115. Distinct Subsequences (String; DP)

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.

class Solution {
public:
    int numDistinct(string S, string T) {
        int tLen = T.length();
        int sLen = S.length();
        if(sLen == 0) return 0;
        vector<vector<int>> dp(sLen,vector<int>(tLen)); //前j+1个T字符可以有多少种S的前i+1个字符变化而来 

        int i=0;
        int j=0;
        if(S[0]==T[0]) dp[0][0] = 1;
        else dp[0][0]=0;
        for(i = 1; i < tLen; i++)
            dp[0][i]=0;
        for(i = 1 ; i < sLen ;i++)
            if(S[i]==T[0])
                dp[i][0] = dp[i-1][0] + 1;
            else
                dp[i][0] = dp[i-1][0]; 

        for(int i = 1;  i < sLen ; i++)
            for(int j = 1; j < tLen ; j++)
                if(S[i]==T[j])
                    dp[i][j] = dp[i-1][j-1] + dp[i-1][j];
                else
                    dp[i][j] = dp[i-1][j];
       return dp[sLen-1][tLen-1];
    }
};