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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

Constraints:

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

solution

class Solution:
    def numDistinct(self, s: str, t: str) -> int:
        n1, n2 = len(t), len(s)
        dp = [[0] * (n2 + 1) for _ in range(n1 + 1)]
        for j in range(0, n2+1):
            dp[0][j] = 1 # 为什么有这个？ 因为单个字符dp计算不对，比如aaa，a的情况
        for i in range(1, n1 + 1):
            for j in range(1, n2 + 1):
                if t[i - 1] == s[j - 1]:
                    dp[i][j] = dp[i-1][j-1]+dp[i][j-1]
                else:
                    dp[i][j] = dp[i][j-1]
        return dp[n1][n2]