K-th lexicographically smallest unique substring of a given string

Last Updated : 27 Apr, 2023

Given a string S. The task is to print the K-th lexicographically the smallest one among the different substrings of s.
A substring of s is a string obtained by taking out a non-empty contiguous part in s.
For example, if s = ababc, a, bab and ababc are substrings of s, while ac, z, and an empty string are not. Also, we say that substrings are different when they are different as strings.

Examples:

Input: str = "aba", k = 4
Output: b
All unique substrings are a, ab, aba, b, ba.
Thus the 4th lexicographically smallest substring is b.

Input: str = "geeksforgeeks", k = 5
Output: eeksf

Approach: For an arbitrary string t, each of its proper suffixes is lexicographically smaller than t, and the lexicographic rank of t is at least |t|. Thus, the length of the answer is at most K. Generate all substrings of s whose lengths are at most K. Sort them, unique them, and print the K-th one, where N = |S|.

Below is the implementation of the above approach:

C++

// C++ implementation of the above approach 
#include<bits/stdc++.h>
using namespace std;

void kThLexString(string st, int k, int n)
{
    
    // Set to store the unique substring 
    set<string> z;
    
    for(int i = 0; i < n; i++)
    {
        
       // String to create each substring 
       string pp;
       
       for(int j = i; j < i + k; j++)
       {
          if (j >= n)
              break;
          pp += st[j];
          
          // Adding to set 
          z.insert(pp);
       }
    }
    
    // Converting set into a list 
    vector<string> fin(z.begin(), z.end());
    
    // Sorting the strings int the list 
    // into lexicographical order 
    sort(fin.begin(), fin.end());

    // Printing kth substring 
    cout << fin[k - 1];
}

// Driver code
int main()
{
    string s = "geeksforgeeks";
    int k = 5;
    int n = s.length();
    
    kThLexString(s, k, n);
}

// This code is contributed by yatinagg

Java

// Java implementation of 
// the above approach 
import java.util.*; 
class GFG{
    
public static void kThLexString(String st, 
                                int k, int n) 
{ 
    // Set to store the unique substring 
    Set<String> z = new HashSet<String>(); 
    
    for(int i = 0; i < n; i++) 
    { 
        // String to create each substring 
        String pp = ""; 
    
        for(int j = i; j < i + k; j++) 
        { 
        if (j >= n) 
            break; 
        pp += st.charAt(j); 
    
        // Adding to set 
        z.add(pp); 
        } 
    } 
    
    // Converting set into a list 
    Vector<String> fin = new Vector<String>();
    fin.addAll(z);
    
    // Sorting the strings int the list 
    // into lexicographical order 
    Collections.sort(fin);
    
    // Printing kth substring
    System.out.print(fin.get(k - 1));
} 

// Driver Code
public static void main(String[] args) 
{
    String s = "geeksforgeeks"; 
    int k = 5; 
    int n = s.length(); 
    kThLexString(s, k, n); 
}
}

// This code is contributed by divyeshrabadiya07

Python3

# Python3 implementation of the above approach
def kThLexString(st, k, n):
    # Set to store the unique substring
    z = set() 

    for i in range(n):
        # String to create each substring
        pp = "" 

        for j in range(i, i + k):

            if (j >= n):

                break

            pp += s[j]
            # adding to set
            z.add(pp) 

    # converting set into a list
    fin = list(z) 
    
    # sorting the strings int the list
    # into lexicographical order
    fin.sort() 

    # printing kth substring
    print(fin[k - 1]) 


s = "geeksforgeeks"

k = 5

n = len(s)
kThLexString(s, k, n)

// C# implementation of 
// the above approach 
using System; 
using System.Collections.Generic;
using System.Collections;

class GFG{
     
public static void kThLexString(string st, 
                                int k, int n) 
{
    
    // Set to store the unique substring 
    HashSet<string> z = new HashSet<string>(); 
     
    for(int i = 0; i < n; i++) 
    { 
        
        // String to create each substring 
        string pp = ""; 
     
        for(int j = i; j < i + k; j++) 
        { 
            if (j >= n) 
                break;
                
            pp += st[j]; 
         
            // Adding to set 
            z.Add(pp); 
        } 
    } 
    
    // Converting set into a list 
    ArrayList fin = new ArrayList();
    
    foreach(string s in z)
    {
        fin.Add(s);
    }
    
    // Sorting the strings int the list 
    // into lexicographical order 
    fin.Sort();
     
    // Printing kth substring
    Console.Write(fin[k - 1]);
} 
 
// Driver Code
public static void Main(string[] args) 
{
    string s = "geeksforgeeks"; 
    int k = 5; 
    int n = s.Length; 
    
    kThLexString(s, k, n); 
}
}

// This code is contributed by rutvik_56

JavaScript

<script>

// JavaScript implementation of the above approach 

function kThLexString(st, k, n)
{
    
    // Set to store the unique substring 
    var z = new Set();
    
    for(var i = 0; i < n; i++)
    {
        
       // String to create each substring 
       var pp = "";
       
       for(var j = i; j < i + k; j++)
       {
          if (j >= n)
              break;
          pp += st[j];
          
          // Adding to set 
          z.add(pp);
       }
    }

    var fin = [];

    z.forEach(element => {
        fin.push(element);
    });
    
    fin.sort();
    
    // Printing kth substring 
    document.write( fin[k-1]);
}

// Driver code

var s = "geeksforgeeks";
var k = 5;
var n = s.length;
kThLexString(s, k, n);

</script>

Output

eeksf

Time Complexity: O(nk log(nk) where n is the length of the string, and k is the length of the substring.

Space Complexity: O(nk)

K-th lexicographically smallest unique substring of a given string

indrajit1

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K-th lexicographically smallest unique substring of a given string

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