public void EdmondsKarpMaxFlow_NegativeCapacity_Throws()
{
const int source = 1;
const int sink = 4;
var graph = new AdjacencyGraph <int, TaggedEdge <int, double> >();
// TaggedEdge.Tag is the capacity of the edge
graph.AddVerticesAndEdgeRange(new[]
{
new TaggedEdge <int, double>(1, 2, 3),
new TaggedEdge <int, double>(1, 4, 4),
new TaggedEdge <int, double>(2, 3, -1),
new TaggedEdge <int, double>(3, 4, 1)
});
EdgeFactory <int, TaggedEdge <int, double> > edgeFactory = (sourceNode, targetNode) => new TaggedEdge <int, double>(sourceNode, targetNode, 0.0);
var reverseEdgesAlgorithm = new ReversedEdgeAugmentorAlgorithm <int, TaggedEdge <int, double> >(graph, edgeFactory);
reverseEdgesAlgorithm.AddReversedEdges();
var algorithm = new EdmondsKarpMaximumFlowAlgorithm <int, TaggedEdge <int, double> >(graph, edge => edge.Tag, edgeFactory, reverseEdgesAlgorithm);
Assert.Throws <NegativeCapacityException>(() => algorithm.Compute(source, sink));
}
/// <summary>
/// Computes the Edmonds-Karp maximums flow
/// for a graph with positive capacities and
/// flows.
/// </summary>
/// <typeparam name="TVertex">The type of the vertex.</typeparam>
/// <typeparam name="TEdge">The type of the edge.</typeparam>
/// <param name="visitedGraph">The visited graph.</param>
/// <param name="edgeCapacities">The edge capacities.</param>
/// <param name="source">The source.</param>
/// <param name="sink">The sink.</param>
/// <param name="flowPredecessors">The flow predecessors.</param>
/// <param name="edgeFactory">the edge factory</param>
/// <returns></returns>
public static double MaximumFlowEdmondsKarp <TVertex, TEdge>(
#if !NET20
this
#endif
IMutableVertexAndEdgeListGraph <TVertex, TEdge> visitedGraph,
Func <TEdge, double> edgeCapacities,
TVertex source,
TVertex sink,
out TryFunc <TVertex, TEdge> flowPredecessors,
EdgeFactory <TVertex, TEdge> edgeFactory
)
where TEdge : IEdge <TVertex>
{
Contract.Requires(visitedGraph != null);
Contract.Requires(edgeCapacities != null);
Contract.Requires(source != null);
Contract.Requires(sink != null);
Contract.Requires(!source.Equals(sink));
// compute maxflow
var flow = new EdmondsKarpMaximumFlowAlgorithm <TVertex, TEdge>(
visitedGraph,
edgeCapacities,
edgeFactory
);
flow.Compute(source, sink);
flowPredecessors = flow.Predecessors.TryGetValue;
return(flow.MaxFlow);
}
public EdmondsKarpMaximumFlowAlgorithm EdmundsKarp()
{
EdmondsKarpMaximumFlowAlgorithm maxFlow = new EdmondsKarpMaximumFlowAlgorithm(
Graph,
Capacities,
ReversedEdges
);
return maxFlow;
}
private void InitializeGraph()
{
GenerateActivityGraph();
_flowAgorithm =
new EdmondsKarpMaximumFlowAlgorithm <int, Edge <int> >(
_graph,
