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 primesvoid 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 frequencyint 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 codeint 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 frequencyimport 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 frequencyimport math as mt# Function to create Sieve to# check primesdef 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 frequencydef 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 codearr = [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 frequencyusing 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 |
Javascript
<script>// Javascript program to find sum of elements// in an array having prime frequency// Function to create Sieve to check primesfunction 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; } }}// Function to return the sum of elements// in an array having prime frequencyfunction sumOfElements(arr, n) { let prime = new Array(n + 1); prime.fill(true) 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.has(arr[i])) m.set(arr[i], m.get(arr[i]) + 1); else m.set(arr[i], 1); } let sum = 0; // Traverse the map using iterators for (let it of m) { // Count the number of elements // having prime frequencies if (prime[it[1]]) { sum += (it[0]); } } return sum;}// Driver codelet arr = [5, 4, 6, 5, 4, 6];let n = arr.length;document.write(sumOfElements(arr, n));// This code is contributed by gfgking</script> |
Output:
15
Time Complexity: O(n3/2)
Auxiliary Space: O(n)
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