Smallest string which not a subsequence of the given string

Given a string str, consisting of lowercase alphabets, the task is to find the shortest string which is not a subsequence of the given string. If multiple strings exist, then print any one of them.

Examples:

Input: str = “abaabcc” 
Output: d 
Explanation:
One of the possible shortest string which is not a subsequence of the given string is “d”. Therefore, the required output is “d”. 

Input: str = “abcdefghijklmnopqrstuvwxyzaabbccdd” 
Output: ze 

Approach: The problem can be solved using Greedy technique. Follow the steps below to solve the problem:

• Initialize a string, say shortestString, to store the shortest string which is not a subsequence of the given string.
• Initialize a Set, say segments, to store all possible characters of each subsegment.
• Traverse the string and insert the character of the string into segments and check if the segments contain all the lowercase alphabets or not. If found to be true, then append the current character into shortestString and remove all the elements from the segments.
• Iterate over all possible lowercase alphabets in the range [a – z] and check if the current character is present in the segment or not. If found to be true, then insert the current character into shortestString.
• Finally, print the value of shortestString.

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find shortest string which
// not a subsequence of the given string
string ShortestSubsequenceNotPresent(string str)
{

    // Stores the shortest string which is
    // not a subsequence of the given string
    string shortestString;

    // Stores length of string
    int N = str.length();

    // Stores distinct character of subsegments
    unordered_set<char> subsegments;

    // Traverse the given string
    for (int i = 0; i < N; i++) {

        // Insert current character
        // into subsegments
        subsegments.insert(str[i]);

        // If all lowercase alphabets
        // present in the subsegment
        if (subsegments.size() == 26) {

            // Insert the last character of
            // subsegment into shortestString
            shortestString.push_back(str[i]);

            // Remove all elements from
            // the current subsegment
            subsegments.clear();
        }
    }

    // Traverse all lowercase alphabets
    for (char ch = 'a'; ch <= 'z'; ch++) {

        // If current character is not
        // present in the subsegment
        if (subsegments.count(ch) == 0) {
            shortestString.push_back(ch);

            // Return shortestString
            return shortestString;
        }
    }
    return shortestString;
}

// Driver Code
int main()
{

    // Given String
    string str
        = "abcdefghijklmnopqrstuvwxyzaabbccdd";

    cout << ShortestSubsequenceNotPresent(str);
    return 0;
}

Java

// Java program to implement
// the above approach

import java.io.*;
import java.util.*;

class GFG {
    public static String
    ShortestSubsequenceNotPresent(String str)
    {
        // Stores the shortest string which is
        // not a subsequence of the given string
        String shortestString = "";

        // Stores length of string
        int N = str.length();

        // Stores distinct character of subsegments
        HashSet<Character> subsegments = new HashSet<>();

        // Traverse the given string
        for (int i = 0; i < N; i++) {

            // Insert current character
            // into subsegments
            subsegments.add(str.charAt(i));

            // If all lowercase alphabets
            // present in the subsegment
            if (subsegments.size() == 26) {

                // Insert the last character of
                // subsegment into shortestString
                shortestString
                    = shortestString + str.charAt(i);

                // Remove all elements from
                // the current subsegment
                subsegments.clear();
            }
        }

        // Traverse all lowercase alphabets
        for (char ch = 'a'; ch <= 'z'; ch++) {

            // If current character is not
            // present in the subsegment
            if (!subsegments.contains(ch)) {
                shortestString = shortestString + ch;

                // Return shortestString
                return shortestString;
            }
        }
        return shortestString;
    }

    // Driver Code
    public static void main(String[] args)
    {
        String str = "abcdefghijklmnopqrstuvwxyzaabbccdd";

        System.out.print(
            ShortestSubsequenceNotPresent(str));
    }
}
// This code is contributed by Manu Pathria

