DistinctSubsequences.java

public class DistinctSubsequences {
    /**
         * Given a string S and a string T, count the number of distinct subsequences of S which equals T.

         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 1:

         Input: S = "rabbbit", T = "rabbit"
         Output: 3
         Explanation:

         As shown below, there are 3 ways you can generate "rabbit" from S.
         (The caret symbol ^ means the chosen letters)

         rabbbit
         ^^^^ ^^
         rabbbit
         ^^ ^^^^
         rabbbit
         ^^^ ^^^
         Example 2:

         Input: S = "babgbag", T = "bag"
         Output: 5
         Explanation:

         As shown below, there are 5 ways you can generate "bag" from S.
         (The caret symbol ^ means the chosen letters)

         babgbag
         ^^ ^
         babgbag
         ^^    ^
         babgbag
         ^    ^^
         babgbag
         ^  ^^
         babgbag
         ^^^
     */

    public static int numDistinct(String s, String t) {
        if(s == null || t == null) return 0;
        int[][] dp = new int[s.length() + 1][t.length() + 1];
        for(int i = 0; i < dp.length; i++) {
            dp[i][0] = 1;
        }
        for(int i = 1; i < dp.length; i++) {
            for(int j = 1; j <= Math.min(i, dp[0].length - 1); j++) {
                if(s.charAt(i - 1) == t.charAt(j - 1)) {
                    dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j];
                } else {
                    dp[i][j] = dp[i - 1][j];
                }
            }
        }
        return dp[s.length()][t.length()];
    }
    public static void main(String[] args) {
        numDistinct("rabbbit", "rabbit");
    }
}