Given a string and an integer k, find the kth sub-string when all the sub-strings are sorted according to the given condition

Given a string str, its sub-strings are formed in such a way that all the sub-strings starting with the first character of the string will occur first in the sorted order of their lengths followed by all the sub-strings starting with the second character of the string in the sorted order of their lengths and so on.
For example for the string abc, its sub-strings in the required order are a, ab, abc, b, bc and c.
Now given an integer k, the task is to find the kth sub-string in the required order.

Examples:

Input: str = abc, k = 4
Output: b
The required order is “a”, “ab”, “abc”, “b”, “bc” and “c”

Input: str = abc, k = 9
Output: -1
Only 6 sub-strings are possible.

Approach: The idea is to use binary search. An array substring will be used to store the number of sub-strings starting with ith character + substring[i – 1]. Now using binary search on the array substring, find the starting index of the required sub-string and then find the ending index for the same sub-string with end = length_of_string – (substring[start] – k).



Below is the implementation of the above approach:

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to prints kth sub-string
void Printksubstring(string str, int n, int k)
{
  
    // Total sub-strings possible
    int total = (n * (n + 1)) / 2;
  
    // If k is greater than total
    // number of sub-strings
    if (k > total) {
        printf("-1\n");
        return;
    }
  
    // To store number of sub-strings starting
    // with ith character of the string
    int substring[n + 1];
    substring[0] = 0;
  
    // Compute the values
    int temp = n;
    for (int i = 1; i <= n; i++) {
  
        // substring[i - 1] is added
        // to store the cumulative sum
        substring[i] = substring[i - 1] + temp;
        temp--;
    }
  
    // Binary search to find the starting index
    // of the kth sub-string
    int l = 1;
    int h = n;
    int start = 0;
  
    while (l <= h) {
        int m = (l + h) / 2;
  
        if (substring[m] > k) {
            start = m;
            h = m - 1;
        }
  
        else if (substring[m] < k)
            l = m + 1;
  
        else {
            start = m;
            break;
        }
    }
  
    // To store the ending index of
    // the kth sub-string
    int end = n - (substring[start] - k);
  
    // Print the sub-string
    for (int i = start - 1; i < end; i++)
        cout << str[i];
}
  
// Driver code
int main()
{
    string str = "abc";
    int k = 4;
    int n = str.length();
  
    Printksubstring(str, n, k);
  
    return 0;
}
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// Java implementation of the approach
  
class GFG 
{
  
    // Function to prints kth sub-string
    static void Printksubstring(String str, int n, int k) 
    {
  
        // Total sub-strings possible
        int total = (n * (n + 1)) / 2;
  
        // If k is greater than total
        // number of sub-strings
        if (k > total)
        {
            System.out.printf("-1\n");
            return;
        }
  
        // To store number of sub-strings starting
        // with ith character of the string
        int substring[] = new int[n + 1];
        substring[0] = 0;
  
        // Compute the values
        int temp = n;
        for (int i = 1; i <= n; i++)
        {
  
            // substring[i - 1] is added
            // to store the cumulative sum
            substring[i] = substring[i - 1] + temp;
            temp--;
        }
  
        // Binary search to find the starting index
        // of the kth sub-string
        int l = 1;
        int h = n;
        int start = 0;
  
        while (l <= h) 
        {
            int m = (l + h) / 2;
  
            if (substring[m] > k)
            {
                start = m;
                h = m - 1;
            
            else if (substring[m] < k) 
            {
                l = m + 1;
            
            else
            {
                start = m;
                break;
            }
        }
  
        // To store the ending index of
        // the kth sub-string
        int end = n - (substring[start] - k);
  
        // Print the sub-string
        for (int i = start - 1; i < end; i++)
        {
            System.out.print(str.charAt(i));
        }
    }
  
    // Driver code
    public static void main(String[] args)
    {
  
        String str = "abc";
        int k = 4;
        int n = str.length();
  
        Printksubstring(str, n, k);
    }
}
  
// This code has been contributed by 29AjayKumar
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# Python3 implementation of the approach
  
# Function to prints kth sub-string
def Printksubstring(str1, n, k):
      
    # Total sub-strings possible
    total = int((n * (n + 1)) / 2)
  
    # If k is greater than total
    # number of sub-strings
    if (k > total):
        print("-1")
        return
  
    # To store number of sub-strings starting
    # with ith character of the string
    substring = [0 for i in range(n + 1)]
    substring[0] = 0
  
