https://leetcode.com/problems/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.

定义f[i][j]表示在S[0,i]中，T[0,j]出现了几次。无论s[i]和t[j]是否相等，如果不匹配s[i]，则f[i][j]=f[i-1][j];若s[i]==s[j]，

f[i][j]=f[i-1][j]+[i-1][j-1]。

另外，当t=""时，只有一种匹配方式，f[i][0]=1；当s="",t!=""时，无论如何无法匹配，此时f[0][j]=0。

 参考：http://www.cnblogs.com/yuzhangcmu/p/4196373.html

int numDistinct(string s, string t) {
        int m=s.size();
        int n=t.size();
        
        vector<vector<int>> f(m+1,vector<int>(n+1,0));
        
        for(int i=0;i<=m;i++)
        {
            for(int j=0;j<=n;j++)
            {
                if(i==0 && j==0)
                  f[i][j]=1;
                else if(i==0)
                  f[i][j]=0;
                else if(j==0)
                  f[i][j]=1;
                else
                f[i][j]=f[i-1][j]+(s[i-1]==t[j-1]?f[i-1][j-1]:0);
            }
        }
        return f[m][n];
    }

Distinct Subsequences