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.

Brute Force Approach:

A simple solution is to first find all the substrings and then check if the count of each character is at most k in each substring. The time complexity of this solution is O(n^3). We can check all the possible substrings ranges from i to j and in this substring we have to check whether the maximum frequency is greater than k or not.if it is less than or equal to k then count this substring in ans .

C++

// 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)
{

    //

    int i, j, n = s.length();
    // variable to store count of substrings.
    // Total non empty substring n*(n+1) /2.
    int ans = n * (n + 1) / 2;
    for (i = 0; i < n; i++) {

        for (j = i; j < n; j++) {
            bool flag = false;
            // hash map storing maximum frequency of each
            // character.

            unordered_map<int, int> m;
            for (int l = i; l <= j; l++) {

                m[s[l]]++;

                if (m[s[l]] > k) {
                    ans--;
                    break;
                    flag = true;
                }
            }
        }
    }

    // return the final count of substrings.
    return ans;
}

// Driver code
int main()
{
    string S = "aaabb";
    int k = 2;
    cout << findSubstrings(S, k);
    return 0;
}

Java

/*package whatever //do not write package name here */
import java.io.*;
import java.util.*;

// java code addition
public class Main {

    // Javat program to count number of substrings
    // in which each character has count less
    // than or equal to k.
    public static int findSubstrings(String s,int k) {
      int n = s.length();

      // variable to store count of substrings.
        // Total non empty substring n*(n+1) /2.
      int ans = (int)Math.floor((n * (n + 1)) / 2);

      for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
          boolean flag = false;

          // hash map storing maximum frequency of each
            // character.
            Map<Character,Integer> m=new HashMap<Character,Integer>();

          for (int l = i; l <= j; l++) {

              if(m.containsKey(s.charAt(l))){
                  m.put(s.charAt(l), m.get(s.charAt(l)) + 1);
              }
              else{
                  m.put(s.charAt(l), 1);
              }

            if (m.get(s.charAt(l)) > k) {
                ans--;
                break;

            }
          }

          if (flag) {
            break;
          }
        }
      }
        // return the final count of substrings.
      return ans;
    }

    public static void main(String[] args) {
        String S = "aaabb";
        int k = 2;
        System.out.println(findSubstrings(S, k));
    }
}

// The code is contributed by Arushi Jindal.

Python3

# Python program to count number of substrings
# in which each character has count less
# than or equal to k.
def find_substrings(s, k):
    # Get the length of the string
    n = len(s)

    # Initialize the variable to store the count of substrings
    ans = n * (n + 1) // 2

    # Iterate through all possible substrings
    for i in range(n):
        for j in range(i, n):
            # Initialize a frequency list to store the count of each character
            freq = [0] * 26

            # Count the frequency of each character in the current substring
            for l in range(i, j + 1):
                freq[ord(s[l]) - ord('a')] += 1

                # If any character occurs more than k times, subtract 1 from the count of substrings
                if max(freq) > k:
                    ans -= 1
                    break

    # Return the final count of substrings
    return ans


# Example usage
S = "aaabb"
k = 2
print(find_substrings(S, k))  # Output: 12

C#

using System;
using System.Collections.Generic;

public class Gfg
{
  public static int findSubstrings(string s, int k)
  {
    int n = s.Length;
    int ans = n * (n + 1) / 2;

    for (int i = 0; i < n; i++)
    {
      for (int j = i; j < n; j++)
      {
        bool flag = false;
        Dictionary<char, int> m = new Dictionary<char, int>();

        for (int l = i; l <= j; l++)
        {
          if (m.ContainsKey(s[l]))
            m[s[l]]++;
          else
            m[s[l]] = 1;

          if (m[s[l]] > k)
          {
            ans--;
            break;
            flag = true;
          }
        }

        if (flag)
          break;
      }
    }

    return ans;
  }

  public static void Main()
  {
    string S = "aaabb";
    int k = 2;
    Console.WriteLine(findSubstrings(S, k));
  }
}

Javascript

// JavaScript program to count number of substrings
// in which each character has count less
// than or equal to k.

function findSubstrings(s, k) {
  const n = s.length;
  // variable to store count of substrings.
    // Total non empty substring n*(n+1) /2.

  let ans = Math.floor((n * (n + 1)) / 2);

  for (let i = 0; i < n; i++) {
    for (let j = i; j < n; j++) {
      let flag = false;
      // hash map storing maximum frequency of each
        // character.

      const m = new Map();

      for (let l = i; l <= j; l++) {
        m.set(s[l], (m.get(s[l]) || 0) + 1);

        if (m.get(s[l]) > k) {
          ans--;
            break;

          flag = true;
        }
      }

      if (flag) {
        break;
      }
    }
  }
    // return the final count of substrings.
  return ans;
}

const S = 'aaabb';
const k = 2;
console.log(findSubstrings(S, k));

Output

12

Time Complexity:O(N³), where N is the length of the string

Space Complexity : O(N), where N is the length of the string

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++

// 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;
}

Java

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

Python 3

# 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

C#

// 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.

Javascript

<script>


// Javascript program to count number of substrings
// in which each character has count less
// than or equal to k.

function findSubstrings(s, k)
{
    // variable to store count of substrings.
    var ans = 0;

    // array to store count of each character.
    var cnt = Array(26);

    var i, j, n = s.length;
    for (i = 0; i < n; i++) {
        cnt = Array(26).fill(0);
        for (j = i; j < n; j++) {

            // increment character count
            cnt[(s[j].charCodeAt(0) - 'a'.charCodeAt(0))]++;

            // 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].charCodeAt(0) - 'a'.charCodeAt(0))] <= 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
var S = "aaabb";
var k = 2;
document.write( findSubstrings(S, k));

// This code is contributed by rrrtnx.
</script>

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++

// 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;
}

Java

// 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

Python

# 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

C#

// 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

Javascript

<script>
// Javascript 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.
    function find_sub(s,k)
    {
        let len = s.length;

        // initialize left and right pointer to 0
        let lp = 0, rp = 0;
        let ans = 0;

        // an array to keep track of count of each alphabet
        let hash_char = new Array(26);
        for(let i = 0; i < hash_char.length; i++)
        {
            hash_char[i] = 0;
        }
        for (; rp < len; rp++)
        {
            hash_char[s[rp].charCodeAt(0) - 'a'.charCodeAt(0)]++;
            while (hash_char[s[rp].charCodeAt(0) - 'a'.charCodeAt(0)] > k)
            {

                // decrement the count
                hash_char[s[lp].charCodeAt(0) - 'a'.charCodeAt(0)]--;

                //increment left pointer
                lp++;
            }
            ans += rp - lp + 1;
        }
        return ans;
    }

    // Driver code
    let S = "aaabb";
    let k = 2;
    document.write(find_sub(S, k));

    // This code is contributed by avanitrachhadiya2155
</script>

Output

12

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