/**
* Kruskal's spanning tree algorithm with union-find
* Skiena: The Algorithm Design Manual, p. 196ff
* Note: the sites are implied: they consist of the end points of the line segments
*/
public static List <LineSegment> Kruskal(List <LineSegment> lineSegments, KruskalType type = KruskalType.MINIMUM)
{
Dictionary <Nullable <Vector2>, Node> nodes = new Dictionary <Nullable <Vector2>, Node>();
List <LineSegment> mst = new List <LineSegment>();
Stack <Node> nodePool = Node.pool;
switch (type)
{
// note that the compare functions are the reverse of what you'd expect
// because (see below) we traverse the lineSegments in reverse order for speed
case KruskalType.MAXIMUM:
lineSegments.Sort(delegate(LineSegment l1, LineSegment l2)
{
return(LineSegment.CompareLengths(l1, l2));
});
break;
default:
lineSegments.Sort(delegate(LineSegment l1, LineSegment l2)
{
return(LineSegment.CompareLengths_MAX(l1, l2));
});
break;
}
for (int i = lineSegments.Count; --i > -1;)
{
LineSegment lineSegment = lineSegments[i];
Node node0 = null;
Node rootOfSet0;
if (!nodes.ContainsKey(lineSegment.p0))
{
node0 = nodePool.Count > 0 ? nodePool.Pop() : new Node();
// intialize the node:
rootOfSet0 = node0.parent = node0;
node0.treeSize = 1;
nodes[lineSegment.p0] = node0;
}
else
{
node0 = nodes[lineSegment.p0];
rootOfSet0 = Find(node0);
}
Node node1 = null;
Node rootOfSet1;
if (!nodes.ContainsKey(lineSegment.p1))
{
node1 = nodePool.Count > 0 ? nodePool.Pop() : new Node();
// intialize the node:
rootOfSet1 = node1.parent = node1;
node1.treeSize = 1;
nodes[lineSegment.p1] = node1;
}
else
{
node1 = nodes[lineSegment.p1];
rootOfSet1 = Find(node1);
}
if (rootOfSet0 != rootOfSet1)
{ // nodes not in same set
mst.Add(lineSegment);
// merge the two sets:
int treeSize0 = rootOfSet0.treeSize;
int treeSize1 = rootOfSet1.treeSize;
if (treeSize0 >= treeSize1)
{
// set0 absorbs set1:
rootOfSet1.parent = rootOfSet0;
rootOfSet0.treeSize += treeSize1;
}
else
{
// set1 absorbs set0:
rootOfSet0.parent = rootOfSet1;
rootOfSet1.treeSize += treeSize0;
}
}
}
foreach (Node node in nodes.Values)
{
nodePool.Push(node);
}
return(mst);
}
public static List <LineSegment> Kruskal(List <LineSegment> lineSegments, KruskalType type = KruskalType.MINIMUM)
{
Dictionary <Vector2?, Node> dictionary = new Dictionary <Vector2?, Node>();
List <LineSegment> list = new List <LineSegment>();
Stack <Node> pool = Node.pool;
if (type == KruskalType.MAXIMUM)
{
lineSegments.Sort((LineSegment l1, LineSegment l2) => LineSegment.CompareLengths(l1, l2));
}
else
{
lineSegments.Sort((LineSegment l1, LineSegment l2) => LineSegment.CompareLengths_MAX(l1, l2));
}
int num = lineSegments.Count;
while (--num > -1)
{
LineSegment lineSegment = lineSegments[num];
Node node = null;
Node node2;
if (!dictionary.ContainsKey(lineSegment.p0))
{
node = ((pool.Count <= 0) ? new Node() : pool.Pop());
node2 = (node.parent = node);
node.treeSize = 1;
dictionary[lineSegment.p0] = node;
}
else
{
node = dictionary[lineSegment.p0];
node2 = Find(node);
}
Node node3 = null;
Node node4;
if (!dictionary.ContainsKey(lineSegment.p1))
{
node3 = ((pool.Count <= 0) ? new Node() : pool.Pop());
node4 = (node3.parent = node3);
node3.treeSize = 1;
dictionary[lineSegment.p1] = node3;
}
else
{
node3 = dictionary[lineSegment.p1];
node4 = Find(node3);
}
if (node2 != node4)
{
list.Add(lineSegment);
int treeSize = node2.treeSize;
int treeSize2 = node4.treeSize;
if (treeSize >= treeSize2)
{
node4.parent = node2;
node2.treeSize += treeSize2;
}
else
{
node2.parent = node4;
node4.treeSize += treeSize;
}
}
}
foreach (Node value in dictionary.Values)
{
pool.Push(value);
}
return(list);
}