POJ 2955 Brackets（区间DP水题）

题意：给出一个括号序列，求出最长的合法序列的长度。

思路：区间DP

#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<vector>
#include<map>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<set>
#include<ctime>
#define eps 1e-6
#define LL long long
#define pii pair<int, int>
//#pragma comment(linker, "/STACK:1024000000,1024000000")
using namespace std;

const int MAXN = 105;
char str[MAXN];
int dp[MAXN][MAXN];
int main() {
    //freopen("input.txt", "r", stdin);
	while(scanf("%s", str+1)==1 && str[1]!='e') {
		memset(dp, 0, sizeof(dp));
		int len = strlen(str+1);
		for(int i = 1; i < len; i++) 
			if((str[i]=='('&&str[i+1]==')' || str[i]=='['&&str[i+1]==']'))
				dp[i][i+1] = 2;
		for(int i = 3; i <= len; i++) {
			for(int j = 1; j+i-1 <= len; j++) {
				if(str[j]=='('&&str[j+i-1]==')' || str[j]=='['&&str[j+i-1]==']') dp[j][j+i-1] = dp[j+1][j+i-2] + 2;
				for(int k = j; k < j+i-1; k++) dp[j][j+i-1] = max(dp[j][j+i-1], dp[j][k]+dp[k+1][j+i-1]);
			}
		}
		cout << dp[1][len] << endl;
	}
    return 0;
}