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

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 7916 Accepted: 4199

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

66406

Source

Stanford Local 2004

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