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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
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. 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 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 Source |
题意：
一个电网包含n个结点，这些结点通过电线连接。
结点一共有三种：
（1）电站：产生电能和传输电能
（2）消费者：消耗电能，也可传输电能
（3）调度站：不产生电能，不消耗电能，只传输电能。
现在要求最大消费电能。电站和消费者有多个。
分析：
新加入一个点作为源点，向每一个电站引一条弧，权值为最大生产电量
新加入一个点作为汇点，每个消费者都向它引一条弧，权值为最大消耗电量。
其他所有点不管是何种都可以看做是调度站，即进入等于输出。
构图完成，用最大流算法求解，本题暂用EK算法，复杂度较高。
代码：
#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
using namespace std;
#define maxn 110
#define INF 0x3f3f3f3f
int ans, s, t, n;
int a[maxn], pre[maxn];
int flow[maxn][maxn];
int cap[maxn][maxn];
void Edmonds_Karp()
{
queue<int> q;
memset(flow, 0, sizeof(flow));
ans = 0;
while(1)
{
memset(a, 0, sizeof(a));
a[s] = INF;
q.push(s);
while(!q.empty()) //bfs找增广路径
{
int u = q.front();
q.pop();
for(int v = 0; v < n; v++)
if(!a[v] && cap[u][v] > flow[u][v])
{
pre[v] = u;
q.push(v);
a[v] = min(a[u], cap[u][v]-flow[u][v]);
}
}
if(a[t] == 0) break;
for(int u = t; u != s; u = pre[u]) //改进网络流
{
flow[pre[u]][u] += a[t];
flow[u][pre[u]] -= a[t];
}
ans += a[t];
}
}
int main()
{
//freopen("poj_1459.txt", "r", stdin);
int m, u, v, c, np, nc;
while(~scanf("%d%d%d%d", &n, &np, &nc, &m))
{
s = n, t = n+1;
n += 2;
//cout << s << " " << t << " " << n << endl;
memset(cap, 0, sizeof(cap));
while(m--)
{
while(getchar() !='(');
scanf("%d,%d)%d", &u, &v, &c);
cap[u][v] = c;
}
while(np--)
{
while(getchar() != '(');
scanf("%d)%d", &v, &c);
cap[s][v] = c;
}
while(nc--)
{
while(getchar() != '(');
scanf("%d)%d", &u, &c);
cap[u][t] = c;
}
/*
for(int i = 0; i < n; i++)
{
for(int j = 0; j < n; j++)
cout << cap[i][j] << " ";
cout << endl;
}
*/
Edmonds_Karp();
printf("%d\n", ans);
}
return 0;
}