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.

Solution:

public class Solution {
    public int numDistinct(String s, String t) {
        int m = t.length();
        int n = s.length();
        int[][] dp = new int[m+1][n+1];
        for(int j=0; j<=n; j++) dp[0][j] = 1;
        for(int i=1; i<=m; i++){
            for(int j=1; j<=n; j++){
                if(s.charAt(j-1)==t.charAt(i-1)) dp[i][j] = dp[i-1][j-1] + dp[i][j-1];
                else dp[i][j] = dp[i][j-1];
            }
        }
        return dp[m][n];
    }
}