leetcode Distinct Subsequences DP

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[i][j] stands for the number of distince subsequences of T(First i characters) in S(First j characters)...


class Solution {
public:
    int numDistinct(string S, string T) {
        // Note: The Solution object is instantiated only once and is reused by each test case.
        vector< vector<int> > dp;
        vector<int> row(S.length()+1,0);
		vector<int> ones(S.length()+1,1);
        int i,j;
        
        if(S.length()<T.length())
            return 0;
        else{
			dp.push_back(ones);
            for(i=1;i<=T.length();i++)
                dp.push_back(row);			
            for(i=1;i<=T.length();i++){
                for(j=i;j<=S.length();j++)
                    if( T[i-1]==S[j-1] )
                        dp[i][j]=dp[i][j-1]+dp[i-1][j-1];
                    else
                        dp[i][j]=dp[i][j-1];
            }
        }
        return dp[T.length()][S.length()];
    }
};


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