distinct-subsequences

题目：

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”
Return3.

程序：

class Solution {public:    int numDistinct(string S, string T) {        int slen = S.length();        int tlen = T.length();                 vector<vector<int>> dp;        vector<int> temp(tlen+1,0);        temp[0] = 1;                 for( int i = 0; i <= slen; i++)            dp.push_back( temp );                 for( int i = 1; i <= slen ; i++)            for(int j = 1 ; j <= tlen ; j++)            {                if( S[i-1] == T[j-1] )                    dp[i][j] = dp[i-1][j] + dp[i-1][j-1];                else                    dp[i][j] = dp[i-1][j];            }         return dp[slen][tlen];    }};