CalculateActivitySuccessorCapacity,
CreateAdditionalEdgeFactory);
}
public static string Test()
{
////////////////////////////////////////
// test maximum flow algorith
//////////////////////////////////////////
var g = new BidirectionalGraph <string, Edge <string> >(true);
string source = "A";
string sink = "G";
//Vertices
//////////////
g.AddVertex("A"); g.AddVertex("B"); g.AddVertex("C"); g.AddVertex("D");
g.AddVertex("E"); g.AddVertex("F"); g.AddVertex("G");
//Edge
////////////
var edgesList = new List <Edge <string> >();
var ad = new Edge <string>("A", "D"); g.AddEdge(ad); edgeCapacitiesDictionaryTest.Add(ad, 2);
var ab = new Edge <string>("A", "B"); g.AddEdge(ab); edgeCapacitiesDictionaryTest.Add(ab, 3);
var bc = new Edge <string>("B", "C"); g.AddEdge(bc); edgeCapacitiesDictionaryTest.Add(bc, 3);
var ca = new Edge <string>("C", "A"); g.AddEdge(ca); edgeCapacitiesDictionaryTest.Add(ca, 4);
var cd = new Edge <string>("C", "D"); g.AddEdge(cd); edgeCapacitiesDictionaryTest.Add(cd, 1);
var de = new Edge <string>("D", "E"); g.AddEdge(de); edgeCapacitiesDictionaryTest.Add(de, 7);
var df = new Edge <string>("D", "F"); g.AddEdge(df); edgeCapacitiesDictionaryTest.Add(df, 4);
var eb = new Edge <string>("E", "B"); g.AddEdge(eb); edgeCapacitiesDictionaryTest.Add(eb, 1);
var ce = new Edge <string>("C", "E"); g.AddEdge(ce); edgeCapacitiesDictionaryTest.Add(ce, 2);
var eg = new Edge <string>("E", "G"); g.AddEdge(eg); edgeCapacitiesDictionaryTest.Add(eg, 3);
var fg = new Edge <string>("F", "G"); g.AddEdge(fg); edgeCapacitiesDictionaryTest.Add(fg, 4);
/////////////////////////////////////
// creating the augmentor
////////////////////////////////////
var reversedEdgeAugmentor = new ReversedEdgeAugmentorAlgorithm <string, Edge <string> >(g, MyEdgeFactoryTest);
reversedEdgeAugmentor.AddReversedEdges();
// (other option) new PushRelabelMaximumFlowAlgorithm
MaximumFlowAlgorithm <string, Edge <string> > algo = new EdmondsKarpMaximumFlowAlgorithm <string, Edge <string> >(g, /*e => 2*/ ComputeCapacityTest, reversedEdgeAugmentor.ReversedEdges);
algo.Compute(source, sink);
//algo.Compute();
StringBuilder sb = new StringBuilder();
sb.AppendLine(string.Format("MaxFlow: {0}", algo.MaxFlow));
sb.AppendLine("Press <ENTER> to complete");
return(sb.ToString());
}
public static double Get(AdjacencyGraph <string, EquatableTaggedEdge <string, double> > graph, string source, string sink)
{
// edgeFactory will be used to create the reversed edges to store residual capacities using the ReversedEdgeAugmentorAlgorithm-class.
// The edgeFactory assigns a capacity of 0.0 for the new edges because the initial (residual) capacity must be 0.0.
