POJ 2955 Brackets

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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;}

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