POJ2955(KB22-C 区间DP)

Brackets

Time Limit: 1000MSMemory Limit: 65536K

Total Submissions: 7823Accepted: 4151

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 … 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 i₁, i₂, …, i_m where 1 ≤ i₁ < i₂ < … < i_m ≤ n, a_i1a_i2 … a_im 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

Stanford Local 2004

 

//2017-05-22
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

int dp[110][110];//dp[l][r]表示区间l-r中括号匹配数
//若位置l和r匹配，dp[l][r] = max(dp[l][r], dp[l+1][r-1]+2)
//否则，dp[l][r] = max(dp[l][r], dp[l][k]+dp[k+1][r]

int main()
{
    string str;
    while(cin>>str) 
    {
        if(str[0] == 'e')break;
        int n = str.length();
        memset(dp, 0, sizeof(dp));
        for(int len = 1; len < n; len++){
            for(int i = 0; i+len < n; i++){
                int j = i+len;
                if((str[i] == '(' && str[j] == ')') || (str[i] == '[' && str[j] == ']'))dp[i][j] = max(dp[i][j], dp[i+1][j-1]+2);
                for(int k = i; k <= j; k++)
                  dp[i][j] = max(dp[i][j], dp[i][k]+dp[k+1][j]);
            }
        }
        cout<<dp[0][n-1]<<endl;
    }

    return 0;
}