[LeetCode] 115. Distinct Subsequences

Problem

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
    ^^^

Solution

class Solution {
    public int numDistinct(String s, String t) {
        int m = s.length(), n = t.length();
        if (m < n) return 0;
        int[][] dp = new int[m+1][n+1];
        for (int i = 0; i <= m; i++) dp[i][0] = 1;
        for (int j = 0; j < n; j++) {
            for (int i = 0; i < m; i++) {
                if (s.charAt(i) == t.charAt(j)) dp[i+1][j+1] = dp[i][j] + dp[i][j+1];
                else dp[i+1][j+1] = dp[i][j+1];
            }
        }
        return dp[m][n];
    }
}