DistinctSubsequences.java

/*
 * 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).

Example
Given S = "rabbbit", T = "rabbit", return 3.

Challenge
Do it in O(n^2) time and O(n) memory.

O(n2) memory is also acceptable if you do not know how to 
optimize memory.
 */
public class DistinctSubsequences {

    /**
     * @param S, T: Two string.
     * @return: Count the number of distinct subsequences
     */
    public int numDistinct(String S, String T) {
        int[] dp = new int[T.length() + 1];
        dp[0] = 1;
        for (int i = 0; i < S.length(); ++i) {
            for (int j = T.length() - 1; j >= 0; --j) {
                if (S.charAt(i) == T.charAt(j)) {
                    dp[j + 1] += dp[j];
                }
            }
        }
        return dp[T.length()];
    }

/*******************************************************************/

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

}