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