POJ 1149

PIGS
Time Limit: 1000MS   Memory Limit: 10000K
Total Submissions: 15724   Accepted: 7023

Description

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 arrives, 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
 
有M个猪圈，从源点到第一个打开每个猪圈的顾客连一条边，容量为猪圈的初始猪数，然后打开同一个猪圈的打开者，按照打开的顺序依次往下一个打开者连一条容量
为无穷大的边，每个顾客向汇点连一条容量为他想买的猪数的边，走最大流
 
  1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <algorithm>
  5 #include <vector>
  6 #include <queue>
  7 
  8 using namespace std;
  9 
 10 const int MAX_M = 1005;
 11 const int MAX_N =105;
 12 int M, N;
 13 int pig[MAX_M];
 14 struct Edge {int from, to, cap, flow;};
 15 vector <int> p[MAX_M];
 16 int buy[MAX_N];
 17 vector <int> G[MAX_M];
 18 vector <Edge> edges;
 19 int _max = 0;
 20 int d[MAX_N];
 21 int cur[MAX_N];
 22 bool vis[MAX_N];
 23 
 24 void add_edge(int from, int to, int cap) {
 25         edges.push_back((Edge) {from, to, cap, 0});
 26         edges.push_back((Edge) {to, from, 0, 0});
 27         int m = edges.size();
 28         G[from].push_back(m - 2);
 29         G[to].push_back(m - 1);
 30 }
 31 
 32 
 33 
 34 void solve() {
 35         for (int i = 1; i <= N; ++i) {
 36                 add_edge(i, N + 1, buy[i]);
 37         }
 38 
 39         for (int i = 1; i <= M; ++i) {
 40                 if (p[i].size()) {
 41                         add_edge(0, p[i][0], pig[i]);
 42                         for (int j = 0; j < p[i].size() - 1; ++j) {
 43                                 add_edge(p[i][j], p[i][j + 1], _max);
 44                         }
 45                 }
 46         }
 47 
 48 }
 49 
 50 bool BFS(int s, int t) {
 51         memset(vis, 0, sizeof(vis));
 52         queue <int> q;
 53         q.push(s);
 54         d[s] = 0;
 55         vis[s] = 1;
 56         while (!q.empty()) {
 57                 int x = q.front(); q.pop();
 58                 for (int i = 0; i < G[x].size(); ++i) {
 59                         Edge &e = edges[ G[x][i] ];
 60                         if (!vis[e.to] && e.cap > e.flow) {
 61                                 vis[ e.to ] = 1;
 62                                 d[e.to] = d[x] + 1;
 63                                 q.push(e.to);
 64                         }
 65                 }
 66         }
 67 
 68         return vis[t];
 69 }
 70 
 71 int DFS(int x, int a, int t) {
 72         if (x == t || a == 0) return a;
 73         int flow = 0, f;
 74         for (int &i = cur[x]; i < G[x].size(); ++i) {
 75                 Edge &e = edges[ G[x][i] ];
 76                 if (d[x] + 1 == d[e.to] &&  (f = DFS(e.to, min(a, e.cap - e.flow), t))> 0) {
 77                         e.flow += f;
 78                         edges[ G[x][i] ^ 1].flow -= f;
 79                         flow += f;
 80                         a -= f;
 81                         if (a == 0) break;
 82                 }
 83         }
 84 
 85         return flow;
 86 }
 87 
 88 int Maxflow(int s, int t) {
 89         int flow = 0;
 90         while (BFS(s, t)) {
 91                 memset(cur, 0, sizeof(cur));
 92                 flow += DFS(s, _max, t);
 93         }
 94 
 95         return flow;
 96 }
 97 
 98 int main()
 99 {
100     //freopen("sw.in", "r", stdin);
101     scanf("%d%d", &M, &N);
102     for (int i = 1; i <= M; ++i) {
103             scanf("%d", &pig[i]);
104             _max += pig[i];
105     }
106     for (int i = 1; i <= N; ++i) {
107             int n;
108             scanf("%d", &n);
109             for (int j = 1; j <= n; ++j) {
110                     int ch;
111                     scanf("%d", &ch);
112                     p[ch].push_back(i);
113             }
114             scanf("%d", &buy[i]);
115     }
116 
117     solve();
118     printf("%d\n", Maxflow(0, N + 1));
119 
120 
121     //cout << "Hello world!" << endl;
122     return 0;
123 }
View Code

 

posted @ 2014-07-16 15:48  hyx1  阅读(134)  评论(0)  编辑  收藏  举报