/*DistinctSubsequences.java

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).

Example

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

Challenge Do it in O(n2) time and O(n) memory. O(n2) memory is also acceptable if you do not know how to optimize memory.

Tags String Dynamic Programming

*/

public class DistinctSubsequences {

/**

* @param S, T: Two string.

* @return: Count the number of distinct subsequences

*/

public int numDistinct(String S, String T) {

// write your code here

if (S == null || S.length() == 0 || T == null || T.length() == 0) {

return 0;

}

int[][] numDistinct = new int[S.length() + 1][T.length() + 1];

for (int i = 0; i <= S.length(); i++) {

numDistinct[i][0] = 1;

}

for (int i = 1; i <= S.length(); i++) {

for (int j = 1; j <= T.length(); j++) {

numDistinct[i][j] = numDistinct[i - 1][j];

if (S.charAt(i - 1) == T.charAt(j - 1)) {

numDistinct[i][j] += numDistinct[i - 1][j - 1];

}

}

}

return numDistinct[S.length()][T.length()];

}

public static void main(String[] args) {

DistinctSubsequences test = new DistinctSubsequences();

int result = test.numDistinct("abballl","abbal");

System.out.println("Expected: 3");

System.out.println(result);

}

}