leetcode_question_115 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.

Recurse:
Judge Small: Accepted!
Judge Large: Time Limit Exceeded

int numDistinct(string S, string T) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        int slen = S.length();        int tlen = T.length();        if(slen <= tlen){            if(S == T) return 1;            else return 0;        }                if(S[slen-1] != T[tlen-1]) return numDistinct(S.substr(0,slen-1), T);        else            return numDistinct(S.substr(0,slen-1), T) + numDistinct(S.substr(0,slen-1), T.substr(0,tlen-1));    }

dp:
Judge Small: Accepted!
Judge Large: Accepted!

int numDistinct(string S, string T) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        int col = S.length() + 1;        int row = T.length() + 1;        int** dp = new int*[row];        for(int i = 0; i < row; ++i)            dp[i] = new int[col];                for(int i = 0; i < row; ++i)            dp[i][0] = 0;        for(int j = 0; j < col; ++j)            dp[0][j] = 1;                for(int i = 1; i < row; ++i)            for(int j = 1; j < col; ++j)                if(T[i-1] == S[j-1]) dp[i][j] = dp[i-1][j-1] + dp[i][j-1];                else dp[i][j] = dp[i][j-1];                        int tmp = dp[row-1][col-1];                for(int i = 0; i < row; ++i)            delete[] dp[i];        delete[] dp;                return tmp;    }