Distinct Subsequences

Desicription

Given a string S and a string T, count the number of distinct subsequences of S which equals T.

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

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