Distinct Subsequences

Given a string S and a string T, count the number of distinct subsequences of S which equals T.

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

public class Solution {
    public int numDistinct(String s, String t) {
        int m = s.length();
        int n = t.length();

        int[][] dp = new int[m + 1][n + 1];

        for(int i = 0; i <= m; i ++ ){
            dp[i][0] = 1;
        }

        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                if (s.charAt(i - 1) == t.charAt(j - 1)) {
                    dp[i][j] = dp[i - 1][j - 1] + dp[i-1][j];
                } else {
                    dp[i][j] = dp[i-1][j];
                }
            }
        }

        return dp[m][n];
    }
}