115 - Distinct Subsequences

2020/11/21

leetcode

Problem

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 relative positions of the remaining characters. (i.e., "ACE" is a subsequence of "ABCDE" while "AEC" is not).

It's guaranteed 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

Solution

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 i in range(m+1):
            dp[0][i] = 1

        for i in range(1, n+1):
            for j in range(1, m+1):
                if s[j-1] == t[i-1]:
                    dp[i][j] = dp[i][j-1] + dp[i-1][j-1]
                else:
                    dp[i][j] = dp[i][j-1]

        return dp[n][m]