Count substrings with each character occurring at most k times

Given a string S. Count number of substrings in which each character occurs at most k times. Assume that the string consists of only lowercase English alphabets.

Examples:

Input : S = ab
        k = 1
Output : 3
All the substrings a, b, ab have
individual character count less than 1. 

Input : S = aaabb
        k = 2
Output : 12
Substrings that have individual character
count at most 2 are: a, a, a, b, b, aa, aa,
ab, bb, aab, abb, aabb.

A simple solution is to first find all the substrings and then check if count of each character is at most k in each substring. Time complexity of this solution is O(n^3).

An efficient solution is to maintain starting and ending point of substrings. Let us fix the starting point to an index i. Keep incrementing the ending point j one at a time. When changing the ending point update the count of corresponding character. Then check for this substring that whether each character has count at most k or not. If yes then increment answer by 1 else increment the starting point and reset ending point. The starting point is incremented because during last update on ending point character count exceed k and it will only increase further. So no subsequent substring with given fixed starting point will be a substring with each character count at most k.

Implementation:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP program to count number of substrings
// in which each character has count less
// than or equal to k.
#include <bits/stdc++.h>
  
using namespace std;
  
int findSubstrings(string s, int k)
{
    // variable to store count of substrings.
    int ans = 0;
  
    // array to store count of each character.
    int cnt[26];
  
    int i, j, n = s.length();
    for (i = 0; i < n; i++) {
  
        // Initialize all characters count to zero.
        memset(cnt, 0, sizeof(cnt));
  
        for (j = i; j < n; j++) {
            // increment character count
            cnt[s[j] - 'a']++;
  
            // check only the count of current character
            // because only the count of this
            // character is changed. The ending point is
            // incremented to current position only if
            // all other characters have count at most
            // k and hence their count is not checked.
            // If count is less than k, then increase ans
            // by 1.
            if (cnt[s[j] - 'a'] <= k)
                ans++;
  
            // if count is less than k, then break as
            // subsequent substrings for this starting
            // point will also have count greater than
            // k and hence are reduntant to check.
            else
                break;
        }
    }
  
    // return the final count of substrings.
    return ans;
}
  
// Driver code
int main()
{
    string S = "aaabb";
    int k = 2;
    cout << findSubstrings(S, k);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

import java.util.Arrays;
  
// Java program to count number of substrings 
// in which each character has count less 
// than or equal to k.
class GFG {
  
    static int findSubstrings(String s, int k) {
        // variable to store count of substrings. 
        int ans = 0;
  
        // array to store count of each character. 
        int cnt[] = new int[26];
  
        int i, j, n = s.length();
        for (i = 0; i < n; i++) {
  
            // Initialize all characters count to zero. 
            Arrays.fill(cnt, 0);
  
            for (j = i; j < n; j++) {
                // increment character count 
                cnt[s.charAt(j) - 'a']++;
  
                // check only the count of current character 
                // because only the count of this 
                // character is changed. The ending point is 
                // incremented to current position only if 
                // all other characters have count at most 
                // k and hence their count is not checked. 
                // If count is less than k, then increase ans 
                // by 1. 
                if (cnt[s.charAt(j) - 'a'] <= k) {
                    ans++;
                } // if count is less than k, then break as 
                // subsequent substrings for this starting 
                // point will also have count greater than 
                // k and hence are reduntant to check. 
                else {
                    break;
                }
            }
        }
  
        // return the final count of substrings. 
        return ans;
    }
  
// Driver code 
    static public void main(String[] args) {
        String S = "aaabb";
        int k = 2;
        System.out.println(findSubstrings(S, k));
    }
}
  
// This code is contributed by 29AjayKumar

chevron_right


Python 3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python 3 program to count number of substrings
# in which each character has count less
# than or equal to k.
  
def findSubstrings(s, k):
  
    # variable to store count of substrings.
    ans = 0
    n = len(s)
    for i in range(n):
          
        # array to store count of each character.
        cnt = [0] * 26
  
        for j in range(i, n):
              
            # increment character count
            cnt[ord(s[j]) - ord('a')] += 1
  
            # check only the count of current character
            # because only the count of this
            # character is changed. The ending point is
            # incremented to current position only if
            # all other characters have count at most
            # k and hence their count is not checked.
            # If count is less than k, then increase 
            # ans by 1.
              
            if (cnt[ord(s[j]) - ord('a')] <= k):
                ans += 1
  
            # if count is less than k, then break as
            # subsequent substrings for this starting
            # point will also have count greater than
            # k and hence are reduntant to check.
            else:
                break
  
    # return the final count of substrings.
    return ans
  
# Driver code
if __name__ == "__main__":
      
    S = "aaabb"
    k = 2
    print(findSubstrings(S, k))
  
# This code is contributed by ita_c

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to count number of substrings
// in which each character has count less
// than or equal to k.
using System;
  
class GFG
{
      
public static int findSubstrings(string s, int k)
{
    // variable to store count of substrings.
    int ans = 0;
  
    // array to store count of each character.
    int []cnt = new int[26];
  
    int i, j, n = s.Length;
    for (i = 0; i < n; i++) 
    {
  
        // Initialize all characters count to zero.
        Array.Clear(cnt, 0, cnt.Length);
  
        for (j = i; j < n; j++)
        {
              
            // increment character count
            cnt[s[j] - 'a']++;
  
