Given a string str and an integer K, the task is to find the length of the longest sub-string S such that every character in S appears at least K times.

Examples:

Input: str = “aabbba”, K = 3
Output: 6
Explanation:
In substring aabbba, each character repeats at least k times and its length is 6.

Input: str = “ababacb”, K = 3
Output: 0
Explanation:
There is no substring where each character repeats at least k times.

Naive Approach: We have discussed the Naive Approach in the previous post.

Approach: In this post, we will discuss the approach using Divide and Conquer technique and Recursion. Below are the steps:

1. Store the frequency of each characters of the given string in a frequency array of size 26.
2. Initialize two variables start with 0 and end which is the length of the string str.
3. Iterate over the string from start to end and count the number of times each character repeats and store it in an array.
4. If any character repeats less than K times, then Divide the string into two halves. If i is the index of the string where we found that the string[i] repeats less than K times, then we divide the string into two halves from start to i and i + 1 to end.
5. Recursively call for the two halves in the above steps i.e., from start to i and i + 1 to end separately and repeat the Step 2 and 3 and return the maximum of the two values reutnr by the above recursive call.
6. If all the characters between start and end is repeated at least K times, then the answer is end – start.

   Below is the implementation of above approach:
   

   C++

   
   

   
   
   

   // C++ program for the above approach  #include <bits/stdc++.h>  using namespace std;     // Function to find the longest substring  int longestSubstring(int start, int end,                      string s, int k)  {      int left, right;         // Array for counting the number of      // times each character repeats      // count the number of times each      // character repeats from start to end      int count[26] = { 0 };         // Store the frequency from s[start...end]      for (int i = start; i < end; i++) {          count[s[i] - 'a'] += 1;      }         // Iterate from [start, end]      for (int i = start; i < end; i++) {             if (count[s[i] - 'a'] < k) {                 // Recursive call for left subpart              left = longestSubstring(start,                                      i,                                      s,                                      k);                 // Recursive call for right subpart              right = longestSubstring(i + 1,                                      end,                                      s,                                      k);                 // Return maximum of left & right              return max(left, right);          }      }         // If all the characters are repeated      // at least k times      return end - start;  }     // Driver Code  int main()  {      // Given String str      string str = "aabbba";      int k = 3;         // Function Call      cout << longestSubstring(0, str.length(),                              str, k)          << endl;      return 0;  }

   Java

   
   

   
   
   

   // Java program for the above approach  import java.util.*;     class GFG{     // Function to find the longest subString  static int longestSubString(int start, int end,                              String s, int k)  {      int left, right;         // Array for counting the number of      // times each character repeats      // count the number of times each      // character repeats from start to end      int count[] = new int[26];         // Store the frequency from s[start...end]      for(int i = start; i < end; i++)      {          count[s.charAt(i) - 'a'] += 1;      }         // Iterate from [start, end]      for(int i = start; i < end; i++)      {          if (count[s.charAt(i) - 'a'] < k)          {                             // Recursive call for left subpart              left = longestSubString(start, i,                                      s, k);                 // Recursive call for right subpart              right = longestSubString(i + 1, end,                                      s, k);                 // Return maximum of left & right              return Math.max(left, right);          }      }         // If all the characters are repeated      // at least k times      return end - start;  }     // Driver Code  public static void main(String[] args)  {         // Given String str      String str = "aabbba";      int k = 3;         // Function Call      System.out.print(longestSubString(0, str.length(),                                          str, k) + "\n");  }  }     // This code is contributed by Amit Katiyar

   Python3

   
   

   
   
   

   # Python3 program for the above approach     # Function to find the longest substring  def longestSubString(start, end, s, k):             # List for counting the number of      # times each character repeats      # count the number of times each      # chracter repeats from start to end      count = [0 for i in range(26)]             # Store the frequency from s[start...end]      for i in range(start, end):          count[ord(s[i]) - ord('a')] += 1            # Iterate from [start, end]      for i in range(start, end):          if(count[ ord(s[i]) - ord('a')] < k):                             # Recursive call for left subpart              left = longestSubString(start, i,                                          s, k)                                                     # Recursive call for right subpart              right = longestSubString(i + 1, end,                                          s, k)                                                     # Return maximum of left & right              return max(left, right)             # If all the characters are repeated      # at least k times      return end - start         # Driver Code     # Given String str  str = "aabbba" k = 3    # Function call  print(longestSubString(0, len(str), str, k))     # This code is contributed by dadimadhav

   C#

   
   

   
   
   

   // C# program for the above approach using System;    class GFG{    // Function to find the longest subString static int longestSubString(int start, int end,                              string s, int k) {     int left, right;        // Array for counting the number of     // times each character repeats     // count the number of times each     // character repeats from start to end     int []count = new int[26];        // Store the frequency from s[start...end]     for(int i = start; i < end; i++)     {         count[s[i] - 'a'] += 1;     }        // Iterate from [start, end]     for(int i = start; i < end; i++)     {         if (count[s[i] - 'a'] < k)          {                            // Recursive call for left subpart             left = longestSubString(start, i,                                     s, k);                // Recursive call for right subpart             right = longestSubString(i + 1, end,                                      s, k);                // Return maximum of left & right             return Math.Max(left, right);         }     }        // If all the characters are repeated     // at least k times     return end - start; }    // Driver Code public static void Main(string[] args) {            // Given String str     string str = "aabbba";     int k = 3;        // Function call     Console.Write(longestSubString(0, str.Length,                                       str, k) + "\n"); } }    // This code is contributed by rutvik_56

   Output:

   6
   

   Time Complexity: O(N*log₂N)

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