public PrimMST(IGraph <TWeight> graph)
{
G = graph;
ipq = new IndexMinHeap <TWeight>(G.V);
marked = new bool[G.V];
MSTEdges = new List <Edge <TWeight> >();
EdgeTo = new Edge <TWeight> [G.V];
// Prim
Visit(0);
while (!ipq.IsEmpty())
{
var v = ipq.ExtractMinIndex();
if (EdgeTo[v] == null)
{
continue;
}
MSTEdges.Add(EdgeTo[v]);
Visit(v);
}
var value = 0.0;
var converter = TypeDescriptor.GetConverter(typeof(TWeight));
foreach (var edge in MSTEdges)
{
value += (double)converter.ConvertTo(edge.Weight, typeof(double));
}
MSTWeight = (TWeight)converter.ConvertTo(value, typeof(TWeight));
}
// X - set of explored vertices of graph G
// V-X - set of unexplored vertices of graph G
//
// Invariant.
// The key of a vertex w belongs to V-X is the min Dijkstra score of an edge with tail v belongs to X
// and head w, or +infinity if no such edge exists.
// key(w) = min len(v) + l(vw)
//
// DijkstraSearch(graph G, vertex s):
// // Initialization
// X = empty set
// H = empty min heap
// key(s) = 0
// for each vertex V in G.vertices do: key(V) = +infinity
// for each vertex V in G.vertices do: H.Insert(V)
// // Main loop
// while H is not empty do:
// w* = H.ExtractMin()
// X.Add(w*)
// len(w*) = key(w*)
// // Update Heap to maintain Invariant
// for every edge(w*, y) do:
// H.Delete(y) // Delete: given a heap H and a pointer to an object y in H, delete y from H.
// key(y) = min {key(y), len(w*) + l(w*y)}
// H.Insert(y)
public static int[] DijkstraMinHeap(IDirectedWeightedGraph <int> weightedGraph, int startVertex)
{
var minHeap = new IndexMinHeap <int>(weightedGraph.VerticesCount);
var exploredVertices = new HashSet <int> {
startVertex
};
var len = new int[weightedGraph.VerticesCount + 1];
for (int i = 1; i <= weightedGraph.VerticesCount; i++)
{
var score = i == startVertex ? 0 : 1000000;
len[i] = score;
minHeap.Insert(i, score);
}
while (!minHeap.IsEmpty())
{
int u = minHeap.GetMin();
len[u] = minHeap.GetItemKey(u);
minHeap.ExtractMin();
exploredVertices.Add(u);
foreach ((int v, int weight) in weightedGraph.GetAdjacentVertices(u))
{
if (!exploredVertices.Contains(v))
{
if (len[v] > len[u] + weight)
{
int vKey = minHeap.GetItemKey(v);
int newScore = Math.Min(len[u] + weight, vKey);
// can use (minHeap.Delete + minHeap.Insert) instead of DecreaseKey
// but this would be less effective
minHeap.DecreaseKey(v, newScore);
len[v] = newScore;
}
}
}
}
return(len);
}
public KruskalMST(IGraph <TWeight> graph)
{
G = graph;
ipq = new IndexMinHeap <Edge <TWeight> >(2 * G.E);
marked = new bool[G.V];
MSTEdges = new List <Edge <TWeight> >();
for (var i = 0; i < G.V; i++)
{
foreach (Edge <TWeight> e in G.GetAdjIterator(i))
{
ipq.Add(e);
}
}
var uf = new UnionFind(G.V);
while (!ipq.IsEmpty() && MSTEdges.Count < graph.V - 1)
{
var e = ipq.ExtractMin();
if (uf.IsConnected(e.V, e.W))
{
continue;
}
MSTEdges.Add(e);
uf.UnionElements(e.V, e.W);
}
var value = 0.0;
var converter = TypeDescriptor.GetConverter(typeof(TWeight));
foreach (var edge in MSTEdges)
{
value += (double)converter.ConvertTo(edge.Weight, typeof(double));
}
MSTWeight = (TWeight)converter.ConvertTo(value, typeof(TWeight));
}