UVa-10817 Headmaster's Headache （位运算）

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Headmaster's Headache

The headmaster of SpringField School is consider-ing employing some newteachers for certain subjects.There are a number of teach-ers applying for the posts.Each teacher is able to teachone or more sub jects. Theheadmaster wants to selectapplicants so that each sub-ject is taught by at least twoteachers, and the overall costis minimized.

Input

The input consists of severaltest cases. The format ofeach of them is explained below:

The first line contains three positive integersS,M andN.S (≤8) is the number of subjects, M(≤20) is the number of serving teachers, andN (≤100) is the number of applicants.

Each of the following Mlines describes a serving teacher. It first gives the cost of employing him/her(10000≤ C≤ 50000), followed by a list of subjects that he/she can teach. The subjects are numberedfrom 1 toS.You must keep on employing all of them. After that there are Nlines, giving thedetails of the applicants in the same format.

Input is terminated by a null case where S = 0. This case should not be processed.

Output

For each test case, give the minimum cost to employ the teachers under the constraints.

Sample Input

2 2 2 

10000 1 

20000 2 

30000 1 2 

40000 1 2 

0 0 0

Sample Output

60000 

题意：

某校有m个教师和n个求职者，需讲授s个课程，已知每人的工资c和能教的课程集合，要求支付最少的工资使得每门课都至少有两名教师能教。在职教师不能辞退。

分析：

本题用到了子集的二进制表示，之前书上看得已经忘了……紫书上又提一遍，这次好好学习一下。

其实内容很简单，如果集合里有n个元素，则(1<

本题用s1表示恰好一个人教的科目集合，s2表示至少有两个人教的科目集合，d(i,s1,s2)表示已经考虑了前i个人时的最小花费。

状态转移方程d(i,s1,s2)=min{d(i+1,s1',s2')+c[i],d(i+1,s1,s2)}  （选与不选）

老师必须聘用，i

最终结果输出dp(0,(1<

如果能够掌握这里的二进制表示方法，其实是简单的dp题。