Lexicographically smallest string which is not a subsequence of given string

0 0 4 minutes read

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#

// 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)

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!