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 |
Javascript
<script> // Javascript program to find sum of elements // in an array having prime frequency // 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 ;
}
}
} // Function to return the sum of elements // in an array having prime frequency function 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 code let 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)