Number of substrings with count of each character as k

Last Updated : 12 Dec, 2022

Given a string and an integer k, find the number of substrings in which all the different characters occur exactly k times.

Examples:

Input : s = "aabbcc" k = 2 Output : 6 The substrings are aa, bb, cc, aabb, bbcc and aabbcc. Input : s = "aabccc" k = 2 Output : 3 There are three substrings aa, cc and cc

Naive Approach: The idea is to traverse through all substrings. We fix a starting point, traverse through all substrings starting with the picked point, we keep incrementing frequencies of all characters. If all frequencies become k, we increment the result. If the count of any frequency becomes more than k, we break and change starting point.

Below is the implementation of the above approach:

C++

// C++ program to count number of substrings
// with counts of distinct characters as k.
#include <bits/stdc++.h>
using namespace std;
const int MAX_CHAR = 26;
 
// Returns true if all values
// in freq[] are either 0 or k.
bool check(int freq[], int k)
{
    for (int i = 0; i < MAX_CHAR; i++)
        if (freq[i] && freq[i] != k)
            return false;
    return true;
}
 
// Returns count of substrings where frequency
// of every present character is k
int substrings(string s, int k)
{
    int res = 0;  // Initialize result
 
    // Pick a starting point
    for (int i = 0; s[i]; i++) {
 
        // Initialize all frequencies as 0
        // for this starting point
        int freq[MAX_CHAR] = { 0 };
 
        // One by one pick ending points
        for (int j = i; s[j]; j++) {
  
            // Increment frequency of current char 
            int index = s[j] - 'a';
            freq[index]++;
 
            // If frequency becomes more than
            // k, we can't have more substrings
            // starting with i
            if (freq[index] > k)
                break;
 
            // If frequency becomes k, then check
            // other frequencies as well.
            else if (freq[index] == k && 
                  check(freq, k) == true)
                res++;
        }
    }
    return res;
}
 
// Driver code
int main()
{
    string s = "aabbcc";
    int k = 2;
    cout << substrings(s, k) << endl;
 
    s = "aabbc";
    k = 2;
    cout << substrings(s, k) << endl;
}

Java

// Java program to count number of substrings
// with counts of distinct characters as k.
import java.io.*;
class GFG
{
 
static int MAX_CHAR = 26;
 
// Returns true if all values
// in freq[] are either 0 or k.
static boolean check(int freq[], int k)
{
    for (int i = 0; i < MAX_CHAR; i++)
        if (freq[i] !=0 && freq[i] != k)
            return false;
    return true;
}
 
// Returns count of substrings where frequency
// of every present character is k
static int substrings(String s, int k)
{
    int res = 0; // Initialize result
 
    // Pick a starting point
    for (int i = 0; i< s.length(); i++)
    {
 
        // Initialize all frequencies as 0
        // for this starting point
        int freq[] = new int[MAX_CHAR];
 
        // One by one pick ending points
        for (int j = i; j<s.length(); j++) 
        {
 
            // Increment frequency of current char 
            int index = s.charAt(j) - 'a';
            freq[index]++;
 
            // If frequency becomes more than
            // k, we can't have more substrings
            // starting with i
            if (freq[index] > k)
                break;
 
            // If frequency becomes k, then check
            // other frequencies as well.
            else if (freq[index] == k && 
                check(freq, k) == true)
                res++;
        }
    }
    return res;
}
 
// Driver code
public static void main(String[] args) 
{
    String s = "aabbcc";
    int k = 2;
    System.out.println(substrings(s, k));
 
    s = "aabbc";
    k = 2;
    System.out.println(substrings(s, k));
}
} 
 
// This code has been contributed by 29AjayKumar

Python3

# Python3 program to count number of substrings 
# with counts of distinct characters as k. 
 
MAX_CHAR = 26
 
# Returns true if all values 
# in freq[] are either 0 or k.
def check(freq, k):
    for i in range(0, MAX_CHAR):
        if(freq[i] and freq[i] != k):
            return False
    return True
 
# Returns count of substrings where 
# frequency of every present character is k 
def substrings(s, k):
    res = 0 # Initialize result
 
