127_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.

1:注意特殊情況；2:設置二維數組保存個數；3:如果T是空串，則返回1；4:動態規劃獲得相應的個數

    int numDistinct(string S, string T)
    {
        if(T.size() == 0)
        {
            return 1;
        }
        if(S.size() == 0 || T.size() > S.size())
        {
            return 0;
        }
        
        int rows = (int)T.length() + 1;
        int columns = (int)S.length() + 1;
        
        vector<vector<int> > result(rows, vector<int>(columns, 0));
        
        for(int i = 0; i < rows; i++)
        {
            for(int j = 0; j < columns; j++)
            {
             
                if(i == 0)
                {
                    result[i][j] = 1;
                }
                else if(j == 0)
                {
                    result[i][j] = 0;
                }
                else
                {
                    result[i][j] = result[i][j-1];
                    if(T[i-1] == S[j-1])
                    {
                        result[i][j] += result[i-1][j-1];
                    }
                }
            }
        }
        
        return result[rows-1][columns-1];
        
    }