EdgeFactory <string, EquatableTaggedEdge <string, double> > edgeFactory = (sourceNode, targetNode) => new EquatableTaggedEdge <string, double>(sourceNode, targetNode, 0.0);
var reverseEdgesAlgorithm = new ReversedEdgeAugmentorAlgorithm <string, EquatableTaggedEdge <string, double> >(graph, edgeFactory);
reverseEdgesAlgorithm.AddReversedEdges();
var algorithm = new EdmondsKarpMaximumFlowAlgorithm <string, EquatableTaggedEdge <string, double> >(graph, edge => edge.Tag, edgeFactory, reverseEdgesAlgorithm);
algorithm.Compute(source, sink);
return(algorithm.MaxFlow);
}
public void EdmondsKarpMaxFlow_WrongVertices_Throws()
{
var graph = new AdjacencyGraph <TestVertex, TaggedEdge <TestVertex, double> >();
EdgeFactory <TestVertex, TaggedEdge <TestVertex, double> > edgeFactory = (source, target) => new TaggedEdge <TestVertex, double>(source, target, 0.0);
var reverseEdgesAlgorithm = new ReversedEdgeAugmentorAlgorithm <TestVertex, TaggedEdge <TestVertex, double> >(graph, edgeFactory);
reverseEdgesAlgorithm.AddReversedEdges();
var algorithm = new EdmondsKarpMaximumFlowAlgorithm <TestVertex, TaggedEdge <TestVertex, double> >(graph, edge => edge.Tag, edgeFactory, reverseEdgesAlgorithm);
var vertex1 = new TestVertex("1");
var vertex2 = new TestVertex("2");
Assert.Throws <InvalidOperationException>(() => algorithm.Compute());
algorithm = new EdmondsKarpMaximumFlowAlgorithm <TestVertex, TaggedEdge <TestVertex, double> >(
graph,
edge => edge.Tag,
edgeFactory,
reverseEdgesAlgorithm)
{
Source = vertex1
};
Assert.Throws <InvalidOperationException>(() => algorithm.Compute());
algorithm = new EdmondsKarpMaximumFlowAlgorithm <TestVertex, TaggedEdge <TestVertex, double> >(
graph,
edge => edge.Tag,
edgeFactory,
reverseEdgesAlgorithm)
{
Source = vertex1,
Sink = vertex2
};
Assert.Throws <VertexNotFoundException>(() => algorithm.Compute());
algorithm = new EdmondsKarpMaximumFlowAlgorithm <TestVertex, TaggedEdge <TestVertex, double> >(
graph,
edge => edge.Tag,
edgeFactory,
reverseEdgesAlgorithm)
{
Source = vertex1,
Sink = vertex2
};
graph.AddVertex(vertex1);
Assert.Throws <VertexNotFoundException>(() => algorithm.Compute());
}
public void NotReachableSink()
{
const string source = "A";
const string sink = "G";
var graph = new AdjacencyGraph <string, TaggedEdge <string, double> >(true);
graph.AddVertexRange(new[] { "A", "B", "C", "D", "E", "F", "G" });
// TaggedEdge.Tag is the capacity of the edge
graph.AddEdgeRange(new[]
{
new TaggedEdge <string, double>("A", "D", 3),
new TaggedEdge <string, double>("A", "B", 3),
new TaggedEdge <string, double>("B", "C", 4),
new TaggedEdge <string, double>("C", "A", 3),
new TaggedEdge <string, double>("C", "D", 1),
new TaggedEdge <string, double>("D", "E", 2),
new TaggedEdge <string, double>("D", "F", 6),
new TaggedEdge <string, double>("E", "B", 1),
new TaggedEdge <string, double>("C", "E", 2)
});
// edgeFactory will be used to create the reversed edges to store residual capacities using the ReversedEdgeAugmentorAlgorithm-class.
// The edgeFactory assigns a capacity of 0.0 for the new edges because the initial (residual) capacity must be 0.0.
