// Kruskal's algorithm is (get the min weight edge from PQ and keep adding to tree if it does not cause a cycle
// repeat until v-1 edges are added to the tree or until all edges are exhausted.
private void Kruskal(EdgeWeightedGraph <V> graph)
{
PriorityQueueHeap <Edge <V> > _pq = new PriorityQueueHeap <Edge <V> >();
foreach (Edge <V> edge in graph.Edges())
{
_pq.Insert(edge);
}
DisjointSets_UnionFind uf = new DisjointSets_UnionFind();
// This should be extractMin (but we can subtract the weight from 100 or something
// such that the min weight becomes the max item
while (!_pq.IsEmpty && _queue.Count < graph.TotalVertices() - 1)
{
var item = _pq.Extract();
V start = item.Either;
V end = item.Other;
var startHash = ModedHash(start.GetHashCode());
var endHash = ModedHash(end.GetHashCode());
// Union find works in iterated logarithm since path compression helps move the children
// near the root or parent of the tree.
if (!uf.Connected(startHash, endHash))
{
uf.MakeSet(startHash);
uf.MakeSet(endHash);
uf.Union(startHash, endHash);
_queue.Enqueue(item);
}
}
}
// Eager prim needs indexed priority queue
// start at first vertex, find the min weight edge and add it to the tree.
// Now find a min weight edge that goes out from the tree to non-tree vertex and add it and so on.
private void LazyPrim(EdgeWeightedGraph <V> graph)
{
var marked = new Boolean[graph.TotalVertices()];
var _pq = new PriorityQueueHeap <Edge <V> >();
LazyPrimVisit(graph, graph.Edges().First().Either, marked, _pq);
while (!_pq.IsEmpty)
{
// This should be extractMin (but we can subtract the weight from 100 or something
// such that the min weight becomes the max item
var item = _pq.Extract();
V start = item.Either;
V end = item.Other;
var startHash = ModedHash(start.GetHashCode());
var endHash = ModedHash(end.GetHashCode());
if (marked[startHash] && marked[endHash])
{
continue;
}
_queue.Enqueue(item);
if (!marked[startHash])
{
LazyPrimVisit(graph, start, marked, _pq);
}
if (!marked[endHash])
{
LazyPrimVisit(graph, end, marked, _pq);
}
}
}