/// <summary>Prim algorithm.</summary>
/// <param name="graph">Undirected weighted graph</param>
/// <param name="source">Starting vertex</param>
/// <returns>Minimal spanning tree</returns>
public static IUndirectedGraph <TVertexId, TVertexProperty, TEdgeProperty> Prim <TVertexId, TVertexProperty, TEdgeProperty>(
IUndirectedGraph <TVertexId, TVertexProperty, TEdgeProperty> graph, Vertex <TVertexId> source)
where TEdgeProperty : IWeighted
{
var mst = new UndirectedSimpleGraph <TVertexId, TVertexProperty, TEdgeProperty>(
graph.Vertices.Select(v => v.Id).ToArray());
var visited = new HashSet <Vertex <TVertexId> >();
var heap = new Heap <(Edge <TVertexId>, Vertex <TVertexId>)>(
(pair1, pair2) => graph.Properties[pair1.Item1].Weight.CompareTo(
graph.Properties[pair2.Item1].Weight)
);
visited.Add(source);
foreach (Edge <TVertexId> adjacentEdge in graph.GetAdjacentEdges(source))
{
Vertex <TVertexId> neighbour = adjacentEdge.GetNeighbour(source);
if (neighbour != source)
{
heap.Push((adjacentEdge, neighbour));
}
}
while (heap.Count > 0)
{
(Edge <TVertexId> edge, Vertex <TVertexId> vertex) = heap.Pop();
if (!visited.Contains(vertex))
{
visited.Add(vertex);
mst.AddEdge(edge, graph.Properties[edge]);
foreach (Edge <TVertexId> adjacentEdge in graph.GetAdjacentEdges(vertex))
{
Vertex <TVertexId> neighbour = adjacentEdge.GetNeighbour(vertex);
if (!visited.Contains(neighbour))
{
heap.Push((adjacentEdge, neighbour));
}
}
}
}
return(mst);
}
