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

.

Solution:

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

return dp[m]
;
}
};