115.distinct-subsequences

Given a string S and a string T, count the number of distinct subsequences of S which equals T.



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



Here is an example:
S = "rabbbit", T = "rabbit"


Return 3.

class Solution(object):
    # space O(n^2)
    def _numDistinct(self, s, t):
        """
        :type s: str
        :type t: str
        :rtype: int
        """
        dp = [[0] * (len(t) + 1) for _ in xrange(0, len(s) + 1)]
        
        for i in xrange(0, len(s) + 1):
            dp[i][0] = 1
        
        for i in xrange(1, len(s) + 1):
            for j in xrange(1, len(t) + 1):
                dp[i][j] += dp[i - 1][j]
                if t[j - 1] == s[i - 1]:
                    dp[i][j] += dp[i - 1][j - 1]
        
        return dp[-1][-1]
        
    def numDistinct(self, s, t):
        """
        :type s: str
        :type t: str
        :rtype: int
        """
        dp = [0] * (len(t) + 1)
        for i in xrange(1, len(s) + 1):
            pre = 1
            for j in xrange(1, len(t) + 1):
                tmp = dp[j]
                if t[j - 1] == s[i - 1]:
                    dp[j] += pre
                pre = tmp
        return dp[-1]