    # Pick a starting point 
    for i in range(0, len(s)):
 
        # Initialize all frequencies as 0 
        # for this starting point
        freq = [0] * MAX_CHAR
 
        # One by one pick ending points
        for j in range(i, len(s)):
             
            # Increment frequency of current char
            index = ord(s[j]) - ord('a')
            freq[index] += 1
 
            # If frequency becomes more than 
            # k, we can't have more substrings 
            # starting with i 
            if(freq[index] > k):
                break
             
            # If frequency becomes k, then check 
            # other frequencies as well
            elif(freq[index] == k and
                 check(freq, k) == True):
                res += 1
             
    return res
 
# Driver Code
if __name__ == "__main__":
    s = "aabbcc"
    k = 2
    print(substrings(s, k))
 
    s = "aabbc"; 
    k = 2; 
    print(substrings(s, k))
 
# This code is contributed 
# by Sairahul Jella

C#

// C# program to count number of substrings
// with counts of distinct characters as k.
using System;
 
class GFG
{
 
static int MAX_CHAR = 26;
 
// Returns true if all values
// in freq[] are either 0 or k.
static bool check(int []freq, int k)
{
    for (int i = 0; i < MAX_CHAR; i++)
        if (freq[i] != 0 && freq[i] != k)
            return false;
    return true;
}
 
// Returns count of substrings where frequency
// of every present character is k
static int substrings(String s, int k)
{
    int res = 0; // Initialize result
 
    // Pick a starting point
    for (int i = 0; i < s.Length; i++)
    {
 
        // Initialize all frequencies as 0
        // for this starting point
        int []freq = new int[MAX_CHAR];
 
        // One by one pick ending points
        for (int j = i; j < s.Length; j++) 
        {
 
            // Increment frequency of current char 
            int index = s[j] - 'a';
            freq[index]++;
 
            // If frequency becomes more than
            // k, we can't have more substrings
            // starting with i
            if (freq[index] > k)
                break;
 
            // If frequency becomes k, then check
            // other frequencies as well.
            else if (freq[index] == k && 
                check(freq, k) == true)
                res++;
        }
    }
    return res;
}
 
// Driver code
public static void Main(String[] args) 
{
    String s = "aabbcc";
    int k = 2;
    Console.WriteLine(substrings(s, k));
 
    s = "aabbc";
    k = 2;
    Console.WriteLine(substrings(s, k));
}
}
 
/* This code contributed by PrinciRaj1992 */

PHP

<?php 
 
// PHP program to count number of substrings
// with counts of distinct characters as k.
$MAX_CHAR = 26;
 
// Returns true if all values
// in freq[] are either 0 or k.
function check(&$freq, $k)
{
    global $MAX_CHAR;
    for ($i = 0; $i < $MAX_CHAR; $i++)
        if ($freq[$i] && $freq[$i] != $k)
            return false;
    return true;
}
 
// Returns count of substrings where frequency
// of every present character is k
function substrings($s, $k)
{
    global $MAX_CHAR;
    $res = 0; // Initialize result
 
    // Pick a starting point
    for ($i = 0; $i < strlen($s); $i++)
    {
 
        // Initialize all frequencies as 0
        // for this starting point
        $freq = array_fill(0, $MAX_CHAR,NULL); 
 
        // One by one pick ending points
        for ($j = $i; $j < strlen($s); $j++)
        {
 
            // Increment frequency of current char 
            $index = ord($s[$j]) - ord('a');
            $freq[$index]++;
 
            // If frequency becomes more than
            // k, we can't have more substrings
            // starting with i
            if ($freq[$index] > $k)
                break;
 
            // If frequency becomes k, then check
            // other frequencies as well.
            else if ($freq[$index] == $k && 
                check($freq, $k) == true)
                $res++;
        }
    }
    return $res;
}
 
// Driver code
$s = "aabbcc";
$k = 2;
echo substrings($s, $k)."\n";
$s = "aabbc";
$k = 2;
echo substrings($s, $k)."\n";
 
// This code is contributed by Ita_c.
?>

Javascript

<script>
 
// Javascript program to count number of 
// substrings with counts of distinct 
// characters as k.
let MAX_CHAR = 26;
 
