[LeetCode] Distinct Subsequences

原题地址：https://oj.leetcode.com/problems/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).

Here is an example:
S = "rabbbit", T = "rabbit"

Return 3.

思路：这道题等效与求T在S中出现的次数。动态规划的思想，golbal[i][j]代表S[0, i]  中 T[0,j]出现的次数。可以退出递推公式

当 S[i] = T[j] ，global[i][j] = global[i - 1][j - 1] + global[i - 1][j]

当 S[i] != T[j]，global[i][j] = global[i - 1][j]

根据递推公式写出代码如下：

public class Solution {    public int numDistinct(String S, String T) {        if (S == null || T == null || S.length() < 1 || T.length() > S.length()) {            return 0;        }                int[] global = new int[T.length() + 1];        global[0] = 1;                for (int i = 0; i < S.length(); i++) {            for (int j = T.length() - 1; j >= 0; j--) {                if (T.charAt(j) == S.charAt(i)) {                    global[j + 1] = global[j] + global[j + 1];                } else {                    global[j + 1] = global[j + 1];                }            }        }                return global[T.length()];    }}