CF417D——Cunning Gena(状态压缩DP)-白红宇

CF417D——Cunning Gena(状态压缩DP)

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发布时间：2019-05-26

本文共 2438 字，大约阅读时间需要 8 分钟。

A boy named Gena really wants to get to the "Russian Code Cup" finals, or at least get a t-shirt. But the offered problems are too complex, so he made an arrangement with his n friends that they will solve the problems for him.

The participants are offered m problems on the contest. For each friend, Gena knows what problems he can solve. But Gena's friends won't agree to help Gena for nothing: the i-th friend asks Gena xi rubles for his help in solving all the problems he can. Also, the friend agreed to write a code for Gena only if Gena's computer is connected to at least ki monitors, each monitor costs b rubles.

Gena is careful with money, so he wants to spend as little money as possible to solve all the problems. Help Gena, tell him how to spend the smallest possible amount of money. Initially, there's no monitors connected to Gena's computer.

Input

The first line contains three integers n, m and b (1 ≤ n ≤ 100; 1 ≤ m ≤ 20; 1 ≤ b ≤ 109) — the number of Gena's friends, the number of problems and the cost of a single monitor.

The following 2n lines describe the friends. Lines number 2i and (2i + 1) contain the information about the i-th friend. The 2i-th line contains three integers xi, ki and mi (1 ≤ xi ≤ 109; 1 ≤ ki ≤ 109; 1 ≤ mi ≤ m) — the desired amount of money, monitors and the number of problems the friend can solve. The (2i + 1)-th line contains mi distinct positive integers — the numbers of problems that thei-th friend can solve. The problems are numbered from 1 to m.

Output

Print the minimum amount of money Gena needs to spend to solve all the problems. Or print -1, if this cannot be achieved.

     Sample test(s) 
       input 
2 2 1100 1 12100 2 11
       output 
202
       input 
3 2 5100 1 11100 1 12200 1 21 2
       output 
205
       input 
1 2 11 1 11
       output 
-1

题意：

有个笨蛋自己不会做题，但是想要获得比赛的胜利，于是就想请外援帮助。但是外援不肯免费帮他，所以要好处。

笨蛋有n个朋友，第i个朋友的收费是Xi，并且要求笨蛋至少有Ki个显示器，每个显示器价格b，并且告诉你这个朋友会做的题目。

笨蛋要想做出所有的题目至少要花多少钱，不能完成输出-1。

分析：

这题给的m比较小只有20。所以可以用状态压缩，用一个int表示一个状态。

如果将显示器也加到状态里面肯定是存不下的，而且也没有必要。

所以dp[i]表示，对于i状态来说所需的最小费用。（没有包含显示器成本）

首先按照要求显示器的数量，将所有的朋友排序，然后按照这个顺序DP。

#include 
   
    #include 
    
     #include 
     
      #include 
      
       #include 
       
        #include 
        
         using namespace std;typedef long long LL;const LL INF = 4e18;struct node{ int x,k,s;}f[105];LL dp[ (1<<20)+10 ];int cmp(node a,node b){ return a.k

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