    # Compute the values
    temp = n
    for i in range(1, n + 1, 1):
          
        # substring[i - 1] is added
        # to store the cumulative sum
        substring[i] = substring[i - 1] + temp
        temp -= 1
  
    # Binary search to find the starting index
    # of the kth sub-string
    l = 1
    h = n
    start = 0
  
    while (l <= h):
        m = int((l + h) / 2)
  
        if (substring[m] > k):
            start = m
            h = m - 1
  
        elif (substring[m] < k):
            l = m + 1
  
        else:
            start = m
            break
  
    # To store the ending index of
    # the kth sub-string
    end = n - (substring[start] - k)
  
    # Print the sub-string
    for i in range(start - 1, end):
        print(str1[i], end = "")
  
# Driver code
if __name__ == '__main__':
    str1 = "abc"
    k = 4
    n = len(str1)
  
    Printksubstring(str1, n, k)
      
# This code is contributed by
# Surendra_Gangwar
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// C# implementation of the approach
using System;
  
class GFG 
  
    // Function to prints kth sub-string 
    static void Printksubstring(String str, int n, int k) 
    
  
        // Total sub-strings possible 
        int total = (n * (n + 1)) / 2; 
  
        // If k is greater than total 
        // number of sub-strings 
        if (k > total) 
        
            Console.Write("-1\n"); 
            return
        
  
        // To store number of sub-strings starting 
        // with ith character of the string 
        int []substring = new int[n + 1]; 
        substring[0] = 0; 
  
        // Compute the values 
        int temp = n; 
        for (int i = 1; i <= n; i++) 
        
  
            // substring[i - 1] is added 
            // to store the cumulative sum 
            substring[i] = substring[i - 1] + temp; 
            temp--; 
        
  
        // Binary search to find the starting index 
        // of the kth sub-string 
        int l = 1; 
        int h = n; 
        int start = 0; 
  
        while (l <= h) 
        
            int m = (l + h) / 2; 
  
            if (substring[m] > k) 
            
                start = m; 
                h = m - 1; 
            
            else if (substring[m] < k) 
            
                l = m + 1; 
            
            else
            
                start = m; 
                break
            
        
  
        // To store the ending index of 
        // the kth sub-string 
        int end = n - (substring[start] - k); 
  
        // Print the sub-string 
        for (int i = start - 1; i < end; i++) 
        
            Console.Write(str[i]); 
        
    
  
    // Driver code 
    public static void Main(String[] args) 
    
  
        String str = "abc"
        int k = 4; 
        int n = str.Length; 
  
        Printksubstring(str, n, k); 
    
  
// This code contributed by Rajput-Ji
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<?php
// PHP implementation of the approach 
  
// Function to prints kth sub-string 
function Printksubstring($str, $n, $k
  
    // Total sub-strings possible 
    $total = floor(($n * ($n + 1)) / 2); 
  
    // If k is greater than total 
    // number of sub-strings 
    if ($k > $total)
    
        printf("-1\n"); 
        return
    
  
    // To store number of sub-strings starting 
    // with ith character of the string 
    $substring = array(); 
    $substring[0] = 0; 
  
    // Compute the values 
    $temp = $n
    for ($i = 1; $i <= $n; $i++)
    
  
        // substring[i - 1] is added 
        // to store the cumulative sum 
        $substring[$i] = $substring[$i - 1] + $temp
        $temp--; 
    
  
    // Binary search to find the starting index 
    // of the kth sub-string 
    $l = 1; 
    $h = $n
    $start = 0; 
  
    while ($l <= $h)
    
        $m = floor(($l + $h) / 2); 
  
        if ($substring[$m] > $k)
        
            $start = $m
            $h = $m - 1; 
        
  
        else if ($substring[$m] < $k
            $l = $m + 1; 
  
        else
        
            $start = $m
            break
        
    
  
    // To store the ending index of 
    // the kth sub-string 
    $end = $n - ($substring[$start] - $k); 
  
    // Print the sub-string 
    for ($i = $start - 1; $i < $end; $i++) 
        print($str[$i]); 
}
  
// Driver code 
$str = "abc"
$k = 4; 
$n = strlen($str);
  
Printksubstring($str, $n, $k); 
  
// This code is contributed by Ryuga
?>
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Output:
b

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