// run Prim's algorithm
private void prim(EdgeWeightedGraph G, int s)
{
scan(G, s);
while (!pq.IsEmpty)
{ // better to stop when mst has V-1 edges
Edge e = pq.DeleteMin(); // smallest edge on pq
int v = e.Either, w = e.other(v); // two endpoints
//assert marked[v] || marked[w];
Contract.Assert(marked[v] || marked[w]);
if (marked[v] && marked[w])
{
continue; // lazy, both v and w already scanned
}
mst.Enqueue(e); // add e to MST
Weight += e.Weight;
if (!marked[v])
{
scan(G, v); // v becomes part of tree
}
if (!marked[w])
{
scan(G, w); // w becomes part of tree
}
}
}
private Queue <Edge> mst = new Queue <Edge>(); // edges in MST
/**
* Compute a minimum spanning tree (or forest) of an edge-weighted graph.
* @param G the edge-weighted graph
*/
public KruskalMST(EdgeWeightedGraph G)
{
// more efficient to build heap by passing array of edges
MinPQ <Edge> pq = new MinPQ <Edge>();
foreach (Edge e in G.Edges)
{
pq.Insert(e);
}
// run greedy algorithm
UF uf = new UF(G.V);
while (!pq.IsEmpty && mst.Size < G.V - 1)
{
Edge e = pq.DeleteMin();
int v = e.Either;
int w = e.other(v);
if (!uf.Connected(v, w))
{ // v-w does not create a cycle
// merge v and w components
uf.Union(v, w);
mst.Enqueue(e); // add edge e to mst
weight += e.Weight;
}
}
// check optimality conditions
//assert ;
Contract.Assert(check(G));
}