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Minimum sum of squares of character counts in a given string after removing k characters

Given a string of lowercase alphabets and a number k, the task is to print the minimum value of the string after removal of ‘k’ characters. The value of a string is defined as the sum of squares of the count of each distinct character. For example consider the string “saideep”, here frequencies of characters are s-1, a-1, i-1, e-2, d-1, p-1 and value of the string is 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 = 9.

Expected Time Complexity : O(n)

Examples:

Input :  str = abccc, K = 1
Output :  6
We remove c to get the value as 12 + 12 + 22

Input :  str = aaab, K = 2
Output :  2

Asked In : Amazon



One clear observation is that we need to remove character with highest frequency. One trick is the character ma

A Simple solution is to use sorting technique through all current highest frequency reduce up to k times. For After every reduce again sort frequency array.

A Better Solution used to Priority Queue which has to the highest element on top.

  1. Initialize empty priority queue.
  2. Count frequency of each character and Store into temp array.
  3. Remove K characters which have highest frequency from queue.
  4. Finally Count Sum of square of each element and return it.

Below is the implementation of the above idea.

C++

// C++ program to find min sum of squares
// of characters after k removals
#include <bits/stdc++.h>
using namespace std;
  
const int MAX_CHAR = 26;
  
// Main Function to calculate min sum of
// squares of characters after k removals
int minStringValue(string str, int k)
{
    int l = str.length(); // find length of string
  
    // if K is greater than length of string
    // so reduced string will become 0
    if (k >= l)
        return 0;
  
    // Else find Frequency of each character and
    // store in an array
    int frequency[MAX_CHAR] = {0};
    for (int i=0; i<l; i++)
        frequency[str[i]-'a']++;
  
    // Push each char frequency into a priority_queue
    priority_queue<int> q;
    for (int i=0; i<MAX_CHAR; i++)
        q.push(frequency[i]);
  
  
    // Removal of K characters
    while (k--)
    {
        // Get top element in priority_queue,
        // remove it. Decrement by 1 and again
        // push into priority_queue
        int temp = q.top();
        q.pop();
        temp = temp-1;
        q.push(temp);
    }
  
    // After removal of K characters find sum
    // of squares of string Value
    int result = 0; // Initialize result
    while (!q.empty())
    {
        int temp = q.top();
        result += temp*temp;
        q.pop();
    }
  
    return result;
}
  
// Driver Code
int main()
{
    string str = "abbccc";   // Input 1
    int k = 2;
    cout << minStringValue(str, k) << endl;
  
    str = "aaab";           // Input 2
    k = 2;
    cout << minStringValue(str, k);
  
    return 0;
}

Java

// Java program to find min sum of squares
// of characters after k removals
import java.util.Comparator;
import java.util.PriorityQueue;
public class GFG {
        
    static final int MAX_CHAR = 26;
      
    // Defining a comparator class
    static class IntCompare implements Comparator<Integer>{
        @Override
        public int compare(Integer arg0, Integer arg1) {
            if(arg0 > arg1)
                return -1;
            else if(arg0 < arg1)
                return 1;
            else
                return 0;
        }
    }
      
    // Main Function to calculate min sum of
    // squares of characters after k removals
    static int minStringValue(String str, int k)
    {
        int l = str.length(); // find length of string
       
        // if K is greater than length of string
        // so reduced string will become 0
        if (k >= l)
            return 0;
       
        // Else find Frequency of each character and
        // store in an array
        int[] frequency = new int[MAX_CHAR];
        for (int i=0; i<l; i++)
            frequency[str.charAt(i)-'a']++;
       
          
        // creating object for comparator
        Comparator<Integer> c = new IntCompare();
          
        // creating a priority queue with comparator
        // such that elements in the queue are in
        // descending order.
        PriorityQueue<Integer> q = new PriorityQueue<>(c);
          
        // Push each char frequency into a priority_queue
        for (int i = 0; i < MAX_CHAR; i++){
            if(frequency[i] != 0)
                q.add(frequency[i]);
        }
       
          
        // Removal of K characters
        while (k != 0)
        {
            // Get top element in priority_queue,
            // remove it. Decrement by 1 and again
            // push into priority_queue
            int temp = q.peek();
            q.poll();
            temp = temp-1;
            q.add(temp);
            k--;
        }
       
        // After removal of K characters find sum
        // of squares of string Value
        int result = 0; // Initialize result
        while (!q.isEmpty())
        {
            int temp = q.peek();
            result += temp*temp;
            q.poll();
        }
          
        return result;
    }
       
    // Driver Code
    public static void main(String args[])
    {
        String str = "abbccc";   // Input 1
        int k = 2;
        System.out.println(minStringValue(str, k));
       
        str = "aaab";           // Input 2
        k = 2;
        System.out.println(minStringValue(str, k));
    }
}
// This code is contributed by Sumit Ghosh

Python 3

# Python3 program to find min sum of 
# squares of characters after k removals 
from queue import PriorityQueue
  
MAX_CHAR = 26
  
# Main Function to calculate min sum of 
# squares of characters after k removals
def minStringValue(str, k):
    l = len(str) # find length of string
  
    # if K is greater than length of string 
    # so reduced string will become 0 
    if(k >= l):
        return 0
      
    # Else find Frequency of each 
    # character and store in an array 
    frequency = [0] * MAX_CHAR
    for i in range(0, l):
        frequency[ord(str[i]) - 97] += 1
  
    # Push each char frequency negative 
    # into a priority_queue as the queue
    # by default is minheap
    q = PriorityQueue()
    for i in range(0, MAX_CHAR):
        q.put(-frequency[i])
  
    # Removal of K characters 
    while(k > 0):
          
        # Get top element in priority_queue
        # multiply it by -1 as temp is negative
        # remove it. Increment by 1 and again 
        # push into priority_queue 
        temp = q.get()
        temp = temp + 1
        q.put(temp, temp)
        k = k - 1
  
    # After removal of K characters find 
    # sum of squares of string Value     
    result = 0; # initialize result
    while not q.empty():
        temp = q.get()
        temp = temp * (-1)
        result += temp * temp
    return result 
  
# Driver Code
if __name__ == "__main__":
    str = "abbccc"
    k = 2
    print(minStringValue(str, k))
  
    str = "aaab"
    k = 2
    print(minStringValue(str, k))
      
# This code is contributed 
# by Sairahul Jella


Output:

6
2

Time Complexity: O(n)

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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