/// <summary>
/// 是否存在一个增广路径
/// </summary>
/// <param name="G"></param>
/// <param name="s">st图的起点</param>
/// <param name="t">汇点</param>
/// <returns></returns>
private bool HasAugmentingPath(FlowNetwork G, int s, int t)
{
marked = new bool[G.V];
edgeTo = new FlowEdge[G.V];
Queue <int> q = new Queue <int>();
marked[s] = true;
q.Enqueue(s);
while (q.Count > 0 && !marked[t])
{
int v = q.Dequeue();
foreach (FlowEdge e in G.GetEdge(v))//类似于 BFS 探测。
{
int w = e.Other(v);
if (!marked[w] && e.ResidualCapacityTo(w) > 0) // w点没有访问，同时返回从 v-> w 的剩余流量（容量-当前的流量）
{
//在剩余网络中，对于任意一条连接到一个未被标记的顶点的边
edgeTo[w] = e;
marked[w] = true;
q.Enqueue(w);
}
}
}
return(marked[t]);
}
private double Excess(FlowNetwork G, int v)
{
double excess = 0.0;
foreach (FlowEdge e in G.GetEdge(v))
{
if (v == e.Src)
{
excess -= e.Flow();
}
else
{
excess += e.Flow();
}
}
return(excess);
}
/// <summary>
/// 检查顶点 v 的局部平衡
/// </summary>
/// <param name="G"></param>
/// <param name="v"></param>
/// <returns></returns>
private bool LocalEq(FlowNetwork G, int v)
{
double netflow = 0.0;//净流量
foreach (FlowEdge e in G.GetEdge(v))
{
if (v == e.Src)
{
netflow -= e.Flow();//流出的流量
}
else
{
netflow += e.Flow();//流入的流量
}
}
return(Math.Abs(netflow) < FLOATING_POINT_EPSILON);
}
private bool IsFeasible(FlowNetwork G, int s, int t)
{
for (int v = 0; v < G.V; v++)
{
foreach (FlowEdge e in G.GetEdge(v))
{
if (e.Flow() < 0.0 || e.Flow() > e.Capacity) // 必须满足限制
{
//JAVA : System.err.println("Edge does not satisfy capacity constraints: " + e);
return(false);
}
}
}
//检查每个顶点的局部平衡
for (int v = 0; v < G.V; v++)
{
if (v != s && v != t && !LocalEq(G, v))
{
return(false);
}
}
return(true);
}
public static void Main(String[] args)
{
if (args.Length < 1)
{
Console.WriteLine("<digraph file>");
return;
}
FlowNetwork flowNetwork = new FlowNetwork(System.IO.File.OpenText(args[0]));
int s = 0, t = flowNetwork.V - 1;
FordFulkerson maxFlow = new FordFulkerson(flowNetwork, s, t);
Console.WriteLine("最大流 从{0} 到 {1}", s, t);
for (int v = 0; v < flowNetwork.V; ++v)
{
foreach (FlowEdge edge in flowNetwork.GetEdge(v))
{
if (v == edge.Src && edge.Flow() > 0)
{
Console.WriteLine("\t" + edge);
}
}
}
Console.WriteLine("最大的流：{0}", maxFlow.Value);
}
public FordFulkerson(FlowNetwork G, int s, int t)
{
if (!IsFeasible(G, s, t))
{
Console.WriteLine("网络配置不可行！");
return;
}
Value = 0.0;
while (HasAugmentingPath(G, s, t))
{
//利用所有存在的增广路径，计算瓶颈容量
double bottle = double.PositiveInfinity;
for (int v = t; v != s; v = edgeTo[v].Other(v))
{
bottle = Math.Min(bottle, edgeTo[v].ResidualCapacityTo(v));
}
//增大流量
for (int v = t; v != s; v = edgeTo[v].Other(v))
{
edgeTo[v].AddResidualFlowTo(v, bottle);//这个需要判断是否是逆路径
}
Value += bottle;
}
}