Skip to content
Related Articles

Related Articles

Table of Contents

Improve Article
Save Article
Like Article

Minimize cost to empty a given string by removing characters alphabetically

  • Last Updated : 19 Oct, 2021

Given string str, the task is to minimize the total cost to remove all the characters from the string in alphabetical order.

The cost of removing any character at i th index from the string will be i. The indexing is 1-based.

Examples:

Input: str = “abcab” 
Output: 8 
Explanation: 
First char ‘a’ at index 1 is removed, str[] becomes “bcab”, 
Then char ‘a’ with index 3 is removed, str[] becomes “bcb” 
After that char ‘b’ with index 1 is removed, str[] becomes “cb”, 
Then char ‘b’ with index 2 is removed, str[] becomes “c”, 
Finally, char ‘c’ is removed. 
Total points = 1+3 + 1 + 2 + 1 = 8. 

Input: str = “def” 
Output: 3

Naive Approach: The simplest approach is to remove the smallest character with a smaller index in the string in each step and keep on adding the cost to the total cost. Print the final cost after this operation.

Time Complexity: O(N2)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized by precomputing for each character, the number of smaller characters preceding it in the given string. Below are the steps:

  1. Initialize the total cost to 0.
  2. Transverse the given string and for each character, count the number of characters that are less than the current character and have occurred before it.
  3. If this count is 0, this means that the current character will be removed at the present index, so add the index of the character to the resultant cost.
  4. Else subtract the count from its current index and then add it to the total cost.
  5. Print the total cost after all the above steps.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
#include <bits/stdc++.h>
#include <vector>
using namespace std;
  
// Function to find the minimum cost
// required to remove each character
// of the string in alphabetical order
int minSteps(string str, int N)
{
    int smaller, cost = 0;
  
    // Stores the frequency of
    // characters of the string
    int f[26] = { 0 };
  
    // Iterate through the string
    for (int i = 0; i < N; i++) {
        int curr_ele = str[i] - 'a';
        smaller = 0;
  
        // Count the number of characters
        // smaller than the present character
        for (int j = 0; j <= curr_ele; j++) {
            if (f[j])
                smaller += f[j];
        }
  
        // If no smaller character
        // precedes current character
        if (smaller == 0)
            cost += (i + 1);
        else
            cost += (i - smaller + 1);
  
        // Increase the frequency of
        // the current character
        f[str[i] - 'a']++;
    }
  
    // Return the
    // total cost
    return cost;
}
  
// Driver Code
int main()
{
    // Given string str
    string str = "abcab";
    int N = str.size();
  
    // Function call
    cout << minSteps(str, N);
    return 0;
}
Java



// Java program for 
// the above approach
import java.io.*;
class GFG{
  
    // Function to find the minimum cost
    // required to remove each character
    // of the string in alphabetical order
    static int minSteps(String str, int N)
    {
        int smaller, cost = 0;
  
        // Stores the frequency of
        // characters of the string
        int f[] = new int[26];
  
        // Iterate through the string
        for (int i = 0; i < N; i++) 
        {
            int curr_ele = str.charAt(i) - 'a';
            smaller = 0;
  
            // Count the number of characters
            // smaller than the present character
            for (int j = 0; j <= curr_ele; j++) 
            {
                if (f[j] != 0)
                    smaller += f[j];
            }
  
            // If no smaller character
            // precedes current character
            if (smaller == 0)
                cost += (i + 1);
            else
                cost += (i - smaller + 1);
  
            // Increase the frequency of
            // the current character
            f[str.charAt(i) - 'a']++;
        }
  
        // Return the
        // total cost
        return cost;
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        // Given string str
        String str = "abcab";
  
        int N = str.length();
  
        // Function call
        System.out.println(minSteps(str, N));
    }
}
  
// This code is contributed by AnkitRai01
Python3



# Python3 program for the above approach 
  
# Function to find the minimum cost
# required to remove each character
# of the string in alphabetical order 
def minSteps(str, N):
  
    cost = 0
  
    # Stores the frequency of
    # characters of the string
    f = [0] * 26
  
    # Iterate through the string
    for i in range(N):
        curr_ele = ord(str[i]) - ord('a')
        smaller = 0
  
        # Count the number of characters
        # smaller than the present character
        for j in range(curr_ele + 1):
            if (f[j]):
                smaller += f[j]
  
        # If no smaller character
        # precedes current character
        if (smaller == 0):
            cost += (i + 1)
        else:
            cost += (i - smaller + 1)
  
        # Increase the frequency of
        # the current character
        f[ord(str[i]) - ord('a')] += 1
  
    # Return the total cost
    return cost
  
# Driver Code
  
# Given string str
str = "abcab"
  
N = len(str)
  
# Function call
print(minSteps(str, N))
  
# This code is contributed by Shivam Singh
C#



// C# program for 
// the above approach
using System;
class GFG{
  
// Function to find the minimum cost
// required to remove each character
// of the string in alphabetical order
static int minSteps(string str, int N)
{
    int smaller, cost = 0;
  
