Lexicographically smallest string which is not a subsequence of given string

Last Updated : 01 Feb, 2023

Given a string S, the task is to find the string which is lexicographically smallest and not a subsequence of the given string S.

Examples:

Input: S = "abcdefghijklmnopqrstuvwxyz"
Output:
aa
Explanation:
String "aa" is the lexicographically smallest string which is not present in the given string as a subsequence.

Input: S = "aaaa"
Output:
aaab
Explanation:
String "aaa" is the lexicographically smallest string which is not present in the given string as a subsequence.

Approach: The idea is to solve the given problem is to find the frequency of the character 'a' in the given string (say f). If the value of f is less than the length of the string, then the answer would be the string formed by concatenating 'a' f+1 number of times as aaa....(f+1 times) will be the required lexicographically smallest string which is not a subsequence. Otherwise, the answer would be the string formed by concatenating 'a' (f-1 times) and 'b' at the end of the string.

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find lexicographically smallest string that
// is not a subsequence of S
string smallestNonSubsequence(string S, int N)
{
    // variable to store frequency of 'a'
    int freq = 0;
    // calculate frequency of 'a'
    for (int i = 0; i < N; i++)
        if (S[i] == 'a')
            freq++;
    // Initialize string consisting of freq number of 'a'
    string ans(freq, 'a');
    // change the last digit to 'b'
    if (freq == N)
        ans[freq - 1] = 'b';
    // add another 'a' to the string
    else
        ans += 'a';
    // return the answer string
    return ans;
}
// Driver code
int main()
{
    // Input
    string S = "abcdefghijklmnopqrstuvwxyz";
    int N = S.length();

    // Function call
    cout << smallestNonSubsequence(S, N) << endl;
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
public class GFG
{

// Function to find lexicographically smallest string that
// is not a subsequence of S
static String smallestNonSubsequence(String S, int N)
{
  
    // variable to store frequency of 'a'
    int freq = 0;
  
    // calculate frequency of 'a'
    for (int i = 0; i < N; i++)
        if (S.charAt(i) == 'a')
            freq++;
  
    // Initialize string consisting of freq number of 'a'
 String ans="";
    for(int i = 0; i < f req; i++){
        ans += 'a';
    }
  
    // change the last digit to 'b'
    if (freq == N)
       ans = ans.replace(ans.charAt(freq - 1), 'b');
  
    // add another 'a' to the string
    else
        ans += 'a';
  
    // return the answer string
    return ans;
}

// Driver Code
public static void main(String args[])
{
    String S = "abcdefghijklmnopqrstuvwxyz";
    int N = S.length();

    // Function call
    System.out.println(smallestNonSubsequence(S, N));
    }
}

// This code is contributed by SoumikMondal

Python3

# Python3 program for the above approach

# Function to find lexicographically smallest 
# string that is not a subsequence of S
def smallestNonSubsequence(S, N):
    
    # Variable to store frequency of 'a'
    freq = 0
    
    # Calculate frequency of 'a'
    for i in range(N):
        if (S[i] == 'a'):
            freq += 1
            
    # Initialize string consisting
    # of freq number of 'a'
    ans = ""
    for i in range(freq):
        ans += 'a'

    # Change the last digit to 'b'
    if (freq == N):
        ans = ans.replace(ans[freq - 1], 'b')
        
    # Add another 'a' to the string
    else:
        ans += 'a'
        
    # Return the answer string
    return ans

# Driver code
if __name__ == '__main__':
    
    # Input
    S = "abcdefghijklmnopqrstuvwxyz"
    N = len(S)

    # Function call
    print(smallestNonSubsequence(S, N))
    
# This code is contributed by SURENDRA_GANGWAR

// C# program equivalent to the above Java program
using System;

class GFG 
{
  
  // Function to find lexicographically smallest string
  // that is not a subsequence of S
  static string SmallestNonSubsequence(string S, int N)
  {
    
    // variable to store frequency of 'a'
    int freq = 0;

    // calculate frequency of 'a'
    for (int i = 0; i < N; i++)
      if (S[i] == 'a')
        freq++;

    // Initialize string consisting of freq number of
    // 'a'
    string ans = "";
    for (int i = 0; i < freq; i++) {
      ans += 'a';
    }

    // change the last digit to 'b'
    if (freq == N)
      ans = ans.Replace(ans[freq - 1], 'b');

    // add another 'a' to the string
    else
      ans += 'a';

    // return the answer string
    return ans;
  }

  // Driver Code
  static void Main(string[] args)
  {
    string S = "abcdefghijklmnopqrstuvwxyz";
    int N = S.Length;

    // Function call
    Console.WriteLine(SmallestNonSubsequence(S, N));
  }
}

// This code is contributed by phasing17

JavaScript

<script>

// JavaScript program for the above approach

// Function to find lexicographically smallest string that
// is not a subsequence of S
function smallestNonSubsequence(S,N)
{

    // variable to store frequency of 'a'
    let freq = 0;
    
    // calculate frequency of 'a'
    for (let i = 0; i < N; i++)
        if (S[i] == 'a')
            freq++;
            
    // Initialize string consisting of freq number of 'a'
    let ans = new Array(freq).fill('a').join('');
    // change the last digit to 'b'
    if (freq == N)
        ans[freq - 1] = 'b';
        
    // add another 'a' to the string
    else
        ans += 'a';
        
    // return the answer string
    return ans;
}

// Driver code

// Input
let S = "abcdefghijklmnopqrstuvwxyz";
let N = S.length;

// Function call
document.write(smallestNonSubsequence(S, N),"</br>");

// This code is contributed by shinjanpatra

</script>

Output

aa

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

Minimum size lexicographically smallest string which is not a substring of given string

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Lexicographically smallest string which is not a subsequence of given string

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