BNUOJ 1268 PIGS

PIGS

Time Limit: 1000ms

Memory Limit: 10000KB

This problem will be judged on  PKU. Original ID: 1149
64-bit integer IO format: %lld      Java class name: Main

 

 

Mirko works on a pig farm that consists of M locked pig-houses and Mirko can't unlock any pighouse because he doesn't have the keys. Customers come to the farm one after another. Each of them has keys to some pig-houses and wants to buy a certain number of pigs. 
All data concerning customers planning to visit the farm on that particular day are available to Mirko early in the morning so that he can make a sales-plan in order to maximize the number of pigs sold. 
More precisely, the procedure is as following: the customer arives, opens all pig-houses to which he has the key, Mirko sells a certain number of pigs from all the unlocked pig-houses to him, and, if Mirko wants, he can redistribute the remaining pigs across the unlocked pig-houses. 
An unlimited number of pigs can be placed in every pig-house. 
Write a program that will find the maximum number of pigs that he can sell on that day.

 

Input

The first line of input contains two integers M and N, 1 <= M <= 1000, 1 <= N <= 100, number of pighouses and number of customers. Pig houses are numbered from 1 to M and customers are numbered from 1 to N. 
The next line contains M integeres, for each pig-house initial number of pigs. The number of pigs in each pig-house is greater or equal to 0 and less or equal to 1000. 
The next N lines contains records about the customers in the following form ( record about the i-th customer is written in the (i+2)-th line): 
A K1 K2 ... KA B It means that this customer has key to the pig-houses marked with the numbers K1, K2, ..., KA (sorted nondecreasingly ) and that he wants to buy B pigs. Numbers A and B can be equal to 0.

 

Output

The first and only line of the output should contain the number of sold pigs.

 

Sample Input

3 3

3 1 10

2 1 2 2

2 1 3 3

1 2 6

Sample Output

7

Source

Croatia OI 2002 Final Exam - First day

 

解题：最大流问题。买猪。建图是关键啊！0为源n+1为汇。把买者看成流网络上的点，最先选择某个猪舍跟源点建立边，容量为这个猪舍猪头数，第二个选择某个猪舍的与第一个选择这个猪舍的买者建立边，容量为无穷大。类推。。。最后把最后与某个猪舍建立边的买者，再与汇建立边，数目为此买者的购买量！为什么这样建图呢？首先是源点！源点到第一个买者，我们考虑的不仅仅是第一个买者的购买力，还要考虑其他人的购买力，所以干脆把整个猪舍的猪都卖掉！假想可以卖完！至于中间的边，就是让尽可能的猪留给后面的人可以来买，但是最后的人的购买力有限，最多只能购买那么多！所以与汇邻接的边的权值为买者的购买量！最后流到汇的就是卖出的猪的头数。

 

之所以可以这样建图，是因为题意是指，第一个人打开某个猪舍后，这个猪舍就不会关了，这里面的猪可以随意卖给其他人。

 

 

 

 

 1 #include <iostream>

 2 #include <cstdio>

 3 #include <cstring>

 4 #include <cstdlib>

 5 #include <vector>

 6 #include <climits>

 7 #include <algorithm>

 8 #include <cmath>

 9 #include <queue>

10 #define LL long long

11 #define INF 0x3f3f3f3f

12 using namespace std;

13 const int maxn = 1005;

14 int n,m,a[maxn],p[maxn];

15 int arc[maxn][maxn],pre[maxn],pigs[maxn];

16 int bfs(){

17     int u,v,f = 0;

18     queue<int>q;

19     while(true){

20         while(!q.empty()) q.pop();

21         memset(a,0,sizeof(a));

22         memset(p,0,sizeof(p));

23         a[0] = INF;

24         q.push(0);

25         while(!q.empty()){

26             u = q.front();

27             q.pop();

28             for(v = 0; v <= n+1; v++){

29                 if(!a[v] && arc[u][v] > 0){

30                     a[v] = min(a[u],arc[u][v]);

31                     p[v] = u;

32                     q.push(v);

33                 }

34             }

35             if(a[n+1]) break;

36         }

37         if(!a[n+1]) break;

38         for(u = n+1; u; u = p[u]){

39             arc[p[u]][u] -= a[n+1];

40             arc[u][p[u]] += a[n+1];

41         }

42         f += a[n+1];

43     }

44     return f;

45 }

46 int main(){

47     int i,j,k,buy,e;

48     while(~scanf("%d%d",&m,&n)){

49         memset(arc,0,sizeof(arc));

50         memset(pre,0,sizeof(pre));

51         for(i = 1; i <= m; i++)

52             scanf("%d",pigs+i);

53         for(i = 1; i <= n; i++){

54             scanf("%d",&k);

55             while(k--){

56                 scanf("%d",&e);

57                 if(pre[e]) arc[pre[e]][i] = INF;

58                 else arc[pre[e]][i] += pigs[e];

59                 pre[e] = i;

60             }

61             scanf("%d",&buy);

62             arc[i][n+1] += buy;

63         }

64         cout<<bfs()<<endl;

65     }

66     return 0;

67 }

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