/// <summary>
/// Runs Karger's algorithm on a graph (that respresents a list of polygons) once, which splits a cluster of polygons into two random parts. https://en.wikipedia.org/wiki/Karger%27s_algorithm
/// Returns two new lists with the splitted continents
/// </summary>
private static KargerGraph SplitClusterOnce(List<GraphPolygon> cluster)
{
// First we need to turn the cluster into a Karger graph (which is just a regular unweighted undirected graph), where the nodes contain information about which polygons they contain
KargerGraph graph = new KargerGraph();
Dictionary<GraphPolygon, KargerGraphVertex> vertices = new Dictionary<GraphPolygon, KargerGraphVertex>();
foreach (GraphPolygon poly in cluster)
{
KargerGraphVertex vertex = new KargerGraphVertex(poly);
graph.Vertices.Add(vertex);
vertices.Add(poly, vertex);
}
List<GraphPolygon> visitedPolygons = new List<GraphPolygon>();
foreach(GraphPolygon poly in cluster)
{
visitedPolygons.Add(poly);
foreach(GraphPolygon neighbourPoly in poly.LandNeighbours.Where(x => cluster.Contains(x) && !visitedPolygons.Contains(x)))
{
KargerGraphEdge edge = new KargerGraphEdge(vertices[poly], vertices[neighbourPoly]);
graph.Edges.Add(edge);
vertices[poly].Edges.Add(edge);
vertices[neighbourPoly].Edges.Add(edge);
}
}
// Debug graph
/*
foreach(KargerGraphEdge edge in graph.Edges)
{
Vector2 from = edge.FromVertex.ContainedPolygons[0].CenterPoi;
Vector2 to = edge.ToVertex.ContainedPolygons[0].CenterPoi;
Debug.DrawLine(new Vector3(from.x, 0f, from.y), new Vector3(to.x, 0f, to.y), Color.red, 30);
}
*/
// Then collapse edges in the graph until only 2 vertices are left
while(graph.Vertices.Count > 2)
{
KargerGraphEdge randomEdge = graph.Edges[Random.Range(0, graph.Edges.Count)];
CollapseEdge(graph, randomEdge);
}
graph.CutSize = graph.Vertices[0].Edges.Count;
return graph;
}
public KargerGraphEdge(KargerGraphVertex fromVertex, KargerGraphVertex toVertex)
{
FromVertex = fromVertex;
ToVertex = toVertex;
}