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Count Substrings with at least one occurrence of first K alphabet

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Given a string S of size N and a positive integer K. The given string only consists of the first K English lowercase alphabets. The task is to find the number of substrings that contain at least one occurrence of all these K characters.

Examples:

Input: S = “abcabc”, K = 3
Output: 10
Explanation: The substrings containing at least one occurrence of the first three characters of English lowercase alphabets (a, b and c) are “abc”, “abca”, “abcab”, “abcabc”, “bca”, “bcab”, “bcabc”, “cab”, “cabc” and “abc”. 

Input: S = “aaacb”, K = 4
Output: 0
Explanation: There is no substring that contains at least one occurrence of all first K characters of English lowercase alphabets (a, b, c and d)

An approach using Hashing and Two-Pointer approach:

The idea is to keep a two-pointer say start and end at the beginning of the string. 

For every start, we’ll find the first valid substring which starts from index start and ends at index end. As this is the first valid substring starting from start but we can also include rest of the character from end index because we already satisfied the minimum criteria of validity. So there would be (N – end) total valid string for this start index. 

We’ll keep adding all these count into result and finally return the result.

Follow the steps below to implement the above idea:

  • Initialize a map for keeping the frequency of characters
  • Initialize a variable start = 0, end = 0, and result = 0.
  • Do it while the end is less than the size of the given string
    • Increment the frequency of character at the end.
    • Check if the size of the map becomes K
      • Initiate a while loop unless the map size is equal to K.
        • Increment the value of the result by N – end, because (N – end) substrings satisfy the given condition
        • Decrement the frequency count of characters at the start of the map
        • Check if the frequency count of the character at the start of the map becomes 0.
          • If true, then remove this character from the map as this character will no longer exist in the valid substring for the new value of start.
        • Move the start pointer to right by incrementing its value by 1
      • Shift the end pointer to right by incrementing its value by 1.
    • Otherwise, Increment the end pointer by 1.
  • Return the value of the result

Below is the implementation of the above approach.

C++




// C++ code to implement the approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the number of substrings
int numberOfSubstrings(string s, int K)
{
    // Initialize a map for keeping
    // frequency of characters
    unordered_map<char, int> unmap;
 
    // Initialize a variable start = 0,
    // end = 0 and result = 0
    int start = 0, end = 0, n = s.size(), result = 0;
 
    // Do while end is less than size
    // of given string
    while (end < n) {
 
        // Increment the frequency of
        // character at end.
        unmap[s[end]]++;
 
        // Check if the size of
        // map becomes K
        if (unmap.size() == K) {
 
            // Initiate a while loop
            // unless map size is
            // equals to K
            while (unmap.size() == K) {
 
                // Increment the value of
                // result by n - end, because (n - end)
                // substring are valid that satisfy the
                // given condition
                result += n - end;
 
                // Decrement the frequency
                // count of character at
                // start from map
                unmap[s[start]]--;
 
                // Check if frequency count
                // of character at start in
                // map becomes 0.
                // If true, then remove this
                // character from the map
                if (unmap[s[start]] == 0)
                    unmap.erase(s[start]);
 
                // Move the start pointer
                // to right by incrementing
                // its value by 1
                start++;
            }
 
            // Increment the end pointer.
            end++;
        }
 
        // Otherwise, Increment
        // the end pointer by 1.
        else {
            end++;
        }
    }
 
    // Return the value of result
    return result;
}
 
// Driver code
int main()
{
    string S = "abcabc";
    int K = 3;
 
    // Function Call
    cout << numberOfSubstrings(S, K);
 
    return 0;
}


Java




// Java code to implement the approach
 
import java.io.*;
import java.util.*;
 
class GFG {
 
  // Function to find the number of substrings
  static int numberOfSubstrings(String s, int K)
  {
    // Initialize a map for keeping
    // frequency of characters
    HashMap<Character, Integer> unmap = new HashMap<>();
 
    // Initialize a variable start = 0,
    // end = 0 and result = 0
    int start = 0, end = 0, n = s.length(), result = 0;
 
    // Do while end is less than size
    // of given string
    while (end < n) {
      // Increment the frequency of
      // character at end.
      unmap.put(s.charAt(end),
                unmap.getOrDefault(s.charAt(end), 0)
                + 1);
 
      // Check if the size of
      // map becomes K
      if (unmap.size() == K) {
 
        // Initiate a while loop
        // unless map size is
        // equals to K
        while (unmap.size() == K) {
 
          // Increment the value of
          // result by n - end, because (n - end)
          // substring are valid that satisfy the
          // given condition
          result += n - end;
 
          // Decrement the frequency
          // count of character at
          // start from map
          unmap.put(s.charAt(start),
                    unmap.get(s.charAt(start))
                    - 1);
 
