# Number of subsequences of the form a^i b^j c^k

Given a string, count number of subsequences of the form aibjck, i.e., it consists of i ’a’ characters, followed by j ’b’ characters, followed by k ’c’ characters where i >= 1, j >=1 and k >= 1.

**Note:** Two subsequences are considered different if the set of array indexes picked for the 2 subsequences are different.

Expected Time Complexity: O(n)

**Examples:**

```
Input  : abbc
Output : 3
Subsequences are abc, abc and abbc

Input  : abcabc
Output : 7
Subsequences are abc, abc, abbc, aabc
abcc, abc and abc
```

```java
class Solution {
    public int countSubsequences(String s) {
        // Initialize counts of different subsequences 
        // caused by different combination of 'a' 
        int aCount = 0; 
        // Initialize counts of different subsequences 
        // caused by different combination of 'a' and 
        // different combination of 'b' 
        int bCount = 0; 
        // Initialize counts of different subsequences 
        // caused by different combination of 'a', 'b' 
        // and 'c'. 
        int cCount = 0; 
        // Traverse all characters of given string 
        for (int i = 0; i < s.length(); i++) { 
            /* If current character is 'a', then 
               there are following possibilities : 
                 a) Current character begins a new 
                    subsequence. 
                 b) Current character is part of aCount 
                    subsequences. 
                 c) Current character is not part of 
                    aCount subsequences. */
            if (s.charAt(i) == 'a') 
                aCount = (1 + 2 * aCount); 
            /* If current character is 'b', then 
               there are following possibilities : 
                 a) Current character begins a new 
                    subsequence of b's with aCount 
                    subsequences. 
                 b) Current character is part of bCount 
                    subsequences. 
                 c) Current character is not part of 
                    bCount subsequences. */
            else if (s.charAt(i) == 'b') 
                bCount = (aCount + 2 * bCount); 
  
            /* If current character is 'c', then 
               there are following possibilities : 
                 a) Current character begins a new 
                    subsequence of c's with bCount 
                    subsequences. 
                 b) Current character is part of cCount 
                    subsequences. 
                 c) Current character is not part of 
                    cCount subsequences. */
            else if (s.charAt(i) == 'c') 
                cCount = (bCount + 2 * cCount); 
        } 
        return cCount; 
    } 
}
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://mayanktyagi3111.gitbook.io/interview-prep/dynamic-programming/number-of-subsequences-of-the-form-a-i-b-j-c-k.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.