// The presented code is based on the implementation shown at:
// https://www.geeksforgeeks.org/greedy-algorithms-set-2-kruskals-minimum-spanning-tree-mst/
public List <Edge <T> > MinimumSpanningTreeKruskal()
{
List <Edge <T> > edges = GetEdges();
edges.Sort((a, b) => a.Weight.CompareTo(b.Weight));
Queue <Edge <T> > queue = new Queue <Edge <T> >(edges);
Subset <T>[] subsets = new Subset <T> [Nodes.Count];
for (int i = 0; i < Nodes.Count; i++)
{
subsets[i] = new Subset <T>()
{
Parent = Nodes[i]
};
}
List <Edge <T> > result = new List <Edge <T> >();
while (result.Count < Nodes.Count - 1)
{
Edge <T> edge = queue.Dequeue();
Node <T> from = GetRoot(subsets, edge.From);
Node <T> to = GetRoot(subsets, edge.To);
if (from != to)
{
result.Add(edge);
Union(subsets, from, to);
}
}
return(result);
}
public UnionFind(int V)
{
subsets = new Subset[V];
for (int i = 0; i < V; i++)
{
subsets[i] = new Subset();
subsets[i].Parent = i;
subsets[i].Rank = 0;
}
}
public List <Edge> Kruskal(WebGraph _graph)
{
int verticesCount = _graph.nodes.Count;
Edge[] result = new Edge[verticesCount];
Edge[] edges = _graph.edges.ToArray();
int i = 0;
int e = 0;
Array.Sort(edges, delegate(Edge a, Edge b)
{
return(a.value.CompareTo(b.value));
});
Subset[] subsets = new Subset[verticesCount];
for (int v = 0; v < verticesCount; ++v)
{
subsets[v].Parent = v;
subsets[v].Rank = 0;
}
while (e < verticesCount - 1)
{
Edge nextEdge = edges[i++];
int x = Find(subsets, nextEdge.to);
int y = Find(subsets, nextEdge.from);
if (x != y)
{
result[e++] = nextEdge;
Union(subsets, x, y);
}
}
List <Edge> Edges = new List <Edge>(result);
Edges.RemoveAt(Edges.Count - 1);
return(Edges);
}