




// C# program to find sum 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[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 sum of elements
    // in an array having prime frequency
    static int sumOfElements(int []arr, int n)
    {
        bool []prime = new bool[n + 1];
        for(int 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 (int i = 0 ; i < n; i++)
        {
            if(m.ContainsKey(arr[i]))
            {
                var val = m[arr[i]];
                m.Remove(arr[i]);
                m.Add(arr[i], val + 1); 
            }
            else
            {
                m.Add(arr[i], 1);
            }
        }
      
        int sum = 0;
      
        // Traverse the map
        foreach(KeyValuePair<int, int> entry in m)
        {
            int key = entry.Key;
            int value = entry.Value;
              
            // Count the number of elements
            // having prime frequencies
            if (prime[value]) 
            {
                sum += (key);
            }
        }
      
        return sum;
    }
      
    // Driver code
    public static void Main(String []args)
    {
        int []arr = { 5, 4, 6, 5, 4, 6 };
        int n = arr.Length;
      
        Console.WriteLine(sumOfElements(arr, n));
    }
}
  
// This code is contributed by 29AjayKumar
Output:
15

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