POJ 1459 Power Network(最大流)

发布时间:2023-06-13 09:28:28



建立超级源s,s到任何发电站i有(s,i,,p[i]) (说明发电站最多能发p[i]电)

建立超级汇点t,任何用户j到t有边(j,t,c[j]) (表示用户最多可以消耗C[j]电)

然后是标题中描述的M条电线(u,v)L, 就有边(u,v,L).


#include <cstdio>#include <queue>#include <cstring>#include <iostream>#include <cstdlib>#include <algorithm>#include <vector>#include <map>#include <string>#include <set>#include <ctime>#include <cmath>#include <cctype>using namespace std;#define maxn 550#define INF 1e9#define LLINF 1LL<<60#define LL long longint cas=1,T;struct Edge{int from,to,cap,flow;Edge(int u,int v,int c,int f):from(u),to(v),cap(c),flow(f){}};int n,m;struct Dinic{//int n,m;    int s,t;vector<Edge>edges;        ////边数的两倍vector<int> G[maxn];      ///邻接表,G[i][j]e数组中的序号bool表示结点i的第j条边 vis[maxn];           ///BFS使用int使用int d[maxn];              ////从起点到int的距离 cur[maxn];            ////当前弧下标void init(){   for (int i=0;i<=n+1;i++)   G[i].clear();   edges.clear();}void AddEdge(int from,int to,int cap){edges.push_back(Edge(from,to,cap,0));edges.push_back(Edge(to,from,0,0));        ///反向弧int mm=edges.size();G[from].push_back(mm-2);G[to].push_back(mm-1);}bool BFS(){memset(vis,0,sizeof(vis));queue<int>q;q.push(s);d[s]=0;vis[s]=1;while (!q.empty()){int x = q.front();q.pop();for (int i = 0;i<G[x].size();i++){Edge &e = edges[G[x][i]];if (!vis[e.to] && e.cap > e.flow){vis[e.to]=1;d[e.to] = d[x]+1;q.push(e.to);}}}return vis[t];}int DFS(int x,int a){if (x==t || a==0)return a;int flow = 0,f;for(int &i=cur[x];i<G[x].size();i++){Edge &e = edges[G[x][i]];if (d[x]+1 == d[e.to] && (f=DFS(e.to,min(a,e.cap-e.flow)))>0){e.flow+=f;edges[G[x][i]^1].flow-=f;flow+=f;a-=f;if (a==0)break;}}return flow;}int Maxflow(int s,int t){this->s=s;this->t=t;int flow = 0;while (BFS()){memset(cur,0,sizeof(cur));flow+=DFS(s,INF);}return flow;}}dc;int main(){int np,nc,m;while (scanf("%d%d%d%d",&n,&np,&nc,&m)!=EOF){dc.init();for (int i = 0;i<m;i++){int u,v,w;scanf(" (%d,%d)%d",&u,&v,&w);            ++u,++v;dc.AddEdge(u,v,w);}for (int i = 0;i<np;i++){int u,w;scanf(" (%d)%d",&u,&w);++u;dc.AddEdge(0,u,w);}for (int i = 0;i<nc;i++){int u,w;scanf(" (%d)%d",&u,&w);++u;dc.AddEdge(u,n+1,w);}printf("%d\n",dc.Maxflow(0,n+1));}//freopen("in","r",stdin); //printf("time=%.3lf",(double)clock()/CLOCKS_PER_SEC);return 0;}


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.


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.


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)207 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



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.

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