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

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 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 q;     for (int i=0; i

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{         @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 c = new IntCompare();                    // creating a priority queue with comparator         // such that elements in the queue are in         // descending order.         PriorityQueue 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 =  * 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)