/// <summary>
/// add all edges e incident to v onto pq if the other endpoint has not yet been scanned
/// </summary>
/// <param name="g"></param>
/// <param name="v"></param>
private void scan(EdgeWeightedGraph g, int v)
{
this._marked[v] = true;
foreach (Edge e in g.Adj[v])
if (!this._marked[e.Other(v)])
this._pq.Insert(e);
}
public LazyPrimMST(EdgeWeightedGraph g)
{
this.MST = new Queue<Edge>();
this._pq = new MinPQ<Edge>();
this._marked = new bool[g.V()];
for (int v = 0; v < g.V(); v++)
if (!this._marked[v])
this.prim(g, v);
}
private void prim(EdgeWeightedGraph g, int s)
{
this._distTo[s] = 0.0d;
this._pq.Insert(s, this._distTo[s]);
while (!this._pq.IsEmpty())
{
int v = this._pq.DelMin();
this.scan(g, v);
}
}
public PrimMST(EdgeWeightedGraph g)
{
this._edgeTo = new Edge[g.V()];
this._distTo = new double[g.V()];
this._marked = new bool[g.V()];
this._pq = new IndexMinPQ<double>(g.V());
for (int v = 0; v < g.V(); v++)
this._distTo[v] = double.PositiveInfinity;
for (int v = 0; v < g.V(); v++)
if (!this._marked[v])
this.prim(g, v);
}
/// <summary>
/// Initializes a new edge-weighted graph that is a deep copy of G.
/// </summary>
/// <param name="G"></param>
public EdgeWeightedGraph(EdgeWeightedGraph G)
: this(G.V())
{
this._e = G.E();
for (int v = 0; v < G.V(); v++)
{
// reverse so that adjacency list is in same order as original
Part1.Stack<Edge> reverse = new Part1.Stack<Edge>();
foreach (Edge e in G.Adj[v])
reverse.Push(e);
foreach (Edge e in reverse)
this.Adj[v].Add(e);
}
}
private void scan(EdgeWeightedGraph g, int v)
{
this._marked[v] = true;
foreach (Edge e in g.Adj[v])
{
int w = e.Other(v);
if (this._marked[w])
continue;
if (e.Weight() < this._distTo[w])
{
this._distTo[w] = e.Weight();
this._edgeTo[w] = e;
if (this._pq.Contains(w))
this._pq.DecreaseKey(w, this._distTo[w]);
else
this._pq.Insert(w, this._distTo[w]);
}
}
}
public KruskalMST(EdgeWeightedGraph g)
{
MinPQ<Edge> pq = new MinPQ<Edge>();
foreach (Edge e in g.Edges())
pq.Insert(e);
Part1.QuickUnion uf = new Part1.QuickUnion(g.V());
while (!pq.IsEmpty() && this._mst.Count < g.V() - 1)
{
Edge e = pq.DelMin();
int v = e.Either();
int w = e.Other(v);
if (!uf.IsConnected(v, w))
{
uf.Union(v, w);
this._mst.Enqueue(e);
this.Weight += e.Weight();
}
}
}
/// <summary>
/// run Prim's algorithm
/// </summary>
/// <param name="g"></param>
/// <param name="s"></param>
private void prim(EdgeWeightedGraph g, int s)
{
this.scan(g, s);
while (!this._pq.IsEmpty())
{
Edge e = this._pq.DelMin();
int v = e.Either(), w = e.Other(v);
if (this._marked[v] && this._marked[w])
{
// lazy, both v and w already scanned
continue;
}
this.MST.Enqueue(e);
this.Weight += e.Weight();
if (!this._marked[v])
this.scan(g, v);
if (!this._marked[w])
this.scan(g, w);
}
}
public void TestKruskalMST()
{
EdgeWeightedGraph g = new EdgeWeightedGraph(8);
g.AddEdge(new Edge(0, 2, 0.26d));
g.AddEdge(new Edge(0, 4, 0.38d));
g.AddEdge(new Edge(0, 7, 0.16d));
g.AddEdge(new Edge(1, 3, 0.29d));
g.AddEdge(new Edge(1, 2, 0.36d));
g.AddEdge(new Edge(1, 5, 0.32d));
g.AddEdge(new Edge(1, 7, 0.19d));
g.AddEdge(new Edge(2, 3, 0.17d));
g.AddEdge(new Edge(2, 7, 0.34d));
g.AddEdge(new Edge(3, 6, 0.52d));
g.AddEdge(new Edge(4, 5, 0.35d));
g.AddEdge(new Edge(4, 7, 0.37d));
g.AddEdge(new Edge(5, 7, 0.28d));
g.AddEdge(new Edge(6, 0, 0.58d));
g.AddEdge(new Edge(6, 2, 0.40d));
g.AddEdge(new Edge(6, 4, 0.93d));
Debug.WriteLine(g);
KruskalMST mst = new KruskalMST(g);
Debug.WriteLine(mst);
}
