Minimum cost to construct a string

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: 

1. Appending a single character cost 1 unit 
2. 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 4

Input :  "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++

// C++ Program to find minimum cost to
// construct a string
#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 = "geeksforgeeks";

    cout << "Total cost to construct "
         << s << " is " << minCost;

    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#

// 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)