public Graph <TVertexNew> SelectVertecies <TVertexNew>(Func <TVertex, TVertexNew> vertexSelector)
where TVertexNew : VertexBase
{
var result = new Graph <TVertexNew>();
result.AddVertexRange(Vertices.Select(vertexSelector));
result.AddEdgeRange(_edgeList
.Select(edge => new EdgeBase <TVertexNew>(
result.NameVertexDictionary[edge.Source.Name],
result.NameVertexDictionary[edge.Target.Name],
edge.Weight)));
return(result);
}
// complexity of O(Ef)
// E = number of edges (BFS part)
// f = maximum flow (main loop)
public double GetGreatestFlowWithFordFulkerson(TVertex source, TVertex sink)
{
var workingGraph = UglyPreperation();
double maxFlow = 0;
while (CheckForPathWithBfs(workingGraph, source, sink, out Dictionary <TVertex, EdgeBase <TVertex> > edgesToParent))
{
double pathFlow = double.PositiveInfinity;
var s = sink;
while (s != source)
{
var edge = edgesToParent[s];
pathFlow = Math.Min(pathFlow, edge.Weight ?? 0);
s = s.GetOtherVertex(edge);
}
maxFlow += pathFlow;
var v = sink;
while (v != source)
{
var edge = edgesToParent[v];
edge.Weight -= pathFlow;
var u = v.GetOtherVertex(edge);
workingGraph.GetEdgeOrCreate(v, u).Weight += pathFlow;
v = u;
}
}
return(maxFlow);
// terminates if it finds the target
bool CheckForPathWithBfs(Graph <TVertex> graph, TVertex start, TVertex end, out Dictionary <TVertex, EdgeBase <TVertex> > edgesToParent)
{
edgesToParent = new Dictionary <TVertex, EdgeBase <TVertex> >();
Queue <(TVertex Vertex, EdgeBase <TVertex> Edge)> queue = new Queue <(TVertex, EdgeBase <TVertex>)>();
HashSet <TVertex> visited = new HashSet <TVertex>();
queue.Enqueue((start, null));
while (!queue.IsEmpty())
{
var curVertexAndEdge = queue.Dequeue();
if ((curVertexAndEdge.Edge?.Weight ?? 1) <= 0 || visited.Contains(curVertexAndEdge.Vertex))
{
continue;
}
visited.Add(curVertexAndEdge.Vertex);
edgesToParent[curVertexAndEdge.Vertex] = curVertexAndEdge.Edge;
if (curVertexAndEdge.Vertex == end)
{
return(true);
}
queue.EnqueueRange(graph
.GetNeighborsWithEdges(curVertexAndEdge.Vertex)
.Distinct());
}
return(false);
}
// this is done to make sure we have a graph with only one connection between every vertex and no self loops
Graph <TVertex> UglyPreperation()
{
var edges = Edges
.GroupBy(edge => edge.Source)
.SelectMany(sourceGrouping => sourceGrouping
.GroupBy(edge => edge.Target)
.Select(targetGrouping => new EdgeBase <TVertex>(sourceGrouping.Key, targetGrouping.Key, targetGrouping.Sum(edge => edge.Weight))))
.GroupBy(edge =>
CultureInfo.CurrentCulture.CompareInfo.Compare(edge.Source.Name, edge.Target.Name) < 0
? (edge.Target, edge.Source)
: (edge.Source, edge.Target))
.Select(grouping => {
var grp = grouping.ToArray();
if (grp.Length == 1)
{
return(grp[0]);
}
else
{
var wDiff = grp[0].Weight - grp[1].Weight;
return(wDiff >= 0
? new EdgeBase <TVertex>(grp[0].Source, grp[0].Target, wDiff)
: new EdgeBase <TVertex>(grp[1].Source, grp[1].Target, -wDiff));
}
})
.Where(edge => edge.Source != edge.Target);
var result = new Graph <TVertex>(true);
result.AddVertexRange(Vertices);
result.AddEdgeRange(edges);
return(result);
}
}