EdgeFactory <string, TaggedEdge <string, double> > edgeFactory = (sourceNode, targetNode) => new TaggedEdge <string, double>(sourceNode, targetNode, 0.0);
var reverseEdgesAlgorithm = new ReversedEdgeAugmentorAlgorithm <string, TaggedEdge <string, double> >(graph, edgeFactory);
reverseEdgesAlgorithm.AddReversedEdges();
var algorithm = new EdmondsKarpMaximumFlowAlgorithm <string, TaggedEdge <string, double> >(graph, edge => edge.Tag, edgeFactory, reverseEdgesAlgorithm);
algorithm.Compute(source, sink);
Assert.AreEqual(source, algorithm.Source);
Assert.AreEqual(sink, algorithm.Sink);
Assert.AreEqual(graph.VertexCount, algorithm.VerticesColors.Count);
foreach (KeyValuePair <string, GraphColor> pair in algorithm.VerticesColors)
{
Assert.AreEqual(
pair.Key == sink ? GraphColor.White : GraphColor.Black,
pair.Value);
}
Assert.AreEqual(0, algorithm.MaxFlow);
}
public void EdmondsKarpMaxFlow_Throws()
{
var graph = new AdjacencyGraph <TestVertex, TaggedEdge <TestVertex, double> >();
EdgeFactory <TestVertex, TaggedEdge <TestVertex, double> > edgeFactory = (source, target) => new TaggedEdge <TestVertex, double>(source, target, 0.0);
var reverseEdgesAlgorithm = new ReversedEdgeAugmentorAlgorithm <TestVertex, TaggedEdge <TestVertex, double> >(graph, edgeFactory);
reverseEdgesAlgorithm.AddReversedEdges();
var algorithm = new EdmondsKarpMaximumFlowAlgorithm <TestVertex, TaggedEdge <TestVertex, double> >(graph, edge => edge.Tag, edgeFactory, reverseEdgesAlgorithm);
var vertex = new TestVertex("1");
// ReSharper disable AssignNullToNotNullAttribute
Assert.Throws <ArgumentNullException>(() => algorithm.Compute(null, vertex));
Assert.Throws <ArgumentNullException>(() => algorithm.Compute(vertex, null));
Assert.Throws <ArgumentNullException>(() => algorithm.Compute(null, null));
// ReSharper restore AssignNullToNotNullAttribute
}
public void GetVertexColor_Throws()
{
var graph = new AdjacencyGraph <int, Edge <int> >();
graph.AddVertexRange(new[] { 0, 1 });
Func <Edge <int>, double> capacities = edge => 1.0;
EdgeFactory <int, Edge <int> > edgeFactory = (source, target) => new Edge <int>(source, target);
var reverseEdgesAlgorithm = new ReversedEdgeAugmentorAlgorithm <int, Edge <int> >(graph, edgeFactory);
reverseEdgesAlgorithm.AddReversedEdges();
var algorithm = new EdmondsKarpMaximumFlowAlgorithm <int, Edge <int> >(graph, capacities, edgeFactory, reverseEdgesAlgorithm);
algorithm.Compute(0, 1);
// ReSharper disable once ReturnValueOfPureMethodIsNotUsed
Assert.Throws <VertexNotFoundException>(() => algorithm.GetVertexColor(2));
}
public void GetVertexColor()
{
var graph = new AdjacencyGraph <int, Edge <int> >();
graph.AddVerticesAndEdge(new Edge <int>(1, 2));
graph.AddVertex(3);
Func <Edge <int>, double> capacities = edge => 1.0;
EdgeFactory <int, Edge <int> > edgeFactory = (source, target) => new Edge <int>(source, target);
var reverseEdgesAlgorithm = new ReversedEdgeAugmentorAlgorithm <int, Edge <int> >(graph, edgeFactory);
reverseEdgesAlgorithm.AddReversedEdges();
var algorithm = new EdmondsKarpMaximumFlowAlgorithm <int, Edge <int> >(graph, capacities, edgeFactory, reverseEdgesAlgorithm);
