Maximize frequency sum of K chosen characters from given string

Given a positive integer K and a string S consisting of N characters, the task is to maximize the sum of the frequencies of exactly K chosen characters from the given string.

Examples:

Input: K – 3, S = ”GEEKSFORGEEKS”
Output: 12
Explanation:
Choose the character E from the given string S, the sum of frequency of 3 E’s is 3*4 = 12, which is the maximum.

Input: K = 10, S = ”GEEKSFORGEEKS”
Output: 28

Approach: The given problem can be solved by using the Greedy Approach by choosing those K characters having the higher frequencies. Follow the steps below to solve the problem:

• Initialize a variable, say sum to 0 that stores the resultant sum of frequencies of exactly K chosen characters from the string S.
• Find the frequencies of each character in the string S and store it in an auxiliary array, say freq[].
• Sort the array freq[] in descending order.
• Traverse the array freq[] and perform the following:
  • If the current frequency is less than K, then add freq[i]*freq[i] to the variable sum as it maximizes the resultant sum and decrements the value of freq[i] from K as freq[i] characters are chosen.
  • Otherwise, add the value of K*freq[i] to the variable sum and break out of the loop as K characters have been chosen.
• After completing the above steps, print the value of the sum as the result.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the maximum sum of
// frequencies of the exactly K chosen
// characters from the string S
int maximumSum(string S, int N, int K)
{
    // Stores the resultant maximum sum
    int sum = 0;

    // Stores the frequency of array
    // elements
    int freq[256] = { 0 };

    // Find the frequency of character
    for (int i = 0; i < N; i++) {
        freq[int(S[i])]++;
    }

    // Sort the frequency array in the
    // descending order
    sort(freq, freq + 256, greater<int>());

    // Iterate to choose K elements greedily
    for (int i = 0; i < 256; i++) {

        // If the freq[i] cards are
        // chosen
        if (K > freq[i]) {
            sum += freq[i] * freq[i];
            K -= freq[i];
        }

        // K cards have been picked
        else {
            sum += freq[i] * K;
            break;
        }
    }

    // Return the resultant sum
    return sum;
}

// Driver Code
int main()
{
    string S = "GEEKSFORGEEKS";
    int K = 10;
    int N = S.length();
    cout << maximumSum(S, N, K);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;
class GFG
{

// Function to find the maximum sum of
// frequencies of the exactly K chosen
// characters from the String S
static int maximumSum(String S, int N, int K)
{

    // Stores the resultant maximum sum
    int sum = 0;

    // Stores the frequency of array
    // elements
    Integer []freq = new Integer[256];
    Arrays.fill(freq, 0);

    // Find the frequency of character
    for(int i = 0; i < N; i++)
    {
        freq[(int)S.charAt(i)] += 1;
    }

    // Sort the frequency array in the
    // descending order
     Arrays.sort(freq, Collections.reverseOrder());

    // Iterate to choose K elements greedily
    for(int i = 0; i < 256; i++)
    {

        // If the freq[i] cards are
        // chosen
        if (K > freq[i])
        {
            sum += freq[i] * freq[i];
            K -= freq[i];
        }

        // K cards have been picked
        else
        {
            sum += freq[i] * K;
            break;
        }
    }

    // Return the resultant sum
    return sum;
}

// Driver Code
public static void main(String args[])
{
    String S = "GEEKSFORGEEKS";
    int K = 10;
    int N = S.length();

    System.out.print(maximumSum(S, N, K));
}
}

// This code is contributed by ipg2016107

Python3

# Python3 program for the above approach

# Function to find the maximum sum of
# frequencies of the exactly K chosen
# characters from the string S
def maximumSum(S, N, K):

    # Stores the resultant maximum sum
    sum = 0

    # Stores the frequency of array
    # elements
    freq = [0] * 256

    # Find the frequency of character
    for i in range(N):
        freq[ord(S[i])] += 1

    # Sort the frequency array in the
    # descending order
    freq = sorted(freq)[::-1]

    # Iterate to choose K elements greedily
    for i in range(256):

        # If the freq[i] cards are
        # chosen
        if (K > freq[i]):
            sum += freq[i] * freq[i]
            K -= freq[i]

        # K cards have been picked
        else:
            sum += freq[i] * K
            break

    # Return the resultant sum
    return sum

# Driver Code
if __name__ == '__main__':

    S = "GEEKSFORGEEKS"
    K = 10
    N = len(S)

    print(maximumSum(S, N, K))

# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

class GFG{

// Function to find the maximum sum of
// frequencies of the exactly K chosen
// characters from the string S
static int maximumSum(string S, int N, int K)
{

    // Stores the resultant maximum sum
    int sum = 0;

    // Stores the frequency of array
    // elements
    int []freq = new int[256];
    Array.Clear(freq, 0, 256);

    // Find the frequency of character
    for(int i = 0; i < N; i++)
    {
        freq[(int)S[i]]++;
    }

    // Sort the frequency array in the
    // descending order
    Array.Sort(freq);
    Array.Reverse(freq);

    // Iterate to choose K elements greedily
    for(int i = 0; i < 256; i++)
    {

        // If the freq[i] cards are
        // chosen
        if (K > freq[i])
        {
            sum += freq[i] * freq[i];
            K -= freq[i];
        }

        // K cards have been picked
        else
        {
            sum += freq[i] * K;
            break;
        }
    }

    // Return the resultant sum
    return sum;
}

// Driver Code
public static void Main()
{
    string S = "GEEKSFORGEEKS";
    int K = 10;
    int N = S.Length;

    Console.Write(maximumSum(S, N, K));
}
}

// This code is contributed by ipg2016107

Javascript

<script>

// JavaScript program for the above approach

// Function to find the maximum sum of
// frequencies of the exactly K chosen
// characters from the string S
function maximumSum(S, N, K)
{

    // Stores the resultant maximum sum
    let sum = 0;

    // Stores the frequency of array
    // elements
    let freq = Array.from({length: 256}, (_, i) => 0);

    // Find the frequency of character
    for(let i = 0; i < N; i++)
    {
        freq[S[i].charCodeAt()]++;
    }

    // Sort the frequency array in the
    // descending order
    freq.sort((a, b) => b - a);

    // Iterate to choose K elements greedily
    for(let i = 0; i < 256; i++)
    {

        // If the freq[i] cards are
        // chosen
        if (K > freq[i])
        {
            sum += freq[i] * freq[i];
            K -= freq[i];
        }

        // K cards have been picked
        else
        {
            sum += freq[i] * K;
            break;
        }
    }

    // Return the resultant sum
    return sum;
}

// Driver Code

    let S = "GEEKSFORGEEKS";
    let K = 10;
    let N = S.length;

    document.write(maximumSum(S.split(''), N, K))

</script>

Output:

28

Time Complexity: O(N)
Auxiliary Space: O(256)