 Open in App
Not now

# Count number of substrings with exactly k distinct characters

• Difficulty Level : Medium
• Last Updated : 08 Nov, 2022

Given a string of lowercase alphabets, count all possible substrings (not necessarily distinct) that has exactly k distinct characters.

Examples:

Input: abc, k = 2
Output: 2
Possible substrings are {“ab”, “bc”}

Input: aba, k = 2
Output: 3
Possible substrings are {“ab”, “ba”, “aba”}

Input: aa, k = 1
Output: 3
Possible substrings are {“a”, “a”, “aa”}

Method 1 (Brute Force): If the length of string is n, then there can be n*(n+1)/2 possible substrings. A simple way is to generate all the substring and check each one whether it has exactly k unique characters or not. If we apply this brute force, it would take O(n*n) to generate all substrings and O(n) to do a check on each one. Thus overall it would go O(n*n*n)

Method 2: The problem can be solved in O(n*n). Idea is to maintain a hash table while generating substring and checking the number of unique characters using that hash table.
The implementation below assume that the input string contains only characters from ‘a’ to ‘z’.

Implementation

## C++

 `// C++ program to count number of substrings with``// exactly k distinct characters in a given string``#include``using` `namespace` `std;` `// Function to count number of substrings``// with exactly k unique characters``int` `countkDist(string str, ``int` `k)``{``    ``int` `n = str.length();` `    ``// Initialize result``    ``int` `res = 0;` `    ``// To store count of characters from 'a' to 'z'``    ``int` `cnt;` `    ``// Consider all substrings beginning with``    ``// str[i]``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``int` `dist_count = 0;` `        ``// Initializing array with 0``        ``memset``(cnt, 0, ``sizeof``(cnt));` `        ``// Consider all substrings between str[i..j]``        ``for` `(``int` `j=i; j k) ``break``;``        ``}``    ``}` `    ``return` `res;``}` `// Driver Program``int` `main()``{``    ``string str = ``"abcbaa"``;``    ``int` `k = 3;``    ``cout << ``"Total substrings with exactly "``         ``<< k <<``" distinct characters :"``         ``<< countkDist(str, k) << endl;``    ``return` `0;``}`

## Java

 `// Java program to CountKSubStr number of substrings``// with exactly distinct characters in a given string``import` `java.util.Arrays;` `public` `class` `CountKSubStr``{``    ``// Function to count number of substrings``    ``// with exactly k unique characters``    ``int` `countkDist(String str, ``int` `k)``    ``{``        ``// Initialize result``        ``int` `res = ``0``;` `        ``int` `n = str.length();` `        ``// To store seen characters from 'a' to 'z'``        ``boolean` `seen[] = ``new` `boolean``[``26``];` `        ``// Consider all substrings beginning with``        ``// str[i]``        ``for` `(``int` `i = ``0``; i < n; i++)``        ``{``            ``int` `distCount = ``0``;` `            ``// mark all chars as unseen``            ``Arrays.fill(seen, ``false``);` `            ``// Consider all substrings between str[i..j]``            ``for` `(``int` `j=i; j