    // Stores the frequency of
    // characters of the string
    int[] f = new int[26];
  
    // Iterate through the string
    for (int i = 0; i < N; i++) 
    {
        int curr_ele = str[i] - 'a';
        smaller = 0;
  
        // Count the number of characters
        // smaller than the present character
        for (int j = 0; j <= curr_ele; j++) 
        {
            if (f[j] != 0)
            smaller += f[j];
        }
          
        // If no smaller character
        // precedes current character
        if (smaller == 0)
            cost += (i + 1);
        else
            cost += (i - smaller + 1);
  
        // Increase the frequency of
        // the current character
        f[str[i] - 'a']++;
    }
  
    // Return the
    // total cost
    return cost;
}
  
// Driver Code
public static void Main()
{
  
    // Given string str
    string str = "abcab";
  
    int N = str.Length;
  
    // Function call
    Console.Write(minSteps(str, N));
}
}
  
// This code is contributed by Chitranayal
Javascript



<script>
  
// JavaScript program for
// the above approach
  
// Function to find the minimum cost
// required to remove each character
// of the string in alphabetical order
function minSteps(str, N)
{
    var smaller,
    cost = 0;
      
    // Stores the frequency of
    // characters of the string
    var f = new Array(26).fill(0);
      
    // Iterate through the string
    for(var i = 0; i < N; i++) 
    {
        var curr_ele = str[i].charCodeAt(0) - 
                          "a".charCodeAt(0);
        smaller = 0;
          
        // Count the number of characters
        // smaller than the present character
        for(var j = 0; j <= curr_ele; j++) 
        {
            if (f[j] !== 0) 
                smaller += f[j];
        }
          
        // If no smaller character
        // precedes current character
        if (smaller === 0) 
            cost += i + 1;
        else 
            cost += i - smaller + 1;
          
        // Increase the frequency of
        // the current character
        f[str[i].charCodeAt(0) - 
             "a".charCodeAt(0)]++;
    }
      
    // Return the
    // total cost
    return cost;
}
  
// Driver Code
  
// Given string str
var str = "abcab";
var N = str.length;
  
// Function call
document.write(minSteps(str, N));
  
// This code is contributed by rdtank
  
</script>
Output: 
8
Time Complexity: O(N)
Auxiliary Space: O(26)

My Personal Notes
arrow_drop_up
Next

Find the elements appearing even number of times in an Array
Recommended Articles
Page :
Minimize cost to empty given array where cost of removing an element is its absolute difference with Time instant
08, Dec 20
Minimum cost to empty Array where cost of removing an element is 2^(removed_count) * arr[i]
20, Jul 20
Minimize cost to make all characters of a Binary String equal to '1' by reversing or flipping characters of substrings
11, Jun 21
Maximize cost to empty given array by repetitively removing K array elements
23, Nov 20
Minimize operations of removing 2i -1 array elements to empty given array
17, Jan 21
Replace consonants with next immediate consonants alphabetically in a String
12, Nov 18
Maximize cost to empty an array by removing contiguous subarrays of equal elements
12, Sep 20
Minimize removal of non-equal adjacent characters required to make a given string empty
18, Jan 21
Sort an Array alphabetically when each number is converted into words
06, May 20
Minimize length of a string by removing suffixes and prefixes of same characters
31, Mar 21
Minimize a binary string by repeatedly removing even length substrings of same characters
03, Dec 20
Minimize cost to sort an Array by swapping any pair of element (X, Y) with cost as (X + Y)
20, Jul 21
Minimize cost to sort the Array by moving elements with cost as the value itself
29, Sep 21
Minimize cost to split an array into K subsets such that the cost of each element is its product with its position in the subset
03, Jan 21
Minimize cost to connect the graph by connecting any pairs of vertices having cost at least 0
27, Sep 21
Minimize cost to convert all 0s to 1s with cost of converting 0s group be X and that of 1 be X/3
09, Nov 21
Minimize Cost to sort a String in Increasing Order of Frequencies of Characters
23, Jul 20
Minimize cost to convert all characters of a binary string to 0s
19, Oct 20
Minimize cost of removals required to make all remaining characters of the string unique
13, Jan 21
Find the winner of game of repeatedly removing the first character to empty given string
03, Jan 21
Check if a string can be made empty by repeatedly removing given subsequence
23, Jul 21
Count of ways to empty given String by recursively removing all adjacent duplicates
06, Sep 21
Minimum cost to remove the spaces between characters of a String by rearranging the characters
31, Aug 20
Cost required to empty a given array by repeated removal of maximum obtained by given operations
04, Sep 20
Article Contributed By :
https://media.geeksforgeeks.org/auth/avatar.png
vatsalanarang
@vatsalanarang
Vote for difficulty





Improved By :
Article Tags :
Practice Tags :
Report Issue

We use cookies to ensure you have the best browsing experience on our website. By using our site, you
acknowledge that you have read and understood our
Cookie Policy &
        Privacy Policy

Lightbox

Start Your Coding Journey Now!