Leetcode: 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[] numberOfSubsequences = new int[T.length()+1];
        numberOfSubsequences[0]=1;
        HashMap<Character,ArrayList<Integer>> positions = new HashMap<Character,ArrayList<Integer>>();
        for(int i=T.length()-1; i>=0; i--)
        {
            if (!positions.containsKey(T.charAt(i)))
                positions.put(T.charAt(i), new ArrayList<Integer>());
            positions.get(T.charAt(i)).add(i);
        }
        for(int i=0; i<S.length(); i++)
        {
            if(positions.containsKey(S.charAt(i)))
            {
                for(Integer pos: positions.get(S.charAt(i)))
                {
                    numberOfSubsequences[pos+1] += numberOfSubsequences[pos];
                }
            }
        }
        return numberOfSubsequences[T.length()];
    }
}