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.

动态规划：

状态转移公式可以写成

   if（T[m-1] == S[n-1])

　　　　ans[m][n] = ans[m-1][n-1] + ans[m-1][n]

   else

　　　　ans[m][n] = ans[m-1][n]

5:确定边界显然所有的问题都可以由ans[i][1]递推得到。其中i = 1,2,3,4。。。。。

6.AC代码

class Solution {
public:
    int numDistinct(string S, string T) {
        vector<vector<int>> dp( S.size() + 1, vector<int>(T.size() + 1,0) );

        int counts = 0;
        for(int i = 1; i <= S.size(); ++i){
            if(S[i - 1] == T[0]){
                ++counts;
            }
            dp[i][1] = counts;
        }
        for(int i = 2; i <= T.size(); ++i)
            for(int j = i; j <= S.size(); ++j){
                f(i,j,dp,S,T);
            }
        return dp[S.size()][T.size()];
    }
    void f(int n, int m, vector<vector<int>> &dp, string &S, string &T){
        if(S[m - 1] == T[n - 1]){
            dp[m][n] = dp[m - 1][n] + dp[m - 1][n - 1];
        }else{
            dp[m][n] = dp[m - 1][n];
        }
    }
};