// Returns true if all values
// in freq[] are either 0 or k.
function check(freq,k)
{
    for(let i = 0; i < MAX_CHAR; i++)
        if (freq[i] != 0 && freq[i] != k)
            return false;
             
    return true;
}
 
// Returns count of substrings where frequency
// of every present character is k
function substrings(s, k)
{
     
    // Initialize result
    let res = 0; 
 
    // Pick a starting point
    for(let i = 0; i< s.length; i++)
    {
         
        // Initialize all frequencies as 0
        // for this starting point
        let freq = new Array(MAX_CHAR);
        for(let i = 0; i < freq.length ;i++)
        {
            freq[i] = 0;
        }
     
        // One by one pick ending points
        for(let j = i; j < s.length; j++)
        {
             
            // Increment frequency of current char
            let index = s[j].charCodeAt(0) - 
                         'a'.charCodeAt(0);
            freq[index]++;
     
            // If frequency becomes more than
            // k, we can't have more substrings
            // starting with i
            if (freq[index] > k)
                break;
     
            // If frequency becomes k, then check
            // other frequencies as well.
            else if (freq[index] == k &&
                check(freq, k) == true)
                res++;
        }
    }
    return res;
}
 
// Driver code
let s = "aabbcc";
let k = 2;
document.write(substrings(s, k) + "<br>");
  
s = "aabbc";
k = 2;
document.write(substrings(s, k) + "<br>");
 
// This code is contributed by avanitrachhadiya2155
     
</script>

Output

6
3

Time Complexity: O(n*n) where n is the length of input string. Function Check() is running a loop of constant length from 0 to MAX_CHAR (ie; 26 always) so this function check() is running in O(MAX_CHAR) time so Time complexity is O(MAX_CHAR*n*n)=O(n^2).
Auxiliary Space: O(1)

Efficient Approach: On very careful observation, we can see that it is enough to check the same for substrings of length [Tex]K\times i,\ \forall\ i\isin[1, D] [/Tex] where [Tex]D [/Tex] is the number of distinct characters present in the given string.

Argument:
Consider a substring S_{i+1}S_{i+2}\dots S_{i+p} of length ‘p’. If this substring has ‘m’ distinct characters and each distinct character occurs exactly ‘K’ times, then the length of the substring, ‘p’, is given by p = K\times m. Since ‘[Tex]p [/Tex]’ is always a multiple of ‘K’ and [Tex]1\le m\le 26 [/Tex] for the given string, it is enough to iterate over the substrings whose length is divisible by ‘K’ and having m, 1 \le m \le 26 distinct characters. We will use Sliding window to iterate over the substrings of fixed length.

Solution:

Find the number of distinct characters present in the given string. Let it be D.
For each i, 1\le i\le D, do the following
- Iterate over the substrings of length $i \times K$, using a sliding window.
- Check if they satisfy the condition – All distinct characters in the substring occur exactly K times.
- If they satisfy the condition, increment the count.

Below is the implementation of the above approach:

C++

#include <iostream>
#include <map>
#include <set>
#include <string>
 
int min(int a, int b) { return a < b ? a : b; }
 
using namespace std;
 
bool have_same_frequency(map<char, int>& freq, int k)
{
    for (auto& pair : freq) {
        if (pair.second != k && pair.second != 0) {
            return false;
        }
    }
    return true;
}
 
int count_substrings(string s, int k)
{
    int count = 0;
    int distinct = (set<char>(s.begin(), s.end())).size();
    for (int length = 1; length <= distinct; length++) {
        int window_length = length * k;
        map<char, int> freq;
        int window_start = 0;
        int window_end = window_start + window_length - 1;
        for (int i = window_start;
             i <= min(window_end, s.length() - 1); i++) {
            freq[s[i]]++;
        }
        while (window_end < s.length()) {
            if (have_same_frequency(freq, k)) {
                count++;
            }
            freq[s[window_start]]--;
            window_start++;
            window_end++;
            if (window_length < s.length()) {
                freq[s[window_end]]++;
            }
        }
    }
    return count;
}
 
int main()
{
    string s = "aabbcc";
    int k = 2;
    cout << count_substrings(s, k) << endl;
    s = "aabbc";
    k = 2;
    cout << count_substrings(s, k) << endl;
    return 0;
}

