【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.

 

class Solution {
public:
    int numDistinct(string s, string t) {
        int lenS=s.size();
        int lenT=t.size();

        vector<vector<int> >f(lenS+1,vector<int>(lenT+1,0));

        for(int i=0;i<=lenS;i++) f[i][0]=1;

        for(int i=1;i<=lenS;i++)
        {
            for(int j=1;j<=lenT;j++)
            {
                if(s[i-1]==t[j-1])
                    f[i][j]=f[i-1][j-1]+f[i-1][j];
                else
                    f[i][j]=f[i-1][j];
            }
        }

        return f[lenS][lenT];


    }
};