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Largest substring where all characters appear at least K times | Set 2

  • Difficulty Level : Hard
  • Last Updated : 15 Sep, 2021

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:
Explanation: 
In substring aabbba, each character repeats at least k times and its length is 6.

Input: str = “ababacb”, K = 3
Output:
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 returned 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

Javascript




<script>
 
// JavaScript program for the above approach
// Function to find the longest subString
function longestSubString(start, end, s, k)
{
    var left, right;
 
    // Array for counting the number of
    // times each character repeats
    // count the number of times each
    // character repeats from start to end
    var count = new Array(26);
 
    // Store the frequency from s[start...end]
    for(var i = start; i < end; i++)
    {
        count[s.charAt(i) - 'a'] += 1;
    }
 
    // Iterate from [start, end]
    for(var 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
// Given String str
var str = "aabbba";
var k = 3;
 
// Function Call
document.write(longestSubString(0, str.length, str, k) + "\n");
 
// this code is contributed by shivanisinghss2110
 
</script>
Output:
6

 

Time Complexity: O(N*log2N)
 

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