algorithm.Compute(1, 2);
Assert.AreEqual(GraphColor.Black, algorithm.GetVertexColor(1));
Assert.AreEqual(GraphColor.White, algorithm.GetVertexColor(2));
Assert.AreEqual(GraphColor.White, algorithm.GetVertexColor(3));
}
public static string Main(BidirectionalGraph <Word, Edge <Word> > g)
{
gr = g;
foreach (var item in g.Edges)
{
//edgeCapacitiesDictionary.Add(item, 0);
}
var reversedEdgeAugmentor = new ReversedEdgeAugmentorAlgorithm <Word, Edge <Word> >(g, MyEdgeFactory);
reversedEdgeAugmentor.AddReversedEdges();
//p.;
// (other option) new PushRelabelMaximumFlowAlgorithm
MaximumFlowAlgorithm <Word, Edge <Word> > algo = new EdmondsKarpMaximumFlowAlgorithm <Word, Edge <Word> >(g, ComputeCapacity, reversedEdgeAugmentor.ReversedEdges);
Dictionary <Edge <Word>, double> d = new Dictionary <Edge <Word>, double>();
foreach (var item in g.Edges)
{
algo = new EdmondsKarpMaximumFlowAlgorithm <Word, Edge <Word> >(g, ComputeCapacity, reversedEdgeAugmentor.ReversedEdges);
double value = algo.Compute(item.Source, item.Target);
d.Add(item, value);
}
//algo.Compute();
//algo.Compute(source, sink);
//return algo.MaxFlow;
StringBuilder sb = new StringBuilder();
foreach (var item in d)
{
sb.AppendLine(item.ToString());
}
return(sb.ToString());
}
public static EdmondsKarpMaximumFlowAlgorithm <T, Edge <T> > CreateAlgorithmAndMaybeDoComputation <T>(
[NotNull] ContractScenario <T> scenario)
{
var graph = new AdjacencyGraph <T, Edge <T> >();
graph.AddVerticesAndEdgeRange(scenario.EdgesInGraph.Select(e => new Edge <T>(e.Source, e.Target)));
graph.AddVertexRange(scenario.SingleVerticesInGraph);
double Capacities(Edge <T> edge) => 1.0;
Edge <T> EdgeFactory(T source, T target) => new Edge <T>(source, target);
var reverseEdgesAlgorithm = new ReversedEdgeAugmentorAlgorithm <T, Edge <T> >(graph, EdgeFactory);
reverseEdgesAlgorithm.AddReversedEdges();
var algorithm = new EdmondsKarpMaximumFlowAlgorithm <T, Edge <T> >(graph, Capacities, EdgeFactory, reverseEdgesAlgorithm);
if (scenario.DoComputation)
{
algorithm.Compute(scenario.Root, scenario.AccessibleVerticesFromRoot.First());
}
return(algorithm);
}
/// <inheritdoc />
protected override void InternalCompute()
{
ICancelManager cancelManager = Services.CancelManager;
BipartiteToMaximumFlowGraphAugmentorAlgorithm <TVertex, TEdge> augmentor = null;
ReversedEdgeAugmentorAlgorithm <TVertex, TEdge> reverser = null;
try
{
if (cancelManager.IsCancelling)
{
return;
}
// Augmenting the graph
augmentor = new BipartiteToMaximumFlowGraphAugmentorAlgorithm <TVertex, TEdge>(
this,
VisitedGraph,
SourceToVertices,
VerticesToSink,
VertexFactory,
EdgeFactory);
augmentor.Compute();
if (cancelManager.IsCancelling)
{
return;
}
// Adding reverse edges
reverser = new ReversedEdgeAugmentorAlgorithm <TVertex, TEdge>(
VisitedGraph,
EdgeFactory);
reverser.AddReversedEdges();
if (cancelManager.IsCancelling)
{
return;
}
// Compute maximum flow
var flow = new EdmondsKarpMaximumFlowAlgorithm <TVertex, TEdge>(
this,
VisitedGraph,
edge => 1.0,
EdgeFactory,
reverser);
flow.Compute(augmentor.SuperSource, augmentor.SuperSink);
