private void CleanForward(FlowNetwork Lf,Verticle v)
{
if(v.NumOfEdgesIn==0)
foreach(Edge e in v.EdgesOut.ToList()){
Lf.G.RemoveEdge(e);
CleanForward(Lf,e.To);
}
}
private void CleanSaturatedEdges(FlowNetwork Lf,Func<Edge,int> f,List<Edge> path)
{
foreach(Edge e in path)
if(f(e) == Lf.c(e)){
Lf.G.RemoveEdge(e);
CleanForward(Lf,e.To);
}
}
//Assuming there is a path between s and t in Nf, and BFS was already done
private FlowNetwork BuildLayeredNetwork(FlowNetwork Nf)
{
Graph Lf = new Graph();
int numOfLayers = Nf.G.GetVerticle(tId).Dist;
foreach(Edge e in Nf.G.Edges)
if(e.To.Dist <= numOfLayers && e.From.Dist+1 == e.To.Dist)
Lf.AddEdge(e);
return new FlowNetwork(Lf,Nf.c,sId,tId);
}
private Func<Edge,int> FindBlockingFlow(FlowNetwork Lf)
{
Func<Edge,int> b = (e=>0);
Verticle t = Lf.G.GetVerticle(tId);
List<Edge> path;
Func<Edge,int> g;
while(t.NumOfEdgesIn>0)
{
path = FindBackwardPath(Lf.G,sId,tId);
g = FindPathFlow(path,Lf.c);
b = AddFlow(b,g);
CleanSaturatedEdges(Lf,b,path);
Lf.G.Bfs(sId);
}
return b;
}
public Func<Edge,int> EdmondKarp(Func<Edge,int> f)
{
Contract.Requires(f!=null);
FlowNetwork Nf = BuildResidualNetwork(f);
Nf.G.Bfs(sId);
List<Edge> path;
Func<Edge,int> g;
while(Nf.G.GetVerticle(tId).Dist<int.MaxValue)
{
path = Nf.G.GetShortestPath(sId,tId,statsReady:true);
g = FindPathFlow(path,Nf.c);
f = AddFlow(f,g);
Nf = BuildResidualNetwork(f);
Nf.G.Bfs(sId);
}
return f;
}
public Func<Edge,int> Dinitz(Func<Edge,int> f)
{
Contract.Requires(f!=null);
FlowNetwork Nf = BuildResidualNetwork(f);
Nf.G.Bfs(sId);
FlowNetwork Lf = BuildLayeredNetwork(Nf);
Func<Edge,int> b;
while(Nf.G.GetVerticle(tId).Dist<int.MaxValue)
{
b = FindBlockingFlow(Lf);
f = AddFlow(f,b);
Nf = BuildResidualNetwork(f);
Nf.G.Bfs(sId);
Lf = BuildLayeredNetwork(Nf);
}
return f;
}
