[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.

接受了Edit Distance的教训，该用了vector<vector<int> >勉强过了大数据。f[i][j]表示S[i]和T[j]相同的情况下，产生的情况个数。

最后sum(f[i][T.size()]), 0<= i <= S.size()，就是结果了。

class Solution {
public:
    int numDistinct(string S, string T) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        vector<vector<int> > f(S.size()+1, vector<int>(T.size()+1));
        
        f[0][0] = 1;
        for(int i = 1; i <= S.size(); i++)
            f[i][0] = 0;
            
        for(int i = 1; i <= T.size(); i++)
            f[0][i] = 0;
            
        for(int i = 1; i <= S.size(); i++)
            for(int j = 1; j <= T.size(); j++)
                if (S[i-1] == T[j-1])
                {
                    f[i][j] = 0;
                    for(int k = 0; k < i; k++)
                        f[i][j] += f[k][j-1];
                }
                else
                    f[i][j] = 0;
        
        int sum = 0;
        for(int i = 0; i <= S.size(); i++)
            sum += f[i][T.size()];
            
        return sum;
    }
};