if (cancelManager.IsCancelling)
{
return;
}
foreach (TEdge edge in VisitedGraph.Edges)
{
if (Math.Abs(flow.ResidualCapacities[edge]) < float.Epsilon)
{
if (edge.Source.Equals(augmentor.SuperSource) ||
edge.Source.Equals(augmentor.SuperSink) ||
edge.Target.Equals(augmentor.SuperSource) ||
edge.Target.Equals(augmentor.SuperSink))
{
// Skip all edges that connect to SuperSource or SuperSink
continue;
}
_matchedEdges.Add(edge);
}
}
}
finally
{
if (reverser != null && reverser.Augmented)
{
reverser.RemoveReversedEdges();
}
if (augmentor != null && augmentor.Augmented)
{
augmentor.Rollback();
}
}
}
protected override void InternalCompute()
{
var cancelManager = this.Services.CancelManager;
this.MatchedEdges.Clear();
BipartiteToMaximumFlowGraphAugmentorAlgorithm <TVertex, TEdge> augmentor = null;
ReversedEdgeAugmentorAlgorithm <TVertex, TEdge> reverser = null;
try
{
if (cancelManager.IsCancelling)
{
return;
}
//augmenting graph
augmentor = new BipartiteToMaximumFlowGraphAugmentorAlgorithm <TVertex, TEdge>(
this,
this.VisitedGraph,
this.VertexSetA,
this.VertexSetB,
this.VertexFactory,
this.EdgeFactory);
augmentor.Compute();
if (cancelManager.IsCancelling)
{
return;
}
//adding reverse edges
reverser = new ReversedEdgeAugmentorAlgorithm <TVertex, TEdge>(
this,
this.VisitedGraph,
this.EdgeFactory
);
reverser.AddReversedEdges();
if (cancelManager.IsCancelling)
{
return;
}
// compute maxflow
var flow = new EdmondsKarpMaximumFlowAlgorithm <TVertex, TEdge>(
this,
this.VisitedGraph,
e => 1,
this.EdgeFactory
);
flow.Compute(augmentor.SuperSource, augmentor.SuperSink);
if (cancelManager.IsCancelling)
{
return;
}
foreach (var edge in this.VisitedGraph.Edges)
{
if (flow.ResidualCapacities[edge] == 0)
{
if (edge.Source.Equals(augmentor.SuperSource) ||
edge.Source.Equals(augmentor.SuperSource) ||
edge.Target.Equals(augmentor.SuperSink) ||
edge.Target.Equals(augmentor.SuperSink))
{
//Skip all edges that connect to SuperSource or SuperSink
continue;
}
this.MatchedEdges.Add(edge);
}
}
}
finally
{
if (reverser != null && reverser.Augmented)
{
reverser.RemoveReversedEdges();
reverser = null;
}
if (augmentor != null && augmentor.Augmented)
{
augmentor.Rollback();
augmentor = null;
}
}
}
public void Constructor()
{
var graph = new AdjacencyGraph <int, Edge <int> >();
Func <Edge <int>, double> capacities = edge => 1.0;
EdgeFactory <int, Edge <int> > edgeFactory = (source, target) => new Edge <int>(source, target);
var reverseEdgesAlgorithm = new ReversedEdgeAugmentorAlgorithm <int, Edge <int> >(graph, edgeFactory);
var algorithm = new EdmondsKarpMaximumFlowAlgorithm <int, Edge <int> >(
graph,
capacities,
edgeFactory,
reverseEdgesAlgorithm);
AssertAlgorithmProperties(
algorithm,
graph,
capacities,
edgeFactory);
algorithm = new EdmondsKarpMaximumFlowAlgorithm <int, Edge <int> >(
null,
graph,
capacities,
edgeFactory,
reverseEdgesAlgorithm);
AssertAlgorithmProperties(
algorithm,
graph,
capacities,
edgeFactory);
#region Local function
void AssertAlgorithmProperties <TVertex, TEdge>(
EdmondsKarpMaximumFlowAlgorithm <TVertex, TEdge> algo,
IMutableVertexAndEdgeListGraph <TVertex, TEdge> g,
