POJ 2955 Brackets

dp[i][j]代表i~j区间内匹配括号的个数，状态转移方程为：

if(str[i]=='('&&str[j]==')'||str[i]=='['&&str[j]==']')
     dp[i][j]=dp[i+1][j-1]+2;
dp[i][j]=max{dp[i][k]+dp[k+1][j]};

代码如下：

#include<iostream>
#include<string>
#include<algorithm>

using namespace std;

string str;
int dp[105][105];

int main() {
    while (cin >> str, str != "end") {
        memset(dp, 0, sizeof(dp));
        int len = str.length();
        for (int k = 1; k < len; ++k) {
            for (int i = 0, j = k; j < len; ++i, ++j) {
                if ((str[i] == '('&&str[j] == ')') || (str[i] == '['&&str[j] == ']')) {
                    dp[i][j] = dp[i + 1][j - 1] + 2;
                }

                for (int x = i; x < j; ++x) {
                    dp[i][j] = max(dp[i][j], dp[i][x] + dp[x+1][j]);
                }
            }
        }
        cout << dp[0][len - 1] << endl;
    }
    return 0;
}