public KruskalMST(Graph g)
{
BinaryHeapPQ <Edge> pq = new BinaryHeapPQ <Edge>();
for (int v = 0; v < g.V; v++)
{
for (int i = 0; i < g.Deg(v); i++)
{
pq.Insert(new Edge()
{
U = v, V = g.AdjV(v, i), W = g.AdjW(v, i)
});
}
}
DisjointSets ds = new DisjointSets(g.V);
while (pq.Count > 0 && mst.Count < g.V - 1)
{
Edge e = pq.ExtractMin();
int v = e.U;
int w = e.V;
if (ds.FindSet(v) != ds.FindSet(w))
{
ds.Union(v, w);
mst.Add(e);
}
}
}
public Graph Tree(int V)
{
if (V == 1)
{
return(new Graph(V, new int[][] { }));
}
int[] prufer = new int[V - 2];
for (int i = 0; i < V - 2; i++)
{
prufer[i] = random.Next(V);
}
int[] degree = new int[V];
for (int v = 0; v < V; v++)
{
degree[v] = 1;
}
for (int i = 0; i < V - 2; i++)
{
degree[prufer[i]]++;
}
BinaryHeapPQ <int> pq = new BinaryHeapPQ <int>();
for (int v = 0; v < V; v++)
{
if (degree[v] == 1)
{
pq.Insert(v);
}
}
List <int[]> edges = new List <int[]>();
for (int i = 0; i < V - 2; i++)
{
int v = pq.ExtractMin();
edges.Add(new int[] { v, prufer[i], 1 });
degree[v]--;
degree[prufer[i]]--;
if (degree[prufer[i]] == 1)
{
pq.Insert(prufer[i]);
}
}
edges.Add(new int[] { pq.ExtractMin(), pq.ExtractMin(), 1 });
Graph g = new Graph(V, edges, false);
return(g);
}