## Python 3

 `# Python3 program to count number of``# substrings with exactly k distinct``# characters in a given string` `# Function to count number of substrings``# with exactly k unique characters``def` `countkDist(str1, k):``    ``n ``=` `len``(str1)``    ` `    ``# Initialize result``    ``res ``=` `0` `    ``# To store count of characters from``    ``# 'a' to 'z'``    ``cnt ``=` `[``0``] ``*` `27` `    ``# Consider all substrings beginning``    ``# with str[i]``    ``for` `i ``in` `range``(``0``, n):``        ``dist_count ``=` `0` `        ``# Initializing array with 0``        ``cnt ``=` `[``0``] ``*` `27` `        ``# Consider all substrings between str[i..j]``        ``for` `j ``in` `range``(i, n):``            ` `            ``# If this is a new character for this``            ``# substring, increment dist_count.``            ``if``(cnt[``ord``(str1[j]) ``-` `97``] ``=``=` `0``):``                ``dist_count ``+``=` `1` `            ``# Increment count of current character``            ``cnt[``ord``(str1[j]) ``-` `97``] ``+``=` `1` `            ``# If distinct character count becomes k,``            ``# then increment result.``            ``if``(dist_count ``=``=` `k):``                ``res ``+``=` `1``            ``if``(dist_count > k):``                ``break` `    ``return` `res    ` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ``str1 ``=` `"abcbaa"``    ``k ``=` `3``    ``print``(``"Total substrings with exactly"``, k,``           ``"distinct characters : "``, end ``=` `"")``    ``print``(countkDist(str1, k))` `# This code is contributed by``# Sairahul Jella`

## C#

 `// C# program to CountKSubStr number of substrings``// with exactly distinct characters in a given string` ` ` `using` `System;``public` `class` `CountKSubStr``{``    ``// Function to count number of substrings``    ``// with exactly k unique characters``    ``int` `countkDist(``string` `str, ``int` `k)``    ``{``        ``// Initialize result``        ``int` `res = 0;`` ` `        ``int` `n = str.Length;`` ` `        ``// To store count of characters from 'a' to 'z'``        ``int``[] cnt = ``new` `int``;`` ` `        ``// Consider all substrings beginning with``        ``// str[i]``        ``for` `(``int` `i = 0; i < n; i++)``        ``{``            ``int` `dist_count = 0;`` ` `            ``// Initializing count array with 0``            ``Array.Clear(cnt, 0,cnt.Length);`` ` `            ``// Consider all substrings between str[i..j]``            ``for` `(``int` `j=i; j

## PHP

 `

## Javascript

 ``

Output

`Total substrings with exactly 3 distinct characters :8`

Time Complexity: O(n*n)
Auxiliary Space: O(1), Only 26 size array is used, which can be considered constant space.

Efficient Approach: The idea is to count all the subarrays with at most K distinct characters and then subtract all the subarrays with atmost K – 1 characters. That leaves us with count of subarrays with exactly K distinct characters.

Below is the implementation of the above approach:

## C++

 `#include ``#include ``#include ``using` `namespace` `std;` `// the number of subarrays with at most K distinct elements``int` `most_k_chars(string& s, ``int` `k)``{``    ``if` `(s.size() == 0) {``        ``return` `0;``    ``}``    ``unordered_map<``char``, ``int``> map;``    ``int` `num = 0, left = 0;` `    ``for` `(``int` `i = 0; i < s.size(); i++) {``        ``map[s[i]]++;``        ``while` `(map.size() > k) {``            ``map[s[left]]--;``            ``if` `(map[s[left]] == 0) {``                ``map.erase(s[left]);``            ``}``            ``left++;``        ``}``        ``num += i - left + 1;``    ``}``    ``return` `num;``}` `int` `exact_k_chars(string& s, ``int` `k)``{``    ``return` `most_k_chars(s, k) - most_k_chars(s, k - 1);``}` `// Driver Program``int` `main()``{``    ``string s1 = ``"pqpqs"``;``    ``int` `k = 2;``    ``cout << ``"Total substrings with exactly "` `<< k``         ``<< ``" distinct characters : "``         ``<< exact_k_chars(s1, k) << endl;` `    ``string s2 = ``"aabab"``;``    ``k = 2;``    ``cout << ``"Total substrings with exactly "` `<< k``         ``<< ``" distinct characters : "``         ``<< exact_k_chars(s2, k) << endl;``}`

