Brackets
Time Limit: 1000MS   Memory Limit: 65536K
Total Submissions: 3624   Accepted: 1879

Description

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 i1i2, …, imwhere 1 ≤ i1 < i2 < … < im ≤ nai1ai2 … 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

Source

 #include<stdio.h>
#include<algorithm>
#include<string.h>
using namespace std;
char st[] ;
int a[][] ; bool check (int a , int b)
{
if (st[a] == '(' && st[b] == ')' )
return ;
if (st[a] == '[' && st[b] == ']' )
return ;
return ;
} int main ()
{
// freopen ("a.txt" , "r" , stdin ) ;
while () {
gets (st) ;
if (strcmp (st , "end") == )
break ;
memset (a , , sizeof(a) ) ;
int len = strlen (st) ;
for (int o = ; o <= len ; o++) {
for (int i = ; i < len - o + ; i++) {
int j = i + o ;
for (int k = i ; k < j ; k++ ) {
a[i][j - ] = max (a[i][j - ] , a[i][k] + a[k + ][j - ] ) ;
if (check (i , j - ) ) {
a[i][j - ] = max (a[i][j - ] , a[i + ][j - - ] + ) ;
}
}
}
}
printf ("%d\n" , a[][len - ] ) ;
}
return ;
}

区间dp感觉和merge sort有异曲同工之妙
从可行的最小区间出发,逐级上去,最终得到整段区间的最终结。

dp[i][j] 指[i , j]这段区间的最优解

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