[Leetcode]Distinct Subsequences

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

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.

dp[i][j]表示T的前j位是S的前i位的子串的情况数。递推公式是如果S的第i位等于T的第j位, dp[i][j] = dp[i-1][j-1] + dp[i-1][j], 如果不等, dp[i][j] = dp[i-1][j]

class Solution:    # @return an integer    def numDistinct(self, S, T):        lenS, lenT = len(S), len(T)        if lenT == 0: return 1        if lenS == 0: return 0        dp = [[0 for j in xrange(lenT + 1)] for i in xrange(lenS + 1)]        for i in xrange(lenS + 1):            dp[i][0] = 1        for i in xrange(1, lenS + 1):            for j in xrange(1, lenT + 1):                dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j] if S[i -1] == T[j - 1] else dp[i - 1][j]        return dp[lenS][lenT]

还有一维动态规划的解法，参考http://blog.csdn.net/linhuanmars/article/details/23589057