[LeetCode]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

.

思考：DP。

class Solution {
public:
int numDistinct(string S, string T) {
int slen = S.size();
int tlen = T.size();
vector<vector<int> > dp(tlen + 1, vector<int>(slen + 1, 0));
for(int i = 0; i <= slen; ++i) dp[0][i] = 1;
for(int i = 1; i <= tlen; ++i)
{
for(int j = 1; j <= slen; ++j)
{
if(S[j - 1] == T[i - 1])
{
dp[i][j] = dp[i][j - 1] + dp[i - 1][j - 1];
}
else
{
dp[i][j] = dp[i][j - 1];
}
}
}
return dp[tlen][slen];
}
};