Minimum cost to construct a string

Last Updated : 15 Feb, 2024

Given a string s (containing lowercase letters only), we have to find the minimum cost to construct the given string. The cost can be determined using the following operations:

Appending a single character cost 1 unit
A sub-string of a new string(intermediate string) can be appended without any cost

Note* Intermediate string is the string formed so far.

Examples:

Input : "geks"
Output : cost: 4
Explanation:
appending 'g' cost 1, string "g"
appending 'e' cost 1, string "ge"
appending 'k' cost 1, string "gek"
appending 's' cost 1, string "geks"
Hence, Total cost to construct "geks" is 4Input :  "abab"
Output : cost: 2
Explanation: 
Appending 'a' cost 1, string "a"
Appending 'b' cost 1, string "ab"
Appending  "ab" cost nothing as it 
is substring of intermediate.
Hence, Total cost to construct "abab" is 2

Naive Approach: Check if there is a sub-string in the remaining string to be constructed which is also a sub-string in the intermediate string, if there is then append it at no cost and if not then append it at the cost of 1 unit per character.

In the above example when the intermediate string was "ab" and we need to construct "abab" then the remaining string was "ab". Hence there is a sub-string in the remaining string which is also a sub-string of intermediate string (i.e. "ab") and therefore costs us nothing.

Better Approach: We will use hashing technique, to maintain whether we have seen a character or not. If we have seen the character, then there is no cost to append the character and if not, then it cost us 1 unit.

Now in this approach, we take one character at a time and not a string. This is because if "ab" is substring of "abab", so is 'a' and 'b' alone and hence make no difference.
This also leads us to the conclusion that the cost to construct a string is never more than 26 in case the string contains all the alphabets (a-z).

Implementation:

C++

#include <iostream> using namespace std;  int minCost(string& s) {     // Initially all characters are un-seen     bool alphabets[26] = { false };      // Marking seen characters     for (int i = 0; i < s.size(); i++)         alphabets[s[i] - 97] = true;      // Count total seen character, and that     // is the cost     int count = 0;     for (int i = 0; i < 26; i++)         if (alphabets[i])             count++;      return count; }  int main() {     // s is the string that needs to be constructed     string s = "geks";      cout << "Total cost to construct "          << s << " is " << minCost(s); // Corrected: call minCost with s      return 0; }

Java

// Java Program to find minimum cost to // construct a string  class GFG  {      static int minCost(char[] s)      {                  // Initially all characters are un-seen         boolean alphabets[] = new boolean[26];          // Marking seen characters         for (int i = 0; i < s.length; i++)          {             alphabets[(int) s[i] - 97] = true;         }          // Count total seen character,          // and that is the cost         int count = 0;         for (int i = 0; i < 26; i++)         {             if (alphabets[i])              {                 count++;             }         }          return count;     }      // Driver code     public static void main(String[] args)      {         // s is the string that needs to be constructed         String s = "geeksforgeeks";         System.out.println("Total cost to construct " +                 s + " is " + minCost(s.toCharArray()));     } }  // This code is contributed by 29AjayKumar

Python3

# Python 3 Program to find minimum cost to # construct a string  def minCost(s):          # Initially all characters are un-seen     alphabets = [False for i in range(26)]      # Marking seen characters     for i in range(len(s)):         alphabets[ord(s[i]) - 97] = True      # Count total seen character, and that     # is the cost     count = 0     for i in range(26):         if (alphabets[i]):             count += 1      return count  # Driver Code if __name__ == '__main__':          # s is the string that needs to      # be constructed     s = "geeksforgeeks"      print("Total cost to construct", s,                        "is", minCost(s))      # This code is contributed by # Surendra_Gangwar

// C# Program to find minimum cost to // construct a string using System;  class GFG  {      static int minCost(char[] s)      {                  // Initially all characters are un-seen         bool []alphabets = new bool[26];          // Marking seen characters         for (int i = 0; i < s.Length; i++)          {             alphabets[(int) s[i] - 97] = true;         }          // Count total seen character,          // and that is the cost         int count = 0;         for (int i = 0; i < 26; i++)         {             if (alphabets[i])              {                 count++;             }         }          return count;     }      // Driver code     public static void Main(String[] args)      {         // s is the string that          // needs to be constructed         String s = "geeksforgeeks";         Console.WriteLine("Total cost to construct " +                 s + " is " + minCost(s.ToCharArray()));     } }  // This code is contributed by Rajput-Ji

JavaScript

<script>       // JavaScript Program to find minimum cost to       // construct a string       function minCost(s)       {                // Initially all characters are un-seen         var alphabets = new Array(26).fill(0);          // Marking seen characters         for (var i = 0; i < s.length; i++) {           alphabets[s[i].charCodeAt(0) - 97] = true;         }          // Count total seen character,         // and that is the cost         var count = 0;         for (var i = 0; i < 26; i++) {           if (alphabets[i]) {             count++;           }         }          return count;       }        // Driver code       // s is the string that       // needs to be constructed       var s = "geeksforgeeks";       document.write(         "Total cost to construct " + s + " is " + minCost(s.split(""))       );              // This code is contributed by rdtank.     </script>

Output

Total cost to construct geeksforgeeks is 1

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

Minimum days to achieve the String

shubham_rana_77

Improve

Article Tags :

Practice Tags :

Minimum cost to construct a string

Similar Reads