[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.

思考：DP。

class Solution {
public:
    int numDistinct(string S, string T) {
        int slen = S.size();
        int tlen = T.size();
        vector<vector<int> > dp(tlen + 1, vector<int>(slen + 1, 0));
        for(int i = 0; i <= slen; ++i) dp[0][i] = 1;
        for(int i = 1; i <= tlen; ++i)
        {
            for(int j = 1; j <= slen; ++j)
            {
                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[tlen][slen];
    }
};