leetcode-115. 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.

思路：

经典的DP问题，用result[i][j]表示长度为i的S转换到长度为j的T的结果数。

s[i-1]==t[j-1]的时候result[i][j]=result[i-1][j-1]+result[i-1][j];

s[i-1]!=t[j-1]的时候result[i][j]=result[i-1][j];

Acceped Code:

class Solution {
public:
    int numDistinct(string s, string t) {
        if(s.empty()||t.empty())
        return 0;
        if(s.length()<t.length())
        return 0;
        int len1=s.length();
        int len2=t.length();
        vector<vector<int>> result(len1+1,vector<int>(len2+1,0));
        for(int i=0;i<=len1;i++)
        result[i][0]=1;
        for(int i=1;i<=len1;i++)
        for(int j=1;j<=len2;j++)
        {
            result[i][j]=result[i-1][j];
            if(s[i-1]==t[j-1])
            result[i][j]+=result[i-1][j-1];
        }
        return result[len1][len2];
    }
};