# LeetCode Distinct Subsequences

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.

DP转移公式如下：

class Solution {
public:
int numDistinct(string s, string t) {
if (s == "")
return 0;
if (t == "")
return 1;
s = "^" + s;
t = "^" + t;
int n = s.size(), m = t.size();
vector<vector<int>> dp(n, vector<int>(m, 0));
for (int i = 0; i < n; i++)
dp[i][0] = 1; // '*' -> '' 1 sub
for (int i = 1; i < n; i++)
{
for (int j = 1; j < m; j++)
{
dp[i][j] = dp[i - 1][j];
if (s[i] == t[j])
dp[i][j] += dp[i - 1][j - 1];
}
}
return dp[n - 1][m - 1];
}
};