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POJ 2955 Brackets (区间DP)


题意:

求区间内  最多正确的括号匹配数。

思路:

令dp[i][j] 表示i~j 区间内 最多正确的括号匹配数。

那么

dp[i][j] = max(dp[i,k] + dp[k+1][j]);

注意边界即可。

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn = 100 + 10;
char s[maxn];

int dp[maxn][maxn];
bool match(int a,int b){
    if (a == '(') return b == ')';
    if (a == '[') return b == ']';
    return 0;
}


int main(){
    while(~scanf("%s",s) && s[0] != 'e'){
        int len = strlen(s);

        for (int i = 0; i < len -1 ; ++i){
            dp[i][i] = 0;
            if (match(s[i], s[i+1])){
                dp[i][i+1] = 2;

            }
            else dp[i][i+1] = 0;

        }
        dp[len-1][len-1] = 0;

        for (int i = 3; i <= len; ++i){
            for (int j = 0; j+i-1 < len; ++j){
                int fi = j;
                int la = j+i-1;
                if (match(s[fi], s[la])){
                    dp[fi][la] = dp[fi+1][la-1] + 2;
                }
                else dp[fi][la] = 0;
                for (int k = fi; k < la; ++k){
                    dp[fi][la] = max(dp[fi][la], dp[fi][k] + dp[k+1][la]);

                }

            }

        }
        printf("%d\n", dp[0][len-1]);
    }

    return 0;
}



Brackets



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


66406


Source



Stanford Local 2004

Time Limit: 1000MS

 

Memory Limit: 65536K

Total Submissions: 7916

 

Accepted: 4199


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