[LeetCode] 027: Distinct Subsequences

[Problem]

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) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        
        // T is empty or S is empty
        if(T.size() == 0)return 1;
        if(S.size() == 0)return 0;
        
        // initial
        int **dp = new int*[T.size()+1];
        for(int i = 0; i <= T.size(); ++i){
            dp[i] = new int[S.size()+1];
        }
        
        // dp
        for(int i = T.size(); i >= 0; --i){
            for(int j = S.size(); j >= 0; --j){
                // set the bottom-right one
                if(i == T.size() && j == S.size()){
                    dp[i][j] = 1;
                }
                else if(i == T.size()){
                    dp[i][j] = 0;
                }
                else if(j == S.size()){
                    dp[i][j] = 0;
                }
                // dp
                else{
                    if(T[i] != S[j]){
                        dp[i][j] = dp[i][j+1];
                    }
                    else{
                        if(i == T.size()-1){
                            dp[i][j] = dp[i][j+1] + 1;
                        }
                        else{
                            dp[i][j] = dp[i][j+1] + dp[i+1][j+1];
                        }
                    }
                }
            }
        }
        return dp[0][0];
    }
};

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