Sum and Product of Prime Frequencies of Characters in a String

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Given a string str containing only lowercase English alphabets, the task is to find the sum and product of all the prime frequencies of the characters in str.

Examples:

Input: str = “zambiatek”
Output: 6, 8
Only characters ‘g’, ‘k’ and ‘s’ have prime frequencies i.e. 2 + 2 + 2 = 6 and 2 * 2* 2 = 8

Character frequency

g 2

e 4

k 2

s 2

f 1

o 1

r 1

Input: str = “algorithms”
Output: 0, 0

Character	frequency
g	2
e	4
k	2
s	2
f	1
o	1
r	1

Approach:

Traverse the string and store the frequencies of all the characters in a hash table.
Find the frequencies which are prime using Sieve Of Eratosthenes.
Calculate the sum and product of all of these prime frequencies and finally print the sum and product.

Below is the implementation of the above approach:

C++

// C++ program to find Sum and product of Prime
// Frequencies of Characters in a String
#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 find the sum of prime frequencies
// of the characters of the given string
void sumProdOfPrimeFreq(string s)
{
    bool prime[s.length() + 1];
    memset(prime, true, sizeof(prime));
 
    SieveOfEratosthenes(prime, s.length() + 1);
 
    int i, j;
 
    // map is used to store
    // character frequencies
    unordered_map<char, int> m;
    for (i = 0; i < s.length(); i++)
        m[s[i]]++;
 
    int sum = 0, product = 1;
 
    // Traverse the map
    for (auto it = m.begin(); it != m.end(); it++) {
 
        // If the frequency is prime
        if (prime[it->second]) {
            sum += it->second;
            product *= it->second;
        }
    }
 
    cout << "Sum = " << sum;
    cout << "\nProduct = " << product;
}
 
// Driver code
int main()
{
    string s = "zambiatek";
 
    sumProdOfPrimeFreq(s);
    return 0;
}

Java

// Java program to find Sum and product of Prime
// Frequencies of Characters in a String
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 find the sum of prime frequencies
    // of the characters of the given string
    static void sumProdOfPrimeFreq(char[] s)
    {
        boolean[] prime = new boolean[s.length + 1];
        Arrays.fill(prime, true);
 
        SieveOfEratosthenes(prime, s.length + 1);
 
        int i, j;
 
        // map is used to store
        // character frequencies
        Map<Character, Integer> mp = new HashMap<>();
        for (i = 0; i < s.length; i++) 
        {
            mp.put(s[i], mp.get(s[i]) == null ? 1 : mp.get(s[i]) + 1);
        }
 
        int sum = 0, product = 1;
 
        // Traverse the map
        for (Map.Entry<Character, Integer> it : mp.entrySet()) 
        {
 
            // If the frequency is prime
            if (prime[it.getValue()])
            {
                sum += it.getValue();
                product *= it.getValue();
            }
        }
 
        System.out.print("Sum = " + sum);
        System.out.println("\nProduct = " + product);
    }
 
    // Driver code
    public static void main(String[] args)
    {
        String s = "zambiatek";
 
        sumProdOfPrimeFreq(s.toCharArray());
    }
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 program to find Sum and product of Prime
# Frequencies of Characters in a String
 
# 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, 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 find the sum of prime frequencies
# of the characters of the given string
def sumProdOfPrimeFreq(s):
    prime = [True] * (len(s) + 2)
 
    SieveofEratosthenes(prime, len(s) + 1)
 
    i = 0
    j = 0
 
    # map is used to store
    # character frequencies
    m = dict()
 
    for i in range(len(s)):
        m[s[i]] = (m[s[i]] + 1) if s[i] in m else 1
 
    s = 0
    product = 1
 
    # Traverse the map
    for it in m:
 
        # If the frequency is prime
        if prime[m[it]]:
            s += m[it]
            product *= m[it]
 
    print("Sum =", s)
    print("Product =", product)
 
# Driver code
if __name__ == "__main__":
    s = "zambiatek"
    sumProdOfPrimeFreq(s)
 
# This code is contributed by
# sanjeev2552

C#

// C# program to find Sum and product of Prime
// Frequencies of Characters in a String
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 find the sum of prime frequencies
    // of the characters of the given string
    static void sumProdOfPrimeFreq(char[] s)
    {
        int i;
        bool[] prime = new bool[s.Length + 1];
        for(i=0;i<s.Length + 1;i++){
            prime[i]=true;
        }
 
        SieveOfEratosthenes(prime, s.Length + 1);
 
         
 
        // map is used to store
        // character frequencies
        Dictionary<char, int> mp = new Dictionary<char, int>();
        for (i = 0 ; i < s.Length; i++)
        {
            if(mp.ContainsKey(s[i]))
            {
                var val = mp[s[i]];
                mp.Remove(s[i]);
                mp.Add(s[i], val + 1); 
            }
            else
            {
                mp.Add(s[i], 1);
            }
        }
 
        int sum = 0, product = 1;
 
        // Traverse the map
        foreach(KeyValuePair<char, int> it in mp)
        {
 
            // If the frequency is prime
            if (prime[it.Value])
            {
                sum += it.Value;
                product *= it.Value;
            }
        }
 
        Console.Write("Sum = " + sum);
        Console.WriteLine("\nProduct = " + product);
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        String s = "zambiatek";
 
        sumProdOfPrimeFreq(s.ToCharArray());
    }
}
 
// This code is contributed by Princi Singh

Javascript

<script>
// Javascript program to find Sum and product of Prime
// Frequencies of Characters in a String
 
// 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 find the sum of prime frequencies
// of the characters of the given string
function sumProdOfPrimeFreq(s) {
    let prime = new Array(s.length + 1);
    prime.fill(true);
 
    SieveOfEratosthenes(prime, s.length + 1);
 
    let i, j;
 
    // map is used to store
    // character frequencies
    let m = new Map();
    for (i = 0; i < s.length; i++)
        m.set(s[i], m.get(s[i]) == null ? 1 : m.get(s[i]) + 1);
 
    let sum = 0, product = 1;
 
    // Traverse the map
    for (let it of m) {
        console.log(m)
        // If the frequency is prime
        if (prime[it[1]]) {
            sum += it[1];
            product *= it[1];
        }
    }
 
    document.write("Sum = " + sum);
    document.write("<br>Product = " + product);
}
 
// Driver code
 
let s = "zambiatek";
 
sumProdOfPrimeFreq(s);
 
// This code is contributed by gfgking
</script>

Output

Sum = 6
Product = 8

Complexity Analysis:

Time Complexity: O(N*log(logN)), where N is the length of the given string.
Auxiliary Space: O(N), since N extra space has been taken.

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