Python3

# Python3 program to implement
# the above approach

# Function to find shortest string which
# not a subsequence of the given string
def ShortestSubsequenceNotPresent(Str):

    # Stores the shortest string which is
    # not a subsequence of the given string
    shortestString = ""

    # Stores length of string
    N = len(Str)

    # Stores distinct character of subsegments
    subsegments = set()

    # Traverse the given string
    for i in range(N):

        # Insert current character
        # into subsegments
        subsegments.add(Str[i])

        # If all lowercase alphabets
        # present in the subsegment
        if (len(subsegments) == 26) :

            # Insert the last character of
            # subsegment into shortestString
            shortestString += Str[i]

            # Remove all elements from
            # the current subsegment
            subsegments.clear()

    # Traverse all lowercase alphabets
    for ch in range(int(26)):

        # If current character is not
        # present in the subsegment
        if (chr(ch + 97) not in subsegments) :

            shortestString += chr(ch + 97)

            # Return shortestString
            return shortestString

    return shortestString

# Driver code
# Given String
Str = "abcdefghijklmnopqrstuvwxyzaabbccdd"

print(ShortestSubsequenceNotPresent(Str))

# This code is contributed by divyeshrabadiya07

C#

// C# program to implement
// the above approach
using System;
using System.Collections.Generic;

class GFG{

public static String ShortestSubsequenceNotPresent(
    String str)
{

    // Stores the shortest string which is
    // not a subsequence of the given string
    String shortestString = "";

    // Stores length of string
    int N = str.Length;

    // Stores distinct character of subsegments
    HashSet<char> subsegments = new HashSet<char>();

    // Traverse the given string
    for(int i = 0; i < N; i++)
    {

        // Insert current character
        // into subsegments
        subsegments.Add(str[i]);

        // If all lowercase alphabets
        // present in the subsegment
        if (subsegments.Count == 26)
        {

            // Insert the last character of
            // subsegment into shortestString
            shortestString = shortestString + str[i];

            // Remove all elements from
            // the current subsegment
            subsegments.Clear();
        }
    }

    // Traverse all lowercase alphabets
    for(char ch = 'a'; ch <= 'z'; ch++)
    {

        // If current character is not
        // present in the subsegment
        if (!subsegments.Contains(ch))
        {
            shortestString = shortestString + ch;

            // Return shortestString
            return shortestString;
        }
    }
    return shortestString;
}

// Driver Code
public static void Main(String[] args)
{
    String str = "abcdefghijklmnopqrstuvwxyzaabbccdd";

    Console.Write(
        ShortestSubsequenceNotPresent(str));
}
}

// This code is contributed by Rajput-Ji

Javascript

<script>


// JavaScript program to implement
// the above approach


// Function to find shortest string which
// not a subsequence of the given string
function ShortestSubsequenceNotPresent(str)
{

    // Stores the shortest string which is
    // not a subsequence of the given string
    var shortestString = [];

    // Stores length of string
    var N = str.length;

    // Stores distinct character of subsegments
    var subsegments = new Set();

    // Traverse the given string
    for (var i = 0; i < N; i++) {

        // Insert current character
        // into subsegments
        subsegments.add(str[i].charCodeAt(0));

        // If all lowercase alphabets
        // present in the subsegment
        if (subsegments.size == 26) {

            // Insert the last character of
            // subsegment into shortestString
            shortestString.push(str[i]);

            // Remove all elements from
            // the current subsegment
            subsegments = new Set();
        }
    }

    // Traverse all lowercase alphabets
    for (var ch = 'a'.charCodeAt(0);
    ch <= 'z'.charCodeAt(0); ch++) {

        // If current character is not
        // present in the subsegment
        if (!subsegments.has(ch)) {
            shortestString.push(String.fromCharCode(ch));

            // Return shortestString
            return shortestString.join("");
        }
    }
    return shortestString.join("");
}

// Driver Code

// Given String
var str = "abcdefghijklmnopqrstuvwxyzaabbccdd";

document.write( ShortestSubsequenceNotPresent(str));


</script>

Output

ze

Time Complexity: O(N)
Auxiliary Space: O(N)