public static FlowGraph <T> FordFulkerson <T>(this FlowGraph <T> graph)
{
if (graph.Edges.Where(e => !e.Capacity.HasValue).Any())
{
throw new ArgumentException("In dem Graphen muss für jede Kante eine Kapazität definiert sein.");
}
// Sicherstellen, dass der Fluss bei allen Kanten initialisiert ist.
foreach (Edge <T> e in graph.Edges.Where(e => !e.Flow.HasValue))
{
e.Flow = 0;
}
// Eine Kopie des Graphens erstellen.
FlowGraph <T> maxFlowGraph = graph.Copy();
// Den Residualgraph erstellen
FlowGraph <T> residualGraph = maxFlowGraph.GetResidualGraph();
while (residualGraph.DepthFirstSearch(residualGraph.Source, residualGraph.Target, out List <Edge <T> > path))
{
int minAugmentingFlow = path.Select(e => Math.Abs(e.Flow.Value)).Min();
foreach (Edge <T> edge in path)
{
//Edge<T> edgeToModify = maxFlowGraph.Edges.Where(e => e.From.Equals(edge.From) && e.To.Equals(edge.To)).Single();
Edge <T> edgeToModify = maxFlowGraph.GetEdge(edge.From, edge.To);
if (edge.Flow.Value > 0)
{
edgeToModify.Flow += minAugmentingFlow;
}
else
{
edgeToModify.Flow -= minAugmentingFlow;
}
// edgeToModify.Flow += edge.Flow;
}
residualGraph = maxFlowGraph.GetResidualGraph();
}
return(maxFlowGraph);
}
public void GetResidualGraph_must_work()
{
// Quelle und Senke erstellen.
Vertex <string> source = new Vertex <string>("s");
Vertex <string> target = new Vertex <string>("t");
// alle weiteren Knoten des Graphens erstellen.
Vertex <string> vA = new Vertex <string>("a");
Vertex <string> vB = new Vertex <string>("b");
Vertex <string> vC = new Vertex <string>("c");
Vertex <string> vD = new Vertex <string>("d");
// Den Graphen erstellen.
FlowGraph <string> flowGraph = new FlowGraph <string>(source, target, new List <Vertex <string> >()
{
source, vA, vB, vC, vD, target
});
// Die Kanten des Graphens erstellen.
flowGraph.AddEdge("s", "a", capacity: 5, flow: 5);
flowGraph.AddEdge("s", "b", capacity: 7, flow: 3);
flowGraph.AddEdge("a", "b", capacity: 7, flow: 3);
flowGraph.AddEdge("a", "c", capacity: 4, flow: 2);
flowGraph.AddEdge("b", "c", capacity: 3, flow: 3);
flowGraph.AddEdge("b", "d", capacity: 3, flow: 3);
flowGraph.AddEdge("c", "d", capacity: 4, flow: 0);
flowGraph.AddEdge("c", "t", capacity: 5, flow: 5);
flowGraph.AddEdge("d", "t", capacity: 6, flow: 3);
FlowGraph <string> residualGraph = flowGraph.GetResidualGraph();
// Die Kanten überprüfen
Assert.AreEqual(13, residualGraph.Edges.Count);
// a --> s
Assert.AreEqual(vA, residualGraph.Edges[0].From);
Assert.AreEqual(source, residualGraph.Edges[0].To);
Assert.AreEqual(5, residualGraph.Edges[0].Capacity);
Assert.AreEqual(-5, residualGraph.Edges[0].Flow);
// s --> b
Assert.AreEqual(source, residualGraph.Edges[1].From);
Assert.AreEqual(vB, residualGraph.Edges[1].To);
Assert.AreEqual(7, residualGraph.Edges[1].Capacity);
Assert.AreEqual(4, residualGraph.Edges[1].Flow);
// b --> s
Assert.AreEqual(vB, residualGraph.Edges[2].From);
Assert.AreEqual(source, residualGraph.Edges[2].To);
Assert.AreEqual(7, residualGraph.Edges[2].Capacity);
Assert.AreEqual(-3, residualGraph.Edges[2].Flow);
// a --> b
Assert.AreEqual(vA, residualGraph.Edges[3].From);
Assert.AreEqual(vB, residualGraph.Edges[3].To);
Assert.AreEqual(7, residualGraph.Edges[3].Capacity);
Assert.AreEqual(4, residualGraph.Edges[3].Flow);
// b --> a
Assert.AreEqual(vB, residualGraph.Edges[4].From);
Assert.AreEqual(vA, residualGraph.Edges[4].To);
Assert.AreEqual(7, residualGraph.Edges[4].Capacity);
Assert.AreEqual(-3, residualGraph.Edges[4].Flow);
// a --> c
Assert.AreEqual(vA, residualGraph.Edges[5].From);
Assert.AreEqual(vC, residualGraph.Edges[5].To);
Assert.AreEqual(4, residualGraph.Edges[5].Capacity);
Assert.AreEqual(2, residualGraph.Edges[5].Flow);
// c --> a
Assert.AreEqual(vC, residualGraph.Edges[6].From);
Assert.AreEqual(vA, residualGraph.Edges[6].To);
Assert.AreEqual(4, residualGraph.Edges[6].Capacity);
Assert.AreEqual(-2, residualGraph.Edges[6].Flow);
// c --> b
Assert.AreEqual(vC, residualGraph.Edges[7].From);
Assert.AreEqual(vB, residualGraph.Edges[7].To);
Assert.AreEqual(3, residualGraph.Edges[7].Capacity);
Assert.AreEqual(-3, residualGraph.Edges[7].Flow);
// d --> b
Assert.AreEqual(vD, residualGraph.Edges[8].From);
Assert.AreEqual(vB, residualGraph.Edges[8].To);
Assert.AreEqual(3, residualGraph.Edges[8].Capacity);
Assert.AreEqual(-3, residualGraph.Edges[8].Flow);
// c --> d
Assert.AreEqual(vC, residualGraph.Edges[9].From);
Assert.AreEqual(vD, residualGraph.Edges[9].To);
Assert.AreEqual(4, residualGraph.Edges[9].Capacity);
Assert.AreEqual(4, residualGraph.Edges[9].Flow);
// t --> c
Assert.AreEqual(target, residualGraph.Edges[10].From);
Assert.AreEqual(vC, residualGraph.Edges[10].To);
Assert.AreEqual(5, residualGraph.Edges[10].Capacity);
Assert.AreEqual(-5, residualGraph.Edges[10].Flow);
// d --> t
Assert.AreEqual(vD, residualGraph.Edges[11].From);
Assert.AreEqual(target, residualGraph.Edges[11].To);
Assert.AreEqual(6, residualGraph.Edges[11].Capacity);
Assert.AreEqual(3, residualGraph.Edges[11].Flow);
// t --> d
Assert.AreEqual(target, residualGraph.Edges[12].From);
Assert.AreEqual(vD, residualGraph.Edges[12].To);
Assert.AreEqual(6, residualGraph.Edges[12].Capacity);
Assert.AreEqual(-3, residualGraph.Edges[12].Flow);
}
