Brackets。区间划分DP，没有限制的区间划分。详见本文内容

Brackets

# 限制

Time Limit: 1000MS
Memory Limit: 65536K

# 描述

We give the following inductive definition of a “regular brackets” sequence:

• the empty sequence is a regular brackets sequence,
• if s is a regular brackets sequence, then (s) and [s] are regular brackets sequences, and
• if a and b are regular brackets sequences, then ab is a regular brackets sequence.
• no other sequence is a regular brackets sequence

For instance, all of the following character sequences are regular brackets sequences:
(), [], (()), ()[], ()[()]
while the following character sequences are not:
(, ], )(, ([)], ([(]
Given a brackets sequence of characters $a_1a_2…a_n$, your goal is to find the length of the longest regular brackets sequence that is a subsequence of $s$. That is, you wish to find the largest $m$ such that for indices $i_1, i_2, …, i_m$ where $1 \le i_1 \lt i_2 \lt … \lt i_m \le n$, $a_{i_1}a_{i_2} … a_{i_m}$ is a regular brackets sequence.
Given the initial sequence ([([]])], the longest regular brackets subsequence is [([])].

# 输入格式

The input test file will contain multiple test cases. Each input test case consists of a single line containing only the characters (, ), [, and ]; each input test will have length between $1$ and $100$, inclusive. The end-of-file is marked by a line containing the word “end” and should not be processed.

# 输出格式

For each input case, the program should print the length of the longest possible regular brackets subsequence on a single line.

# 思路

dp[a][b]存的是区间[a,b]内满足要求的符号表达式的最大长度。

16行的i是对区间长度进行迭代。17行的j是对不同的区间起始节点进行迭代。18行是对[j,j+i]区间的不同划分点进行迭代。