Count Subsequence Occurrences with Different Characters

Given two strings s and w, find the number of times w appears as a subsequence of string s where every character of string s can be included in forming at most one subsequence.

Examples :

Input: s = "abcdeacbced", w = "bcd" 
Output: 2
Explanation: The two subsequences of string w are highlighted in abcdeabced. The first subsequence is formed by (s[1], s[2] and s[3]) and second by (s[7], s[8] and s[10])

Input: s = "abcde", w = "fgh" 
Output: 0
Explanation: No valid subsequences are possible. 

The idea is to repeatedly try to form the subsequence w. Whenever a character from s is used in a subsequence, mark it so it cannot be reused again. Continue this process until no more subsequences can be formed.

Let us understand with an example:
Input: s = "abcdeacbced", w = "bcd"
Initialize res = 0.
Traverse the string and try to form the subsequence "bcd".

• Ignore 'a'
• Match 'b', 'c' and 'd'
• Mark them as '*'

Updated string: a***eacbced
One subsequence is formed, so increment result: res = 1
Again traverse the string to form another "bcd" subsequence.

• Ignore already marked characters
• Match next 'b', 'c' and 'd'
• Mark them as '*'

Updated string: a***eac**e*
Another subsequence is formed: res = 2
Traverse again, No more valid "bcd" subsequences can be formed.
Final result: 2

2

Time Complexity: O(n^2)
Auxiliary Space: O(1)