distinct-subsequences

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Description

Given two strings s and t, return the number of distinct subsequences of s which equals t.

A string's subsequence is a new string formed from the original string by deleting some (can be none) of the characters without disturbing the remaining characters' relative positions. (i.e., "ACE" is a subsequence of "ABCDE" while "AEC" is not).

The test cases are generated so that the answer fits on a 32-bit signed integer.

 

Example 1:

Input: s = "rabbbit", t = "rabbit"
Output: 3
Explanation:
As shown below, there are 3 ways you can generate "rabbit" from S.
rabbbit
rabbbit
rabbbit

Example 2:

Input: s = "babgbag", t = "bag"
Output: 5
Explanation:
As shown below, there are 5 ways you can generate "bag" from S.
babgbag
babgbag
babgbag
babgbag
babgbag

 

Constraints:

• 1 <= s.length, t.length <= 1000
• s and t consist of English letters.

Solution(Python)

class Solution:
    @cache
    def numDistinct(self, s: str, t: str) -> int:
        if len(t) == 0:
            return 1

        elif len(s) == 0:
            return 0

        elif s[-1] == t[-1]:
            return self.numDistinct(s[:-1], t[:-1]) + self.numDistinct(s[:-1], t)

        else:
            return self.numDistinct(s[:-1], t)