C

#include <stdbool.h>
#include <stdio.h>
#include <string.h>
 
int min(int a, int b) { return a < b ? a : b; }
 
bool have_same_frequency(int freq[], int k)
{
    for (int i = 0; i < 26; i++) {
        if (freq[i] != 0 && freq[i] != k) {
            return false;
        }
    }
    return true;
}
 
int count_substrings(char* s, int n, int k)
{
    int count = 0;
    int distinct = 0;
    bool have[26] = { false };
    for (int i = 0; i < n; i++) {
        have[s[i] - 'a'] = true;
    }
    for (int i = 0; i < 26; i++) {
        if (have[i]) {
            distinct++;
        }
    }
    for (int length = 1; length <= distinct; length++) {
        int window_length = length * k;
        int freq[26] = { 0 };
        int window_start = 0;
        int window_end = window_start + window_length - 1;
        for (int i = window_start;
             i <= min(window_end, n - 1); i++) {
            freq[s[i] - 'a']++;
        }
        while (window_end < n) {
            if (have_same_frequency(freq, k)) {
                count++;
            }
            freq[s[window_start] - 'a']--;
            window_start++;
            window_end++;
            if (window_end < n) {
                freq[s[window_end] - 'a']++;
            }
        }
    }
    return count;
}
 
int main()
{
    char* s = "aabbcc";
    int k = 2;
    printf("%d\n", count_substrings(s, 6, k));
    s = "aabbc";
    k = 2;
    printf("%d\n", count_substrings(s, 5, k));
    return 0;
}

Java

import java.util.*;
 
class GFG {
 
    static boolean have_same_frequency(int[] freq, int k)
    {
        for (int i = 0; i < 26; i++) {
            if (freq[i] != 0 && freq[i] != k) {
                return false;
            }
        }
        return true;
    }
 
    static int count_substrings(String s, int k)
    {
        int count = 0;
        int distinct = 0;
        boolean[] have = new boolean[26];
        Arrays.fill(have, false);
        for (int i = 0; i < s.length(); i++) {
            have[((int)(s.charAt(i) - 'a'))] = true;
        }
        for (int i = 0; i < 26; i++) {
            if (have[i]) {
                distinct++;
            }
        }
        for (int length = 1; length <= distinct; length++) {
            int window_length = length * k;
            int[] freq = new int[26];
            Arrays.fill(freq, 0);
            int window_start = 0;
            int window_end
                = window_start + window_length - 1;
            for (int i = window_start;
                 i <= Math.min(window_end, s.length() - 1);
                 i++) {
                freq[((int)(s.charAt(i) - 'a'))]++;
            }
            while (window_end < s.length()) {
                if (have_same_frequency(freq, k)) {
                    count++;
                }
                freq[(
                    (int)(s.charAt(window_start) - 'a'))]--;
                window_start++;
                window_end++;
                if (window_end < s.length()) {
                    freq[((int)(s.charAt(window_end)
                                - 'a'))]++;
                }
            }
        }
        return count;
    }
    public static void main(String[] args)
    {
        String s = "aabbcc";
        int k = 2;
        System.out.println(count_substrings(s, k));
        s = "aabbc";
        k = 2;
        System.out.println(count_substrings(s, k));
    }
}

Python3

from collections import defaultdict
 
 
def have_same_frequency(freq: defaultdict, k: int):
    return all([freq[i] == k or freq[i] == 0 for i in freq])
 
 
def count_substrings(s: str, k: int) -> int:
    count = 0
    distinct = len(set([i for i in s]))
    for length in range(1, distinct + 1):
        window_length = length * k
        freq = defaultdict(int)
        window_start = 0
        window_end = window_start + window_length - 1
        for i in range(window_start, min(window_end + 1, len(s))):
            freq[s[i]] += 1
        while window_end < len(s):
            if have_same_frequency(freq, k):
                count += 1
            freq[s[window_start]] -= 1
            window_start += 1
            window_end += 1
            if window_end < len(s):
                freq[s[window_end]] += 1
    return count
 
 
if __name__ == '__main__':
    s = "aabbcc"
    k = 2
    print(count_substrings(s, k))
    s = "aabbc"
    k = 2
    print(count_substrings(s, k))

