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题目链接：

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 a1a2 … an, 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 i1, i2, …, im where 1 ≤ i1 < i2 < … < im ≤ n, ai1ai2 … aim is a regular brackets sequence.

Given the initial sequence ([([]])], the longest regular brackets subsequence is [([])].

Input

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.

Output

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

Sample Input

((()))

()()()

([]])

)[)(

([][][)

end

Sample Output

6

6

4

0

6

题目翻译：

‎我们给出了"常规括号"序列的以下归纳定义:‎

• ‎空序列是一个常规括号序列,‎
• ‎如果‎‎s‎‎是常规括号序列,则 (‎‎s‎‎) 和‎‎*‎‎s = 是常规括号序列,并且‎
• ‎如果‎‎a‎‎和‎‎b‎‎是常规括号序列,则‎‎ab‎‎是常规括号序列。‎
• ‎没有其他序列是常规括号序列‎

‎例如,以下所有字符序列都是常规括号序列:‎

(), [], (()), ()[], ()[()]

‎而以下字符序列不是:‎

(, ], )(, ([)], ([(]

‎给定一个字符的括号序列‎‎1‎‎a 2‎‎ ...‎‎a n‎‎,您的目标是找到最长的常规括号序列的长度,该括号序列是‎‎s‎‎的子序列。也就是说,您希望找到最大的 m,因此‎‎对于索引 i ‎‎1‎‎, ‎‎i‎‎2‎‎, ..., ‎‎i‎‎m‎‎其中 1 = ‎‎i‎‎1‎‎ < ‎‎i‎‎2‎‎ < ...< ‎‎i‎‎m‎‎ ‎‎ = ‎‎n‎‎, ‎‎a‎‎i‎‎1‎‎a‎‎i‎‎2‎‎ ‎‎ ...‎‎a‎‎m‎‎是一个常规括号序列。‎

‎给定初始序列,最长的常规括号子序列为 。‎([([]])][([])]

‎输入‎

‎输入测试文件将包含多个测试用例。每个输入测试用例由一行组成,仅包含字符 、 和 。每个输入测试的长度将在 1 到 100 之间,包括。文件结尾用包含单词"end"的行标记,不应进行处理。‎()[]

‎输出‎

‎对于每个输入情况,程序应在一行上打印尽可能长的常规括号子序列的长度。

‎

这道题可以说是最最经典的区间dp题了，也是一道十分好的题。

状态dp[i][j]表示从i区间到j区间内的匹配括号数。

状态转移方程

if(i和j匹配)

      dp[i][j]=dp[i+1][j-1]+2

dp[i][j]=max{dp[i][k]+dp[k][j]}k为最优分割点

#include 
   
    #include
    
     #include
     
      #include
      
        using namespace std;int main(int argc, char** argv) {	char str[1005]; 	int dp[105][105];	while(scanf("%s",str+1)!=EOF&&strcmp(str+1,"end")!=0)	{		int n=strlen(str+1);		memset(dp,0,sizeof(dp));		for(int len=2;len<=n;len++){			for(int i = 1;i<=n;i++){				int j = i+len-1;				if(j>n) break;				if(str[i]=='['&&str[j]==']'||str[i]=='('&&str[j]==')')				    dp[i][j]=dp[i+1][j-1]+2; 				for(int k = i;k
      
     
    
   

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