poj 1459 -- Power Network

浏览数：32 / 时间：2015年06月09日

Power Network

Time Limit: 2000MS		Memory Limit: 32768K
Total Submissions: 22517		Accepted: 11800

Description

A power network consists of nodes (power stations, consumers and dispatchers) connected by power transport lines. A node u may be supplied with an amount s(u) >= 0 of power, may produce an amount 0 <= p(u) <= p_max(u) of power, may consume an amount 0 <= c(u) <= min(s(u),c_max(u)) of power, and may deliver an amount d(u)=s(u)+p(u)-c(u) of power. The following restrictions apply: c(u)=0 for any power station, p(u)=0 for any consumer, and p(u)=c(u)=0 for any dispatcher. There is at most one power transport line (u,v) from a node u to a node v in the net; it transports an amount 0 <= l(u,v) <= l_max(u,v) of power delivered by u to v. Let Con=Σ_uc(u) be the power consumed in the net. The problem is to compute the maximum value of Con.

An example is in figure 1. The label x/y of power station u shows that p(u)=x and p_max(u)=y. The label x/y of consumer u shows that c(u)=x and c_max(u)=y. The label x/y of power transport line (u,v) shows that l(u,v)=x and l_max(u,v)=y. The power consumed is Con=6. Notice that there are other possible states of the network but the value of Con cannot exceed 6.

Input

There are several data sets in the input. Each data set encodes a power network. It starts with four integers: 0 <= n <= 100 (nodes), 0 <= np <= n (power stations), 0 <= nc <= n (consumers), and 0 <= m <= n^2 (power transport lines). Follow m data triplets (u,v)z, where u and v are node identifiers (starting from 0) and 0 <= z <= 1000 is the value of l_max(u,v). Follow np doublets (u)z, where u is the identifier of a power station and 0 <= z <= 10000 is the value of p_max(u). The data set ends with nc doublets (u)z, where u is the identifier of a consumer and 0 <= z <= 10000 is the value of c_max(u). All input numbers are integers. Except the (u,v)z triplets and the (u)z doublets, which do not contain white spaces, white spaces can occur freely in input. Input data terminate with an end of file and are correct.

Output

For each data set from the input, the program prints on the standard output the maximum amount of power that can be consumed in the corresponding network. Each result has an integral value and is printed from the beginning of a separate line.

Sample Input

2 1 1 2 (0,1)20 (1,0)10 (0)15 (1)20
7 2 3 13 (0,0)1 (0,1)2 (0,2)5 (1,0)1 (1,2)8 (2,3)1 (2,4)7
         (3,5)2 (3,6)5 (4,2)7 (4,3)5 (4,5)1 (6,0)5
         (0)5 (1)2 (3)2 (4)1 (5)4

Sample Output

15
6

Hint

The sample input contains two data sets. The first data set encodes a network with 2 nodes, power station 0 with pmax(0)=15 and consumer 1 with cmax(1)=20, and 2 power transport lines with lmax(0,1)=20 and lmax(1,0)=10. The maximum value of Con is 15. The second data set encodes the network from figure 1.

第一道网络流的题。必须加两个点作为源点和汇点。（a，b）c 相当与a--b间的容量为c

（a）b相当于从源点到a点的容量或者从a点到汇点的容量，建图后，用dinic即可求出。

  1 /*======================================================================
  2  *           Author :   kevin
  3  *         Filename :   PowerNetwork.cpp
  4  *       Creat time :   2014-07-16 09:41
  5  *      Description :
  6  ========================================================================*/
  7 #include <iostream>
  8 #include <algorithm>
  9 #include <cstdio>
 10 #include <cstring>
 11 #include <queue>
 12 #include <cmath>
 13 #define clr(a,b) memset(a,b,sizeof(a))
 14 #define M 105
 15 #define INF 0x7f7f7f7f
 16 using namespace std;
 17 struct Edge{
 18     int from,to,cap,flow;
 19 };
 20 int n,np,nc,m,supers,supert;
 21 vector<Edge> edges;
 22 vector<int> G[M];
 23 bool vis[M];
 24 int d[M],cur[M];
 25 bool BFS()
 26 {
 27     clr(vis,0);
 28     queue<int>Q;
 29     Q.push(supers);
 30     d[supers] = 0;
 31     vis[supers] = 1;
 32     while(!Q.empty()){
 33         int x = Q.front(); Q.pop();
 34         int len = G[x].size();
 35         for(int i = 0; i < len; i++){
 36             Edge& e = edges[G[x][i]];
 37             if(!vis[e.to] && e.cap > e.flow){
 38                 vis[e.to] = 1;
 39                 d[e.to] = d[x]+1;
 40                 Q.push(e.to);
 41             }
 42         }
 43     }
 44     return vis[supert];
 45 }
 46 int DFS(int x,int a)
 47 {
 48     if(x == supert || a == 0) return a;
 49     int flow = 0,f;
 50     int len = G[x].size();
 51     for(int& i = cur[x]; i < len; i++){
 52         Edge& e = edges[G[x][i]];
 53         if(d[x] + 1 == d[e.to] && (f = DFS(e.to,min(a,e.cap-e.flow))) > 0){
 54             e.flow += f;
 55             edges[G[x][i]^1].flow -= f;
 56             flow += f;
 57             a -= f;
 58             if(a == 0) break;
 59         }
 60     }
 61     return flow;
 62 }
 63 void AddEdge(int from,int to,int cap)
 64 {
 65     edges.push_back((Edge) {from,to,cap,0});
 66     edges.push_back((Edge) {to,from,0,0});
 67     int m = edges.size();
 68     G[from].push_back(m-2);
 69     G[to].push_back(m-1);
 70 }
 71 int Dinic(int s,int t)
 72 {
 73     int flow = 0;
 74     while(BFS()){
 75         clr(cur,0);
 76         flow += DFS(s,INF);
 77     }
 78     return flow;
 79 }
 80 int main(int argc,char *argv[])
 81 {
 82     int u,v,cap;
 83     while(scanf("%d%d%d%d",&n,&np,&nc,&m)!=EOF){
 84         char str[10];
 85         for(int i = 0; i < m; i++){
 86             scanf("%s",str);
 87             sscanf(str,"(%d,%d)%d",&u,&v,&cap);
 88             AddEdge(u,v,cap);
 89         }
 90         supers = n;
 91         int num;
 92         for(int i = 0; i < np; i++){
 93             scanf("%s",str);
 94             sscanf(str,"(%d)%d",&num,&cap);
 95             AddEdge(supers,num,cap);
 96         }
 97         supert = n+1;
 98         for(int i = 0; i < nc; i++){
 99             scanf("%s",str);
100             sscanf(str,"(%d)%d",&num,&cap);
101             AddEdge(num,supert,cap);
102         }
103         int ans = Dinic(supers,supert);
104         printf("%d\n",ans);
105         edges.clear();
106         for(int i = 0; i < M; i++)
107             G[i].clear();
108     }
109     return 0;
110 }