Power Network
| Time Limit: 2000MS | Memory Limit: 32768K | |
| Total Submissions: 20743 | Accepted: 10866 |
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) <= pmax(u) of power, may consume an amount
0 <= c(u) <= min(s(u),cmax(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) <= lmax(u,v) of power delivered by u to v. Let Con=Σuc(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 pmax(u)=y. The label x/y of consumer u shows that c(u)=x and cmax(u)=y. The label x/y of power transport line (u,v) shows that l(u,v)=x and lmax(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.
An example is in figure 1. The label x/y of power station u shows that p(u)=x and pmax(u)=y. The label x/y of consumer u shows that c(u)=x and cmax(u)=y. The label x/y of power transport line (u,v) shows that l(u,v)=x and lmax(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 lmax(u,v). Follow np doublets (u)z, where u is the identifier of a power station and 0 <= z <= 10000 is the value of pmax(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 cmax(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.
Source
-----------测模板用的。
-----------
/** head-file **/
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <algorithm>
/** define-for **/
#define REP(i, n) for (int i=0;i<int(n);++i)
#define FOR(i, a, b) for (int i=int(a);i<int(b);++i)
#define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)
#define REP_1(i, n) for (int i=1;i<=int(n);++i)
#define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)
#define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)
#define REP_N(i, n) for (i=0;i<int(n);++i)
#define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)
#define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)
#define REP_1_N(i, n) for (i=1;i<=int(n);++i)
#define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)
#define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)
/** define-useful **/
#define clr(x,a) memset(x,a,sizeof(x))
#define sz(x) int(x.size())
#define see(x) cerr<<#x<<" "<<x<<endl
#define se(x) cerr<<" "<<x
#define pb push_back
#define mp make_pair
/** test **/
#define Display(A, n, m) {
REP(i, n){
REP(j, m) cout << A[i][j] << " ";
cout << endl;
}
}
#define Display_1(A, n, m) {
REP_1(i, n){
REP_1(j, m) cout << A[i][j] << " ";
cout << endl;
}
}
using namespace std;
/** typedef **/
typedef long long LL;
/** Add - On **/
const int direct4[4][2]={ {0,1},{1,0},{0,-1},{-1,0} };
const int direct8[8][2]={ {0,1},{1,0},{0,-1},{-1,0},{1,1},{1,-1},{-1,1},{-1,-1} };
const int direct3[6][3]={ {1,0,0},{0,1,0},{0,0,1},{-1,0,0},{0,-1,0},{0,0,-1} };
const int MOD = 1000000007;
const int INF = 0x3f3f3f3f;
const long long INFF = 1LL << 60;
const double EPS = 1e-9;
const double OO = 1e15;
const double PI = acos(-1.0); //M_PI;
const int maxm=1111111;
const int maxn=12222;
struct edgenode
{
int to,flow,next;
};
struct Dinic
{
int node,src,dest,edge;
int head[maxn],work[maxn],dis[maxn],q[maxn];
edgenode edges[maxm];
void prepare(int _node,int _src,int _dest)
{
node=_node,src=_src,dest=_dest;
for (int i=0; i<node; i++) head[i]=-1;
edge=0;
}
void addedge(int u,int v,int c)
{
edges[edge].flow=c,edges[edge].to=v,edges[edge].next=head[u],head[u]=edge++;
edges[edge].flow=0,edges[edge].to=u,edges[edge].next=head[v],head[v]=edge++;
}
bool Dinic_bfs()
{
int i,u,v,l,r=0;
for (i=0; i<node; i++) dis[i]=-1;
dis[q[r++]=src]=0;
for (l=0; l<r; l++){
for (i=head[u=q[l]]; i!=-1; i=edges[i].next){
if (edges[i].flow&&dis[v=edges[i].to]<0){
dis[q[r++]=v]=dis[u]+1;
if (v==dest) return true;
}
}
}
return false;
}
int Dinic_dfs(int u,int exp)
{
if (u==dest) return exp;
for (int &i=work[u],v,tmp; i!=-1; i=edges[i].next){
if (edges[i].flow&&dis[v=edges[i].to]==dis[u]+1&&
(tmp=Dinic_dfs(v,min(exp,edges[i].flow)))>0){
edges[i].flow-=tmp;
edges[i^1].flow+=tmp;
return tmp;
}
}
return 0;
}
int Dinic_flow()
{
int i,ret=0,delta;
while (Dinic_bfs()){
for (i=0; i<node; i++) work[i]=head[i];
while ( delta=Dinic_dfs(src,INF) ) ret+=delta;
}
return ret;
}
}solver;
int main()
{
int n,np,nc,m;
char cc;
//while (~scanf("%d%d%d%d",&n,&np,&nc,&m))
while (cin>>n>>np>>nc>>m)
{
solver.prepare(n+2,n,n+1);
REP(i,m)
{
int u,v,z;
//scanf("(%d,%d)%d",&u,&v,&z);
cin>>cc>>u>>cc>>v>>cc>>z;
solver.addedge(u,v,z);
}
REP(i,np)
{
int u,z;
//scanf("(%d)%d",&u,&z);
cin>>cc>>u>>cc>>z;
solver.addedge(n,u,z);
}
REP(i,nc)
{
int u,z;
//scanf("(%d)%d",&u,&z);
cin>>cc>>u>>cc>>z;
solver.addedge(u,n+1,z);
}
//printf("%d
",solver.Dinic_flow());
cout<<solver.Dinic_flow()<<endl;
}
return 0;
}