// add all adjacent edges to v which are **not already** on the mst for
// consideration
private void visit(EdgeWeightedGraph G, int v) {
marked[v] = true;
for (WeightedEdge e : G.adj(v)) {
int w = e.other(v);
if (!marked[w]) pq.add(e);
}
}
public LazyPrimMST(EdgeWeightedGraph G) {
pq = new PriorityQueue<WeightedEdge>();
mst = new LinkedList<WeightedEdge>();
marked = new boolean[G.V()];
// Determine the initial candidates w.r.t. the vertex 0
// The candidates are inserted into pq
visit(G, 0);
while (!pq.isEmpty()) {
// Remove the edge with the smallest weight from among the
// candidates
WeightedEdge e = pq.remove();
int v = e.either(), w = e.other(v);
// Lazy exclusion of ineligible edges(edges already in the mst) from
// the candidates
// Note that these edges were eligible when they were selected as
// candidates as one of their vertices was a non-mst vertex. They
// have in due course of adding other edges to the mst become
// ineligible as they now connect vertices in the mst
// Is the edge already on the mst?
// Would have been more intuitive if the mst had been a ST instead
// of a bag. Could have done a mst.exists(). This is more efficient
// though
if (marked[v] && marked[w]) continue;
// Add e to the mst
mst.add(e);
weight += e.weight();
// Visit the neighbouring vertices to discover the fresh candidates
// now that a new edge has been added to the MST
if (!marked[v]) visit(G, v);
if (!marked[w]) visit(G, w);
}
}