network flow （网络流模板题）-优快云博客

本文介绍了一种计算网络中两节点间最大带宽的方法，利用了包交换技术和网络流算法。通过实例展示如何在网络的不同路径上同时传输数据，以达到最大传输效率。

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Internet Bandwidth

On the Internet, machines (nodes) are richly interconnected, and many paths may exist between a given pair of nodes. The total message-carrying capacity (bandwidth) between two given nodes is the maximal amount of data per unit time that can be transmitted from one node to the other. Using a technique called packet switching, this data can be transmitted along several paths at the same time.

For example, the following figure shows a network with four nodes (shown as circles), with a total of five connections among them. Every connection is labeled with a bandwidth that represents its data-carrying capacity per unit time.

In our example, the bandwidth between node 1 and node 4 is 25, which might be thought of as the sum of the bandwidths 10 along the path 1-2-4, 10 along the path 1-3-4, and 5 along the path 1-2-3-4. No other combination of paths between nodes 1 and 4 provides a larger bandwidth.

You must write a program that computes the bandwidth between two given nodes in a network, given the individual bandwidths of all the connections in the network. In this problem, assume that the bandwidth of a connection is always the same in both directions (which is not necessarily true in the real world).

Input

The input file contains descriptions of several networks. Every description starts with a line containing a single integer n (2 ≤n ≤100), which is the number of nodes in the network. The nodes are numbered from 1 to n. The next line contains three numbers s, t, and c. The numbers s and t are the source and destination nodes, and the number c is the total number of connections in the network. Following this are c lines describing the connections. Each of these lines contains three integers: the first two are the numbers of the connected nodes, and the third number is the bandwidth of the connection. The bandwidth is a non-negative number not greater than 1000.

There might be more than one connection between a pair of nodes, but a node cannot be connected to itself. All connections are bi-directional, i.e. data can be transmitted in both directions along a connection, but the sum of the amount of data transmitted in both directions must be less than the bandwidth.

A line containing the number 0 follows the last network description, and terminates the input.

Output

For each network description, first print the number of the network. Then print the total bandwidth between the source node s and the destination node t, following the format of the sample output. Print a blank line after each test case.

Sample Input Output for the Sample Input

1 4 5

1 2 20

1 3 10

2 3 5

2 4 10

3 4 20

0 Network 1

The bandwidth is 25.

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ACM World Finals 2000, Problem E

#include <iostream>
#include <queue>
using namespace std;
#define N 101
int map[N][N],flow[N][N];
int f[N];

int network_flow(int n,int s,int t)
{
memset(flow,0,sizeof(flow));
    int rem[N],sum=0,d;
queue<int> q;
int u,v;
while(1)
{
  memset(rem,0,sizeof(rem));
  rem[s]=1001;
  q.push(s);
  while(!q.empty())
  {
   u=q.front();q.pop();
   for(v=1;v<=n;v++)
   {
    d=map[u][v]-flow[u][v];
    if(rem[v]==0&&d>0)
    {
     q.push(v);
     rem[v]=(rem[u]>d?d:rem[u]);
     f[v]=u;
    }
   }
  }
  if(rem[t]==0) break;
  for(v=t;v!=s;v=f[v])
  {
   flow[f[v]][v]+=rem[t];
   flow[v][f[v]]-=rem[t];
  }
  sum+=rem[t];
}
return sum;
}

int main()
{
int n;
int s,t,c;
int a,b,k;
int count=0;
while(cin>>n&&n)
{
  count++;
  cin>>s>>t>>c;
  while(c--)
  {
   cin>>a>>b>>k;
   map[a][b]=k;
   map[b][a]=k;
  }
  cout<<"Network "<<count<<endl;
  cout<<"The handwidth is "<<network_flow(n,s,t)<<endl;
}
return 0;
}