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