115. Distinct Subsequences

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


        for i in range(len(s) + 1):
            dp[0][i] = 1


        for i in range(1, len(t) + 1):
            for j in range(1, len(s) + 1):
                dp[i][j] = dp[i][j - 1]
                if t[i - 1] == s[j - 1]:
                    dp[i][j] += dp[i - 1][j - 1]
        return dp[len(t)][len(s)]

class Solution(object):
    def numDistinct(self, s, t):
        dp = {}

        def backtrack(i, j):
            if j == len(t):
                return 1
            if i == len(s):
                return 0

            if (i, j) in dp:
                return dp[(i, j)]

            if s[i] == t[j]:
                dp[(i,j)] = backtrack(i + 1, j + 1) + backtrack(i + 1, j)
            else:
                dp[(i, j)] = backtrack(i + 1, j)

            return dp[(i, j)]

        return backtrack(0, 0)