115.leetcode Distinct Subsequences(hard)[动态规划]

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.

题目的含义是要求T成为S的子串的形成方式的个数。组成动态规划状态数组L[t.length()+1][s.length()+1].

class Solution {public:    int numDistinct(string s, string t) {        if(s.length()<t.length()||t.length()==0||s.length()==0) return 0;        int n = s.length(),m = t.length();        int L[m+1][n+1];        for(int i=0;i<=m;i++)            for(int j=0;j<=n;j++)              L[i][j] = 0;        for(int j=0;j<=n;j++)              L[0][j] = 1;        for(int i=1;i<=m;i++)        {            for(int j = i; j<=n;j++)            {                if(s[j-1] == t[i-1])                {                     L[i][j] = L[i-1][j-1]+L[i][j-1];                }else                     L[i][j] = L[i][j-1];                            }                }        return L[m][n];    }                                                                                                                                          };