          // Check if frequency count
          // of character at start in
          // map becomes 0.
          // If true, then remove this
          // character from the map
          if (unmap.get(s.charAt(start)) == 0) {
            unmap.remove(s.charAt(start));
          }
 
          // Move the start pointer
          // to right by incrementing
          // its value by 1
          start++;
        }
 
        // Increment the end pointer.
        end++;
      }
 
      // Otherwise, Increment
      // the end pointer by 1.
      else {
        end++;
      }
    }
 
    // Return the value of result
    return result;
  }
 
  public static void main(String[] args)
  {
    String S = "abcabc";
    int K = 3;
 
    // Function call
    System.out.print(numberOfSubstrings(S, K));
  }
}
 
// This code is contributed by lokesh


Python3




#  Python code to implement the approach
 
#  Function to find the number of substrings
def numberOfSubstrings(s, K):
   
    #  Initialize a map for keeping
    #  frequency of characters
    unmap = {}
     
    #  Initialize a variable start = 0,
    #  end = 0 and result = 0
    start = 0
    end = 0
    n = len(s)
    result = 0
     
    #  Do while end is less than size
    #  of given string
    while (end < n):
       
        #  Increment the frequency of
        #  character at end.
        unmap[s[end]] = unmap.get(s[end], 0)+1
         
        #   Check if the size of
        #   map becomes K
        if len(unmap) == K:
 
            #  Initiate a while loop
            #  unless map size is
            #  equals to K
            while len(unmap) == K:
               
                #  Increment the value of
                #  result by n - end, because (n - end)
                #  substring are valid that satisfy the
                #  given condition
                result += n-end
 
                #  Decrement the frequency
                #  count of character at
                #  start from map
                unmap[s[start]] -= 1
 
                #  Check if frequency count
                #  of character at start in
                #  map becomes 0.
                #  If true, then remove this
                #  character from the map
                if unmap[s[start]] == 0:
                    unmap.pop(s[start])
                     
                #  Move the start pointer
                #  to right by incrementing
                #  its value by 1
                start += 1
 
            #  Increment the end pointer.
            end += 1
 
        #  Otherwise, Increment
        #  the end pointer by 1.
        else:
            end += 1
 
    #  Return the value of result
    return result
 
#  Driver code
S = "abcabc"
K = 3
print(numberOfSubstrings(S, K))
 
# This Code is Contributed By Vivek Maddeshiya


C#




// C# code to implement the approach
using System;
using System.Collections.Generic;
 
public class GFG {
 
  // Function to find the number of substrings
  static int numberOfSubstrings(string s, int K)
  {
     
    // Initialize a map for keeping
    // frequency of characters
    Dictionary<char, int> unmap = new Dictionary<char, int>();
 
    // Initialize a variable start = 0,
    // end = 0 and result = 0
    int start = 0, end = 0, n = s.Length, result = 0;
 
    // Do while end is less than size
    // of given string
    while (end < n) {
      // Increment the frequency of
      // character at end.
      if(unmap.ContainsKey(s[end])){
        int temp = unmap[s[end]] + 1;
        unmap[s[end]] = temp;
      }
      else{
        unmap[s[end]] = 1;
      }
 
      // Check if the size of
      // map becomes K
      if (unmap.Count == K) {
 
        // Initiate a while loop
        // unless map size is
        // equals to K
        while (unmap.Count == K) {
 
          // Increment the value of
          // result by n - end, because (n - end)
          // substring are valid that satisfy the
          // given condition
          result += n - end;
 
          // Decrement the frequency
          // count of character at
          // start from map
          unmap[s[start]] = unmap[s[start]] - 1;
 
          // Check if frequency count
          // of character at start in
          // map becomes 0.
          // If true, then remove this
          // character from the map
          if (unmap[s[start]] == 0) {
            unmap.Remove(s[start]);
          }
 
          // Move the start pointer
          // to right by incrementing
          // its value by 1
          start++;
        }
 
        // Increment the end pointer.
        end++;
      }
 
      // Otherwise, Increment
      // the end pointer by 1.
      else {
        end++;
      }
    }
 
    // Return the value of result
    return result;
  }
 
  static public void Main()
  {
 
    // Code
    string S = "abcabc";
    int K = 3;
 
    // Function call
    Console.Write(numberOfSubstrings(S, K));
  }
}
 
// This code is contributed by lokeshmvs21


Javascript




// Javascript code
 
function numberOfSubstrings(s, K)
{
 
    // Initialize a map for keeping
    // frequency of characters
    let unmap = {};
     
    // Initialize a variable start = 0,
    // end = 0 and result = 0
    let start = 0, end = 0, n = s.length, result = 0;
 
