Problem Distinct Subsequence

Problem Desciption : 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 : 采用动态编程 (Dynamic Programming)的思路。mat[i][j]表示子问题S = S.substring(0, i-1), T= T.substring(0,j-1)的结果

public int numDistinct(String S, String T) {
        int slen = S.length();
        int tlen = T.length();
        if (slen == 0) return 0;
        if (tlen == 0) return 1;
        int[][] mat = new int[slen + 1][tlen +1];
        for (int i = 0; i <= slen; i++) mat[i][0] = 1;
        for (int i = 1; i <= slen; i++) 
            for (int j = 1; j <= tlen; j++) {
                if (S.charAt(i-1) == T.charAt(j-1))
                    mat[i][j] = mat[i-1][j-1] + mat[i-1][j];
                else 
                    mat[i][j] = mat[i-1][j];
        }

        return mat[slen][tlen];
    }