// creates a List of Edges representing the members of a Minimum spanning tree
// using the distance between Vertexes as edge weights
public static List <Edge> MinimumSpanningTree(List <Edge> edges, Vertex start)
{
var openSet = new HashSet <Vertex>();
var closedSet = new HashSet <Vertex>();
// add all Vertexes to the open set
foreach (var edge in edges)
{
openSet.Add(edge.U);
openSet.Add(edge.V);
}
// add the starting Vertex to the closed set
closedSet.Add(start);
// the list of Edges representing the MST
var results = new List <Edge>();
// repeat until all Vertexes have been closed
while (openSet.Count > 0)
{
// indicates the current Edge has the smallest cost
var chosen = false;
// the Edge that has the smallest cost so far
Edge chosenEdge = null;
// the cost of the Edge that has the smallest cost so far
var minWeight = float.PositiveInfinity;
foreach (var edge in edges)
{
// check if the Edge is connected to the closed set, but not inside the closed set
var closedVertices = 0;
if (!closedSet.Contains(edge.U))
{
closedVertices++;
}
if (!closedSet.Contains(edge.V))
{
closedVertices++;
}
if (closedVertices != 1)
{
continue;
}
// if this Edge is closer than the chosen Edge, replace it as the chosen Edge
if (edge.Distance < minWeight)
{
chosenEdge = edge;
chosen = true;
minWeight = edge.Distance;
}
}
// if no Edges have been chosen, the MST won't change anymore, so break out of the while loop
if (!chosen)
{
break;
}
results.Add(chosenEdge);
openSet.Remove(chosenEdge.U);
openSet.Remove(chosenEdge.V);
closedSet.Add(chosenEdge.U);
closedSet.Add(chosenEdge.V);
}
return(results);
}
public bool Equals(Edge e)
{
return(this == e);
}
