Brackets

Time Limit: 1000MS   Memory Limit: 65536K
Total Submissions: 8716   Accepted: 4660

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, …, im where 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

分析

dp[l][r]表示区间[l,r]的答案。

状态转移方程,详见代码

  • dp[i][j] = max(dp[i+1][j],dp[i][j-1]);
  • if ((s[i]=='('&&s[j]==')')||(s[i]=='['&&s[j]==']'))
      dp[i][j]=dp[i+1][j-1]+2;
  • dp[l][r]=max(dp[l][r],dp[l][k]+dp[k+1][r]);

code

 #include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
char s[];
int dp[][]; int main()
{
while (scanf("%s",s)!=EOF)
{
memset(dp,,sizeof(dp));
if (s[]=='e') break;
int len = strlen(s);
for (int i=len-; i>=; --i)
{
for (int j=i; j<len; ++j)
{
dp[i][j] = max(dp[i+][j],dp[i][j-]);
if ((s[i]=='('&&s[j]==')')||(s[i]=='['&&s[j]==']'))
dp[i][j]=dp[i+][j-]+;
for (int k=i; k<j; ++k)
dp[i][j] = max(dp[i][j],dp[i][k]+dp[k+][j]);
}
}
printf("%d\n",dp[][len-]);
}
return ;
}

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