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.

用一个二维数组进行DP，map[i][j] 表示T在长度前j位在S长度前i位合法的个数。当第i位和第j位char不同，我们只能考虑删掉第i位，相同时还能考虑保留第i为。

public class Solution {
    //Time: O(m * n)  Space: O(m * n)
    public int numDistinct(String S, String T) {
        if (S.length() < T.length()) {
            return 0;
        }
        
        int m = S.length();
        int n = T.length();
        int[][] map = new int[m + 1][n + 1];
        for (int i = 0; i <= m; i++) {
            map[i][0] = 1;
        }
        
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                map[i][j] += map[i - 1][j];
                if (S.charAt(i - 1) == T.charAt(j - 1)) {
                    map[i][j] += map[i - 1][j - 1];
                }
            }
        }
        return map[m][n];
    }
}