    // Do while end is less than size
    // of given string
    while (end < n)
    {
     
        // Increment the frequency of
        // character at end.
        if (unmap[s[end]]) {
            unmap[s[end]]++;
        } else {
            unmap[s[end]] = 1;
        }
        // Check if the size of
        // map becomes K
        if (Object.keys(unmap).length == K)
        {
         
            // Initiate a while loop
            // unless map size is
            // equals to K
            while (Object.keys(unmap).length == K)
            {
             
                // Increment the value of
                // result by n - end, because (n - end)
                // substring are valid that satisfy the
                // given condition
                result += n - end;
                 
                // Decrement the frequency
                // count of character at
                // start from map
                unmap[s[start]]--;
                 
                // Check if frequency count
                // of character at start in
                // map becomes 0.
                // If true, then remove this
                // character from the map
                if (unmap[s[start]] == 0)
                    delete unmap[s[start]];
                     
                // Move the start pointer
                // to right by incrementing
                // its value by 1
                start++;
            }
             
            // Increment the end pointer.
            end++;
        }
         
        // Otherwise, Increment
        // the end pointer by 1.
        else {
            end++;
        }
    }
     
    // Return the value of result
    return result;
}
 
// Driver code
console.log(numberOfSubstrings("abcabc", 3));
 
// This code is contributed by ksam24000


Output

10

Time Complexity: O(N)
Auxiliary Space: O(N)

Another Approach: Using sliding window technique 

1)Initialize an array freq of size K to keep track of the frequency of each character in the window. Also, initialize a variable uniqueCount to 0 to keep track of the number of unique characters in the window, and a variable ans to 0 to keep track of the count of valid substrings.

2)Initialize two pointers left and right to 0, which represent the start and end of the current window.

3)While the right pointer is less than the length of the string, do the following:

  • Update the frequency of the current character at the right pointer by incrementing the corresponding index in the freq array.
  • If the frequency of the current character is 1 (i.e., this character was not previously present in the window), increment the uniqueCount variable.
  • Check if uniqueCount is equal to K. If it is, it means that the current window contains all K characters, so we can count the number of valid substrings that can be formed using the current window ending at the right pointer. This count is equal to the length of the substring from the right pointer to the end of the string, which is s.size() – right.
  • Slide the window to the right by incrementing the right pointer.
  • If uniqueCount is not equal to K, continue sliding the window to the right until it does.

4)When the loop in step 3 ends, return the ans variable, which contains the count of valid substrings.

Below is the implementation of the above approach.

C++




// C++ code to implement the approach
 
#include <bits/stdc++.h>
 
using namespace std;
 
// Function to find the number of substrings
 
int numberOfSubstrings(string s, int K)
{
 
    int freq[K] = { 0 }; // array to keep track of frequency
                         // of characters in window
 
    int uniqueCount = 0; // variable to keep track of unique
                         // characters in window
 
    int ans = 0; // variable to keep track of count of valid
                 // substrings
 
    int left = 0, right = 0; // pointers for sliding window
 
    while (right < s.size()) {
 
        // update frequency of current character and unique
        // count
 
        freq[s[right] - 'a']++;
 
        if (freq[s[right] - 'a'] == 1) {
 
            uniqueCount++;
        }
 
        // if all K characters are present in window
 
        while (uniqueCount == K) {
 
            ans += (s.size()
                    - right); // count of substrings with
                              // current window ending at
                              // right pointer
 
            // update frequency and unique count for
            // leftmost character in window
 
            freq[s[left] - 'a']--;
 
            if (freq[s[left] - 'a'] == 0) {
 
                uniqueCount--;
            }
 
            left++; // move left pointer to slide window
        }
 
        right++; // move right pointer to slide window
    }
 
    return ans;
}
 
// Driver code
 
int main()
 
{
 
    string S = "abcabc";
 
    int K = 3;
 
    // Function Call
 
    cout << numberOfSubstrings(S, K);
 
    return 0;
}


Java




import java.util.HashMap;
 
public class Main {
   
      // Function to find the number of substrings
    public static int numberOfSubstrings(String s, int K) {
       
          // array to keep track of frequency
        // of characters in window
        int[] freq = new int[K];
       
          // variable to keep track of unique
        // characters in window
        int uniqueCount = 0;
       
          // variable to keep track of count of valid
        // substrings
        int ans = 0;
       
          // pointers for sliding window
        int left = 0, right = 0;
        while (right < s.length()) {
           
              // update frequency of current character and unique
            // count
            freq[s.charAt(right) - 'a']++;
            if (freq[s.charAt(right) - 'a'] == 1) {
                uniqueCount++;
            }
           
              // if all K characters are present in window
            while (uniqueCount == K) {
                ans += (s.length() - right);
               
