115. Distinct Subsequences

Problem Link

Description

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

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

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Python3

class Solution:
    def numDistinct(self, s: str, t: str) -> int:
        m, n = len(s), len(t)
        dp = [[0] * (m + 1) for _ in range(n + 1)]
        
        for j in range(m + 1):
            dp[0][j] = 1
        
        for i in range(n):
            for j in range(m):
                dp[i + 1][j + 1] = dp[i + 1][j]
                if t[i] == s[j]:
                    dp[i + 1][j + 1] += dp[i][j]
        
        return dp[n][m]