LeetCode 115. Distinct Subsequences

题意：

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.

题意开始没懂。 其实就是T有多少个自序列串可以构成S。

思路： 类似编辑距离的dp。

AC代码：

class Solution {
public:

    int numDistinct(string s, string t) {
        int n = s.length();
        int m = t.length();
        int inf = 1<<29;
        vector<int> temp(m+2, 0);
        vector< vector<int> > dp(n+2, temp);
        for(int i=0; i<=n; i++)
            dp[i][0] = 1;
        for(int i=1; i<=n; i++)
        {
            for(int j=1; j<=m; j++)
            {
                if(s[i-1]==t[j-1])
                    dp[i][j] += dp[i-1][j-1] + dp[i-1][j];
                else dp[i][j] += dp[i-1][j];
            }
        }
        return dp[n][m];
    }
};