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.

#include<iostream>
#include<vector>
#include<string>
using namespace std;

int numDistinct(string S, string T) {
	int lengthS = S.size();
	int lengthT = T.size();

	vector<vector<int>>M(lengthS+1,vector<int>(lengthT+1,0));
	for (int i =0;i!=M.size();++i)
		M[i][0] =1;
	for (int i =1;i!=M.size();++i)
	{
		for (int j =1;j!=lengthT+1;++j)
		{
			if (S[i-1]==T[j-1])
				M[i][j] = M[i-1][j-1]+M[i-1][j];
			else
				M[i][j] = M[i-1][j];
		}
	}
	return M[lengthS][lengthT];
}

Distinct Subsequences

原文：http://blog.csdn.net/li_chihang/article/details/44778775