Func <TEdge, double> c,
EdgeFactory <int, Edge <int> > eFactory)
where TEdge : IEdge <TVertex>
{
AssertAlgorithmState(algo, g);
CollectionAssert.IsEmpty(algo.Predecessors);
Assert.AreSame(c, algo.Capacities);
CollectionAssert.IsEmpty(algo.ResidualCapacities);
if (eFactory is null)
{
Assert.IsNotNull(algo.EdgeFactory);
}
else
{
Assert.AreSame(eFactory, algo.EdgeFactory);
}
CollectionAssert.IsEmpty(algo.ReversedEdges);
Assert.AreEqual(default(TVertex), algo.Source);
Assert.AreEqual(default(TVertex), algo.Sink);
Assert.AreEqual(0.0, algo.MaxFlow);
CollectionAssert.IsEmpty(algo.VerticesColors);
}
#endregion
}
protected override void InternalCompute()
{
this.matchedEdges.Clear();
AllVerticesGraphAugmentorAlgorithm <TVertex, TEdge> augmentor = null;
ReversedEdgeAugmentorAlgorithm <TVertex, TEdge> reverser = null;
try
{
if (this.IsAborting)
{
return;
}
//augmenting graph
augmentor = new AllVerticesGraphAugmentorAlgorithm <TVertex, TEdge>(
this.VisitedGraph,
this.VertexFactory,
this.EdgeFactory);
augmentor.Compute();
if (this.IsAborting)
{
return;
}
// adding reverse edges
reverser = new ReversedEdgeAugmentorAlgorithm <TVertex, TEdge>(
this.VisitedGraph,
this.EdgeFactory
);
reverser.AddReversedEdges();
if (this.IsAborting)
{
return;
}
// compute maxflow
EdmondsKarpMaximumFlowAlgorithm <TVertex, TEdge> flow = new EdmondsKarpMaximumFlowAlgorithm <TVertex, TEdge>(
this.VisitedGraph,
AlgoUtility.ConstantCapacities(this.VisitedGraph, 1),
reverser.ReversedEdges
);
flow.Compute(augmentor.SuperSource, augmentor.SuperSink);
if (this.IsAborting)
{
return;
}
foreach (TEdge edge in this.VisitedGraph.Edges)
{
if (this.IsAborting)
{
return;
}
if (flow.ResidualCapacities[edge] == 0)
{
this.matchedEdges.Add(edge);
}
}
}
finally
{
if (reverser != null && reverser.Augmented)
{
reverser.RemoveReversedEdges();
reverser = null;
}
if (augmentor != null && augmentor.Augmented)
{
augmentor.Rollback();
augmentor = null;
}
}
}
public void SimpleFlow()
{
const string source = "A";
const string sink = "G";
var graph = new AdjacencyGraph <string, EquatableTaggedEdge <string, double> >(true);
graph.AddVertexRange(new[] { "A", "B", "C", "D", "E", "F", "G" });
// TaggedEdge.Tag is the capacity of the edge
graph.AddEdgeRange(new[]
{
new EquatableTaggedEdge <string, double>("A", "D", 3),
new EquatableTaggedEdge <string, double>("A", "B", 3),
new EquatableTaggedEdge <string, double>("B", "C", 4),
new EquatableTaggedEdge <string, double>("C", "A", 3),
new EquatableTaggedEdge <string, double>("C", "D", 1),
new EquatableTaggedEdge <string, double>("D", "E", 2),
new EquatableTaggedEdge <string, double>("D", "F", 6),
new EquatableTaggedEdge <string, double>("E", "B", 1),
new EquatableTaggedEdge <string, double>("C", "E", 2),
new EquatableTaggedEdge <string, double>("E", "G", 1),
new EquatableTaggedEdge <string, double>("F", "G", 9)
});
// edgeFactory will be used to create the reversed edges to store residual capacities using the ReversedEdgeAugmentorAlgorithm-class.
// The edgeFactory assigns a capacity of 0.0 for the new edges because the initial (residual) capacity must be 0.0.
