1459 Power Network 网络流 SAP
2010-07-22 23:17
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Power Network
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.
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
Sample Output
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
#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int inf=(1<<31)-1;
const int point_num=300;
int cap[point_num][point_num],dist[point_num],gap[point_num];//初始化见main里面
int s0,t0,n;//源,汇和点数
int find_path(int p,int limit=0x3f3f3f3f)
{
if(p==t0) return limit;
for(int i=0;i<n;i++)
if(dist[p]==dist[i]+1 && cap[p][i]>0)
{
int t=find_path(i,min(cap[p][i],limit));
if(t<0) return t;
if(t>0)
{
cap[p][i]-=t;
cap[i][p]+=t;
return t;
}
}
int label=n;
for(int i=0;i<n;i++) if(cap[p][i]>0) label=min(label,dist[i]+1);
if(--gap[dist[p]]==0 || dist[s0]>=n ) return -1;
++gap[dist[p]=label];
return 0;
}
int sap()
{
//初始化s0,t0;
int t=0,maxflow=0;
gap[0]=n;
while((t=find_path(s0))>=0) maxflow+=t;
return maxflow;
}
int main()
{
int nb,nc,m;
int x,y,c;
while(scanf("%d%d%d%d",&n,&nb,&nc,&m)!=EOF)
{
//初始化
s0=n,t0=n+1;
memset(cap,0,sizeof(cap));
memset(dist,0,sizeof(dist));
memset(gap,0,sizeof(gap));
//初始化cap
for(int i=0;i<m;i++)
{
while(getchar()!='(');
scanf("%d,%d)%d",&x,&y,&c);
cap[x][y]+=c;
}
for(int i=0;i<nb;i++)
{
while(getchar()!='(');
scanf("%d)%d",&x,&c);
cap[s0][x]+=c;
}
for(int i=0;i<nc;i++)
{
while(getchar()!='(');
scanf("%d)%d",&x,&c);
cap[x][t0]+=c;
}
n+=2;//点数加2增加了源和汇
int ans=sap();
printf("%d/n",ans);
}
return 0;
}
Time Limit: 2000MS | Memory Limit: 32768K | |
Total Submissions: 10412 | Accepted: 5705 |
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.
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
#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int inf=(1<<31)-1;
const int point_num=300;
int cap[point_num][point_num],dist[point_num],gap[point_num];//初始化见main里面
int s0,t0,n;//源,汇和点数
int find_path(int p,int limit=0x3f3f3f3f)
{
if(p==t0) return limit;
for(int i=0;i<n;i++)
if(dist[p]==dist[i]+1 && cap[p][i]>0)
{
int t=find_path(i,min(cap[p][i],limit));
if(t<0) return t;
if(t>0)
{
cap[p][i]-=t;
cap[i][p]+=t;
return t;
}
}
int label=n;
for(int i=0;i<n;i++) if(cap[p][i]>0) label=min(label,dist[i]+1);
if(--gap[dist[p]]==0 || dist[s0]>=n ) return -1;
++gap[dist[p]=label];
return 0;
}
int sap()
{
//初始化s0,t0;
int t=0,maxflow=0;
gap[0]=n;
while((t=find_path(s0))>=0) maxflow+=t;
return maxflow;
}
int main()
{
int nb,nc,m;
int x,y,c;
while(scanf("%d%d%d%d",&n,&nb,&nc,&m)!=EOF)
{
//初始化
s0=n,t0=n+1;
memset(cap,0,sizeof(cap));
memset(dist,0,sizeof(dist));
memset(gap,0,sizeof(gap));
//初始化cap
for(int i=0;i<m;i++)
{
while(getchar()!='(');
scanf("%d,%d)%d",&x,&y,&c);
cap[x][y]+=c;
}
for(int i=0;i<nb;i++)
{
while(getchar()!='(');
scanf("%d)%d",&x,&c);
cap[s0][x]+=c;
}
for(int i=0;i<nc;i++)
{
while(getchar()!='(');
scanf("%d)%d",&x,&c);
cap[x][t0]+=c;
}
n+=2;//点数加2增加了源和汇
int ans=sap();
printf("%d/n",ans);
}
return 0;
}
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