                  // count of substrings with
                // current window ending at
                // right pointer
  
                // update frequency and unique count for
                // leftmost character in window
                freq[s.charAt(left) - 'a']--;
                if (freq[s.charAt(left) - 'a'] == 0) {
                    uniqueCount--;
                }
               
                  // move left pointer to slide window
                left++;
            }
           
              // move right pointer to slide window
            right++;
        }
        return ans;
    }
 
      // Driver code
    public static void main(String[] args) {
        String S = "abcabc";
        int K = 3;
        System.out.println(numberOfSubstrings(S, K));
    }
}


Python3




# code
def numberOfSubstrings(s, K):
    freq = [0]*# list to keep track of frequency
    # of characters in window
 
    uniqueCount = 0  # variable to keep track of unique
    # characters in window
 
    ans = 0  # variable to keep track of count of valid
    # substrings
 
    left = 0
    right = 0  # pointers for sliding window
 
    while right < len(s):
 
        # update frequency of current character and unique
        # count
 
        freq[ord(s[right]) - ord('a')] += 1
 
        if freq[ord(s[right]) - ord('a')] == 1:
 
            uniqueCount += 1
 
        # if all K characters are present in window
 
        while uniqueCount == K:
 
            ans += len(s) - right  # count of substrings with
            # current window ending at
            # right pointer
 
            # update frequency and unique count for
            # leftmost character in window
 
            freq[ord(s[left]) - ord('a')] -= 1
 
            if freq[ord(s[left]) - ord('a')] == 0:
 
                uniqueCount -= 1
 
            left += 1  # move left pointer to slide window
 
        right += 1  # move right pointer to slide window
 
    return ans
 
# Driver code
 
 
S = "abcabc"
K = 3
 
# Function Call
print(numberOfSubstrings(S, K))


C#




// C# code to implement the approach
using System;
 
class Program
{
   
  // Function to find the number of substrings
  static int numberOfSubstrings(string s, int K)
  {
 
    int[] freq = new int[K]; // array to keep track of
    // frequency of characters
    // in window
    int uniqueCount = 0; // variable to keep track of
    // unique characters in window
    int ans = 0; // variable to keep track of count of
    // valid substrings
 
    int left = 0, right
      = 0; // pointers for sliding window
 
    while (right < s.Length) {
 
      // update frequency of current character and
      // unique count
 
      freq[s[right] - 'a']++;
 
      if (freq[s[right] - 'a'] == 1) {
 
        uniqueCount++;
      }
 
      // if all K characters are present in window
 
      while (uniqueCount == K) {
 
        ans += (s.Length
                - right); // count of substrings
        // with current window
        // ending at right pointer
 
        // update frequency and unique count for
        // leftmost character in window
 
        freq[s[left] - 'a']--;
 
        if (freq[s[left] - 'a'] == 0) {
 
          uniqueCount--;
        }
 
        left++; // move left pointer to slide window
      }
 
      right++; // move right pointer to slide window
    }
 
    return ans;
  }
 
  // Driver code
  static void Main()
  {
 
    string S = "abcabc";
    int K = 3;
 
    // Function Call
    Console.WriteLine(numberOfSubstrings(S, K));
  }
}
 
// This code is contributed by user_dtewbxkn77n


Javascript




// JS code to implement the approach
 
// Function to find the number of substrings
function numberOfSubstrings(s, K) {
 
    const freq = new Array(K).fill(0); // array to keep track of frequency
                                       // of characters in window
 
    let uniqueCount = 0; // variable to keep track of unique
                         // characters in window
 
    let ans = 0; // variable to keep track of count of valid
                 // substrings
 
    let left = 0, right = 0; // pointers for sliding window
 
    while (right < s.length) {
 
        // update frequency of current character and unique
        // count
 
        freq[s[right].charCodeAt(0) - 97]++;
 
        if (freq[s[right].charCodeAt(0) - 97] == 1) {
 
            uniqueCount++;
        }
 
        // if all K characters are present in window
 
        while (uniqueCount == K) {
 
            ans += (s.length
                    - right); // count of substrings with
                              // current window ending at
                              // right pointer
 
            // update frequency and unique count for
            // leftmost character in window
 
            freq[s[left].charCodeAt(0) - 97]--;
 
            if (freq[s[left].charCodeAt(0) - 97] == 0) {
 
                uniqueCount--;
            }
 
            left++; // move left pointer to slide window
        }
 
        right++; // move right pointer to slide window
    }
 
    return ans;
}
 
// Driver code
 
const S = "abcabc";
const K = 3;
 
// Function Call
 
console.log(numberOfSubstrings(S, K));


Output

10

Time Complexity: O(N)
Auxiliary Space: O(K)



Last Updated : 14 Sep, 2023
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