## Java

 `import` `java.io.*;``import` `java.util.HashMap;``public` `class` `GFG``{``  ` `  ``// the number of subarrays with at most K distinct``  ``// elements``  ``static` `int` `most_k_chars(String s, ``int` `k)``  ``{``    ``if` `(s.length() == ``0``) {``      ``return` `0``;``    ``}``    ``HashMap map = ``new` `HashMap<>();``    ``int` `num = ``0``, left = ``0``;` `    ``for` `(``int` `i = ``0``; i < s.length(); i++) {``      ``map.put(s.charAt(i),``              ``map.getOrDefault(s.charAt(i), ``0``) + ``1``);``      ``while` `(map.size() > k) {``        ``map.put(s.charAt(left),``                ``map.getOrDefault(s.charAt(left), ``0``)``                ``- ``1``);``        ``if` `(map.get(s.charAt(left)) == ``0``) {``          ``map.remove(s.charAt(left));``        ``}``        ``left++;``      ``}``      ``num += i - left + ``1``;``    ``}``    ``return` `num;``  ``}``  ``static` `int` `exact_k_chars(String s, ``int` `k)``  ``{``    ``return` `most_k_chars(s, k) - most_k_chars(s, k - ``1``);``  ``}``  ``public` `static` `void` `main(String[] args)``  ``{``    ``String s1 = ``"pqpqs"``;``    ``int` `k = ``2``;``    ``System.out.println(``"Total substrings with exactly "``                       ``+ k + ``" distinct characters : "``                       ``+ exact_k_chars(s1, k));` `    ``String s2 = ``"aabab"``;``    ``k = ``2``;``    ``System.out.println(``"Total substrings with exactly "``                       ``+ k + ``" distinct characters : "``                       ``+ exact_k_chars(s2, k));``  ``}``}` `// This code is contributed by garg28harsh.`

## C#

 `using` `System;``using` `System.Collections.Generic;``class` `GFG {` `  ``// the number of subarrays with at most K distinct``  ``// elements``  ``static` `int` `most_k_chars(``string` `s, ``int` `k)``  ``{``    ``if` `(s.Length == 0) {``      ``return` `0;``    ``}``    ``Dictionary<``char``, ``int``> map``      ``= ``new` `Dictionary<``char``, ``int``>();``    ``int` `num = 0, left = 0;` `    ``for` `(``int` `i = 0; i < s.Length; i++) {``      ``if` `(map.ContainsKey(s[i])) {``        ``int` `val = map[s[i]];``        ``map.Remove(s[i]);``        ``map.Add(s[i], val + 1);``      ``}``      ``else``        ``map.Add(s[i], 1);``      ``while` `(map.Count > k) {``        ``if` `(map.ContainsKey(s[left])) {``          ``int` `val = map[s[left]];``          ``map.Remove(s[left]);``          ``map.Add(s[left], val - 1);``        ``}``        ``else``          ``map.Add(s[left], -1);``        ``if` `(map[s[left]] == 0) {``          ``map.Remove(s[left]);``        ``}``        ``left++;``      ``}``      ``num += i - left + 1;``    ``}``    ``return` `num;``  ``}``  ``static` `int` `exact_k_chars(String s, ``int` `k)``  ``{``    ``return` `most_k_chars(s, k) - most_k_chars(s, k - 1);``  ``}``  ``public` `static` `void` `Main(``string` `[]args)``  ``{``    ``string` `s1 = ``"pqpqs"``;``    ``int` `k = 2;``    ``Console.WriteLine(``"Total substrings with exactly "``                      ``+ k + ``" distinct characters : "``                      ``+ exact_k_chars(s1, k));` `    ``string` `s2 = ``"aabab"``;``    ``k = 2;``    ``Console.WriteLine(``"Total substrings with exactly "``                      ``+ k + ``" distinct characters : "``                      ``+ exact_k_chars(s2, k));``  ``}``}` `// This code is contributed by garg28harsh.`

Output

```Total substrings with exactly 2 distinct characters : 7
Total substrings with exactly 2 distinct characters : 9```

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

This article is contributed by Rahul Agrawal and Ankit Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

My Personal Notes arrow_drop_up