C#

using System;
 
class GFG{
 
static bool have_same_frequency(int[] freq, int k)
{
    for(int i = 0; i < 26; i++) 
    {
        if (freq[i] != 0 && freq[i] != k) 
        {
            return false;
        }
    }
    return true;
}
 
static int count_substrings(string s, int k)
{
    int count = 0;
    int distinct = 0;
    bool[] have = new bool[26];
    Array.Fill(have, false);
     
    for(int i = 0; i < s.Length; i++) 
    {
        have[((int)(s[i] - 'a'))] = true;
    }
     
    for(int i = 0; i < 26; i++) 
    {
        if (have[i]) 
        {
            distinct++;
        }
    }
     
    for(int length = 1; length <= distinct; length++) 
    {
        int window_length = length * k;
        int[] freq = new int[26];
        Array.Fill(freq, 0);
        int window_start = 0;
        int window_end = window_start + 
                         window_length - 1;
                          
        for(int i = window_start;
                i <= Math.Min(window_end, s.Length - 1);
                i++) 
        {
            freq[((int)(s[i] - 'a'))]++;
        }
        while (window_end < s.Length) 
        {
            if (have_same_frequency(freq, k))
            {
                count++;
            }
            freq[((int)(s[window_start] - 'a'))]--;
            window_start++;
            window_end++;
             
            if (window_end < s.Length) 
            {
                freq[((int)(s[window_end] - 'a'))]++;
            }
        }
    }
    return count;
}
 
// Driver code
public static void Main(string[] args)
{
    string s = "aabbcc";
    int k = 2;
    Console.WriteLine(count_substrings(s, k));
     
    s = "aabbc";
    k = 2;
    Console.WriteLine(count_substrings(s, k));
}
}
 
// This code is contributed by gaurav01

Javascript

<script>
 
function have_same_frequency(freq,k)
{
    for (let i = 0; i < 26; i++) {
            if (freq[i] != 0 && freq[i] != k) {
                return false;
            }
        }
        return true;
}
 
function count_substrings(s,k)
{
    let count = 0;
        let distinct = 0;
        let have = new Array(26);
        for(let i=0;i<26;i++)
        {
            have[i]=false;
        }
        for (let i = 0; i < s.length; i++) {
            have[((s[i].charCodeAt(0) - 
            'a'.charCodeAt(0)))] = true;
        }
        for (let i = 0; i < 26; i++) {
            if (have[i]) {
                distinct++;
            }
        }
        for (let length = 1; length <= distinct; length++) {
            let window_length = length * k;
            let freq = new Array(26);
            for(let i=0;i<26;i++)
                freq[i]=0;
            let window_start = 0;
            let window_end
                = window_start + window_length - 1;
            for (let i = window_start;
                 i <= Math.min(window_end, s.length - 1);
                 i++) {
                freq[((s[i].charCodeAt(0) - 
                'a'.charCodeAt(0)))]++;
            }
            while (window_end < s.length) {
                if (have_same_frequency(freq, k)) {
                    count++;
                }
                freq[(
                    (s[window_start].charCodeAt(0) - 
                    'a'.charCodeAt(0)))]--;
                window_start++;
                window_end++;
                if (window_end < s.length) {
                    freq[(s[window_end].charCodeAt(0)
                                - 'a'.charCodeAt(0))]++;
                }
            }
        }
        return count;
}
 
let s = "aabbcc";
let k = 2;
document.write(count_substrings(s, k)+"<br>");
s = "aabbc";
k = 2;
document.write(count_substrings(s, k)+"<br>");
 
 
// This code is contributed by rag2127
 
</script>

Output

6
3

Time Complexity: O(N * D) where D is the number of distinct characters present in the string and N is the length of the string.
Auxiliary Space: O(N)

Count of strings with frequency of each character at most K

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Number of substrings with count of each character as k

C++

Java

Python3

C#

PHP

Javascript

Solution:

C++

C

Java

Python3

C#

Javascript

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