115. 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).

Input: S = "rabbbit", T = "rabbit"
Output: 3
Explanation:


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

Idea : 

Build a 2d matrix
 if the s[I] == t[j]., then 
Two options: 
pick the last Char of t, then matrix[I][j] += matrix[I - 1][j - 1]
Not pick the last char of t, matrix[I][j] += matrix[I][j - 1]


 if the s[I] != t[j], 

matrix[I][j] += matrix[I][j - 1]