Distinct Subsequences

Description

Given two strings S and 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

Example 1:

Input: S = "rabbbit", T = "rabbit"
Output: 3
Explanation: You could remove any 'b' in S, so there are 3 ways to get T.

Example 2:

Input: S = "abcd", T = ""
Output: 1
Explanation: There is only 1 way to get T - remove all chars in S.

Challenge

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

O(n^2​​) memory is also acceptable if you do not know how to optimize memory.

 

 public int numDistinct(String S, String T) {
        if (S == null || T == null) {
            return 0;
        }

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

        for (int i = 0; i <= S.length(); i++) {
            nums[i][0] = 1;
        }
        for (int i = 1; i <= S.length(); i++) {
            for (int j = 1; j <= T.length(); j++) {
                nums[i][j] = nums[i - 1][j];
                if (S.charAt(i - 1) == T.charAt(j - 1)) {
                    nums[i][j] += nums[i - 1][j - 1];
                }
            }
        }
        return nums[S.length()][T.length()];
    }

　　

 

来源：https://www.cnblogs.com/FLAGyuri/p/12078446.html