Distinct Subsequences.java

Distinct SubsequencesOct 19 '12
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.

f(i, j) = f(i - 1, j) + S[i] == T[j]? f(i - 1, j - 1) : 0 Where f(i, j) is the number of distinct sub-sequence for T[0:j] in S[0:i].

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