/// <summary>Kruskal algorithm.</summary>
/// <param name="graph">Undirected weighted graph</param>
/// <returns>Minimal spanning tree</returns>
public static IUndirectedGraph <TVertexId, TVertexProperty, TEdgeProperty> Kruskal <TVertexId, TVertexProperty, TEdgeProperty>(
this IUndirectedGraph <TVertexId, TVertexProperty, TEdgeProperty> graph)
where TEdgeProperty : IWeighted
{
var mst = new UndirectedSimpleGraph <TVertexId, TVertexProperty, TEdgeProperty>(
graph.Vertices.Select(v => v.Id).ToArray());
var vertexSets = new DisjointSets <Vertex <TVertexId> >(graph.Vertices);
var edgeHeap = new Heap <Edge <TVertexId> >(
(edge1, edge2) => graph.Properties[edge1].Weight.CompareTo(graph.Properties[edge2].Weight)
);
foreach (Edge <TVertexId> edge in graph.Edges)
{
edgeHeap.Push(edge);
}
while (vertexSets.Count > 1 && edgeHeap.Count > 0)
{
Edge <TVertexId> edge = edgeHeap.Pop();
if (!vertexSets.IsSameSet(edge.Source, edge.Destination))
{
mst.AddEdge(edge, graph.Properties[edge]);
}
vertexSets.UnionSet(edge.Source, edge.Destination);
}
return(mst);
}