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.
int numDistinct(string S, string T) {
vector<vector<int> > dp(S.size() + 1, vector<int>(T.size() + 1, 0));
for(int i = 0; i <= S.size(); ++i) dp[i][0] = 1;
for(int i = 1; i <= S.size(); ++i){
for(int j = 1; j <= T.size(); ++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[S.size()][T.size()];
}
Leetcode dp Distinct Subsequences
原文：http://blog.csdn.net/zhengsenlie/article/details/39323571