滚动数组优化DP空间复杂度

用DP + 滚动数组优化空间

题目： 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.

此题用二维DP解决，通常DP 时间复杂度O(N * M)，空间复杂度也为O(N * M), 但是我们可以用滚动数组优化空间降低到O(N)。对于二维DP, 可以优化为一维的空间，如何优化比较tricky，如果有初始化的，需要动态初始化，因为滚动数组要重复使用该值，非常重要的一点是 这里被优化的维度必须在外层循环。

参见程序如下

共三种方式解决