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# 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 ` `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 m=``new` `HashMap(); ` `          ``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 ` `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

 ``

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` `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``(;rpk){``            ``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<

## 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

 ``

Output

`12`

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