EdgeFactory <string, EquatableTaggedEdge <string, double> > edgeFactory = (sourceNode, targetNode) => new EquatableTaggedEdge <string, double>(sourceNode, targetNode, 0.0);
var reverseEdgesAlgorithm = new ReversedEdgeAugmentorAlgorithm <string, EquatableTaggedEdge <string, double> >(graph, edgeFactory);
reverseEdgesAlgorithm.AddReversedEdges();
var algorithm = new EdmondsKarpMaximumFlowAlgorithm <string, EquatableTaggedEdge <string, double> >(graph, edge => edge.Tag, edgeFactory, reverseEdgesAlgorithm);
algorithm.Compute(source, sink);
Assert.AreEqual(source, algorithm.Source);
Assert.AreEqual(sink, algorithm.Sink);
Assert.AreEqual(5, algorithm.MaxFlow);
CheckReversedEdges();
CheckPredecessors();
CheckResidualCapacities();
#region Local function
void CheckReversedEdges()
{
Assert.IsTrue(algorithm.ReversedEdges.Count % 2 == 0);
foreach (var pair in algorithm.ReversedEdges)
{
Assert.AreEqual(pair.Key.Source, pair.Value.Target);
Assert.AreEqual(pair.Key.Target, pair.Value.Source);
}
}
void CheckPredecessors()
{
Assert.AreEqual(graph.VertexCount - 1, algorithm.Predecessors.Count);
CollectionAssert.AreEquivalent(
new Dictionary <string, EquatableTaggedEdge <string, double> >
{
["B"] = new EquatableTaggedEdge <string, double>("A", "B", 3),
["C"] = new EquatableTaggedEdge <string, double>("B", "C", 4),
["D"] = new EquatableTaggedEdge <string, double>("E", "D", 0),
["E"] = new EquatableTaggedEdge <string, double>("C", "E", 2),
["F"] = new EquatableTaggedEdge <string, double>("D", "F", 6),
["G"] = new EquatableTaggedEdge <string, double>("F", "G", 9),
},
algorithm.Predecessors);
}
void CheckResidualCapacities()
{
Assert.AreEqual(graph.EdgeCount, algorithm.ResidualCapacities.Count);
CollectionAssert.AreEquivalent(
new Dictionary <EquatableTaggedEdge <string, double>, double>
{
[new EquatableTaggedEdge <string, double>("A", "B", 3)] = 1,
[new EquatableTaggedEdge <string, double>("A", "C", 0)] = 0,
[new EquatableTaggedEdge <string, double>("A", "D", 3)] = 0,
[new EquatableTaggedEdge <string, double>("B", "A", 0)] = 2,
[new EquatableTaggedEdge <string, double>("B", "C", 4)] = 2,
[new EquatableTaggedEdge <string, double>("B", "E", 0)] = 0,
[new EquatableTaggedEdge <string, double>("C", "A", 3)] = 3,
[new EquatableTaggedEdge <string, double>("C", "B", 0)] = 2,
[new EquatableTaggedEdge <string, double>("C", "D", 1)] = 0,
[new EquatableTaggedEdge <string, double>("C", "E", 2)] = 1,
[new EquatableTaggedEdge <string, double>("D", "A", 0)] = 3,
[new EquatableTaggedEdge <string, double>("D", "C", 0)] = 1,
[new EquatableTaggedEdge <string, double>("D", "E", 2)] = 2,
[new EquatableTaggedEdge <string, double>("D", "F", 6)] = 2,
[new EquatableTaggedEdge <string, double>("E", "B", 1)] = 1,
[new EquatableTaggedEdge <string, double>("E", "C", 0)] = 1,
[new EquatableTaggedEdge <string, double>("E", "D", 0)] = 0,
[new EquatableTaggedEdge <string, double>("E", "G", 1)] = 0,
[new EquatableTaggedEdge <string, double>("F", "D", 0)] = 4,
[new EquatableTaggedEdge <string, double>("F", "G", 9)] = 5,
[new EquatableTaggedEdge <string, double>("G", "E", 0)] = 1,
[new EquatableTaggedEdge <string, double>("G", "F", 0)] = 4,
},
algorithm.ResidualCapacities);
}
#endregion
}