            // check only the count of current character
            // because only the count of this
            // character is changed. The ending point is
            // incremented to current position only if
            // all other characters have count at most
            // k and hence their count is not checked.
            // If count is less than k, then increase ans
            // by 1.
            if (cnt[s[j] - 'a'] <= k)
                ans++;
  
            // if count is less than k, then break as
            // subsequent substrings for this starting
            // point will also have count greater than
            // k and hence are reduntant to check.
            else
                break;
        }
    }
  
    // return the final count of substrings.
    return ans;
}
  
// Driver code
public static int Main()
{
    string S = "aaabb";
    int k = 2;
    Console.WriteLine(findSubstrings(S, k));
    return 0;
}
}
  
// This code is contributed by SoM15242.

chevron_right


Output:

 12

Time complexity: O(n^2)
Auxiliary Space: O(1)

Another efficient solution is to use sliding window technique. In which we will maintain two pointers left and right.We initialize left and the right pointer to 0, move the right pointer until the count of each alphabet is less than k, when the count is greater than we start incrementing left pointer and decrement the count of the corresponding alphabet, once the condition is satisfied we add (right-left + 1) to the answer.
Implementation:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP program to count number of substrings
// in which each character has count less
// than or equal to k.
#include<bits/stdc++.h>
  
using namespace std;
  
//function to find number of substring 
//in which each character has count less
// than or equal to k.
  
int find_sub(string s,int k){
    int len=s.length();
    int lp=0,rp=0;             // initialize left and right pointer to 0
    int ans=0;
    int hash_char[26]={0};     // an array to keep track of count of each alphabet
    for(;rp<len;rp++){
        hash_char[s[rp]-'a']++;
        while(hash_char[s[rp]-'a']>k){
            hash_char[s[lp]-'a']--;   // decrement the count 
            lp++;         //increment left pointer 
        }
        ans+=rp-lp+1;
    }
    return ans;
}
  
// Driver code
int main(){
    string s="aaabb";
    int k=2;
    cout<<find_sub(s,k)<<endl;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to count number of substrings 
// in which each character has count less 
// than or equal to k.
class GFG 
{
      
    //function to find number of substring 
    //in which each character has count less 
    // than or equal to k. 
    static int find_sub(String s, int k) 
    {
        int len = s.length();
  
        // initialize left and right pointer to 0 
        int lp = 0, rp = 0;
        int ans = 0;
  
        // an array to keep track of count of each alphabet 
        int[] hash_char = new int[26];
        for (; rp < len; rp++) 
        {
            hash_char[s.charAt(rp) - 'a']++;
            while (hash_char[s.charAt(rp) - 'a'] > k) 
            {
                // decrement the count 
                hash_char[s.charAt(lp) - 'a']--;
  
                //increment left pointer 
                lp++;
            }
            ans += rp - lp + 1;
        }
        return ans;
    }
  
    // Driver code 
    public static void main(String[] args)
    {
        String S = "aaabb";
        int k = 2;
        System.out.println(find_sub(S, k));
    }
  
// This code is contributed by PrinciRaj1992

chevron_right


Python

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to count number of substrings
# in which each character has count less
# than or equal to k.
  
  
# function to find number of substring
# in which each character has count less
# than or equal to k.
  
def find_sub(s, k):
  
    Len = len(s)
      
    # initialize left and right pointer to 0
    lp, rp = 0, 0
                  
    ans = 0
  
    # an array to keep track of count of each alphabet
    hash_char = [0 for i in range(256)] 
    for rp in range(Len):
  
        hash_char[ord(s[rp])] += 1
  
        while(hash_char[ord(s[rp])] > k):
            hash_char[ord(s[lp])] -= 1 # decrement the count
            lp += 1      #increment left pointer
  
        ans += rp - lp + 1
  
    return ans
  
# Driver code
s = "aaabb"
k = 2;
print(find_sub(s, k))
  
# This code is contributed by mohit kumar

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to count number of substrings
// in which each character has count less
// than or equal to k.
using System;
  
class GFG 
{
    //function to find number of substring 
    //in which each character has count less
    // than or equal to k.
    static int find_sub(string s, int k)
    {
        int len = s.Length;
      
        // initialize left and right pointer to 0
        int lp = 0,rp = 0;             
        int ans = 0;
      
        // an array to keep track of count of each alphabet
        int []hash_char = new int[26];     
        for(;rp < len; rp++)
        {
            hash_char[s[rp] - 'a']++;
            while(hash_char[s[rp] - 'a'] > k)
            {
                // decrement the count 
                hash_char[s[lp] - 'a']--; 
              
                 //increment left pointer 
                lp++;        
            }
            ans += rp - lp + 1;
        }   
        return ans;
     }
  
    // Driver code 
    static public void Main() 
    {
        String S = "aaabb";
        int k = 2;
        Console.WriteLine(find_sub(S, k));
    }
}
  
// This code is contributed by Rajput-Ji

chevron_right


Output:

 12

Time complexity: O(n)
Auxiliary Space: O(1)



My Personal Notes arrow_drop_up

A Programmer and A Machine learning Enthusiast

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.