public void Test1()
{
ArrayDisjointSet <int> Disj = new ArrayDisjointSet <int>();
Disj.CreateSet(3); Disj.CreateSet(4);
Disj.Join(4, 3);
WriteLine($"{Disj.GetRepresentative(3)}; {Disj.GetRepresentative(4)}");
}
/// <summary>
/// Try and join K-Minimum Spanning Tree such that all connected components are
/// having a size less than the given threshold.
/// TODO: Test this more carefully.
/// </summary>
public virtual void KMinKruskal()
{
// mapping integer representative to the partition size.
IDictionary <int, int> ComponentSizes = new SortedDictionary <int, int>();
// Disjoint set for kruskal.
IDisjointSet <Point> ds = new ArrayDisjointSet <Point>();
SortedSet <Edge> ChosenEdges = new SortedSet <Edge>();
// Maping Component's rerepsentative to partitions of type PointCollection.
SortedDictionary <int, PointCollection> Partitions = new SortedDictionary <int, PointCollection>();
// A set of set of points, each represents all vertices that are in the same component.
SortedSet <PointCollection> ClustersSet = new SortedSet <PointCollection>();
for (int I = 0; I < Idx_V.Count; I++)
{
ds.CreateSet(Idx_V[I]);
ComponentSizes[I] = 1; // Integer representative starts indexing from 1.
PointCollection pc = new PointCollection(Idx_V[I]);
Partitions[I] = pc;
ClustersSet.Add(pc);
}
foreach (Edge e in E)
{
Point u = e.a, v = e.b;
if (ds.FindSet(u) == ds.FindSet(v))
{
continue;
}
int JoinedSize = ComponentSizes[ds.FindSet(u) - 1] + ComponentSizes[ds.FindSet(v) - 1];
if (JoinedSize > Threshold)
{
continue;
}
PointCollection P1 = Partitions[ds.FindSet(v) - 1], P2 = Partitions[ds.FindSet(u) - 1];
PointCollection JoinedPartition = P1 + P2;
ds.Join(u, v);
ComponentSizes[ds.FindSet(u) - 1] = JoinedSize;
Partitions[ds.FindSet(u) - 1] = JoinedPartition;
ClustersSet.Remove(P1);
ClustersSet.Remove(P2);
ClustersSet.Add(JoinedPartition);
ChosenEdges.Add(e);
}
ChosenE = ChosenEdges;
KComponents = ClustersSet;
}
/// <summary>
/// Run Kruskal and establish the boolean edges selection.
/// * return the size of max partition while running the kruskal.
/// </summary>
/// <returns>
/// Max Partitions.
/// </returns>
protected virtual IList <int> EstablishMST()
{
// A list of maximum size for each iteration.
IList <int> MaxSize = new List <int>();
// Disjoint set for kruskal.
IDisjointSet <Point> ds = new ArrayDisjointSet <Point>();
// Keep track of max partition.
SortedSet <int> CompSizes = new SortedSet <int>();
// mapping integer representative to the partition size.
IDictionary <int, int> PartitionSizes = new SortedDictionary <int, int>();
for (int I = 0; I < V.Count; I++)
{
ds.CreateSet(V[I]);
PartitionSizes[I] = 1; // Integer representative starts indexing from 1.
}
SortedSet <Edge> ChosenEdges = new SortedSet <Edge>();
MaxSize.Add(1);
int TotalComponentCount = V.Count - 1;
foreach (Edge e in E)
{
Point u = e.a, v = e.b;
if (ds.FindSet(u) != ds.FindSet(v))
{
int MergedSize = PartitionSizes[ds.FindSet(u) - 1] + PartitionSizes[ds.FindSet(v) - 1];
ds.Join(u, v);
PartitionSizes[ds.FindSet(u) - 1] = MergedSize;
CompSizes.Add(MergedSize);
ChosenEdges.Add(e);
--TotalComponentCount;
}
MaxSize.Add(CompSizes.Max);
if (TotalComponentCount == 0)
{
break;
}
}
// Establish Field.
ChosenE = ChosenEdges;
return(MaxSize);
}
public void TestDisjointSetBasic()
{
IDisjointSet <int> d = new ArrayDisjointSet <int>();
for (int i = 0; ++i <= 4;)
{
d.CreateSet(i);
}
d.Join(3, 4);
Assert.IsTrue(d.GetRepresentative(3) == 3);
Assert.IsTrue(d.GetRepresentative(4) == 3);
d.Join(3, 2);
Assert.AreEqual(d.FindSet(3), d.FindSet(2));
Assert.AreEqual(d.FindSet(2), d.FindSet(4));
d.Join(2, 4);
TestDelegate dele = () =>
{
d.Join(2, 5);
};
AssertThrowException <InvalidArgumentException>(dele);
}
/// <summary>
/// * Run Kruskal again with the information about the max breaking edge
/// in the graph.
/// </summary>
protected virtual SortedSet <PointCollection> KrusktalAagain()
{
int TerminateIndex = base.IdentifyMaxBreakingEdge();
ArrayDisjointSet <Point> ds = new ArrayDisjointSet <Point>();
SortedDictionary <int, PointCollection> Partitions = new SortedDictionary <int, PointCollection>();
SortedSet <PointCollection> ClustersSet = new SortedSet <PointCollection>();
for (int I = 0; I < V.Count; I++)
{
ds.CreateSet(V[I]);
PointCollection pc = new PointCollection(V[I]);
Partitions[I] = pc;
ClustersSet.Add(pc);
}
foreach (Edge e in E)
{
Point v = e.a, u = e.b;
if (ChosenE.Contains(e))
{
PointCollection P1 = Partitions[ds.FindSet(v) - 1], P2 = Partitions[ds.FindSet(u) - 1];
PointCollection JoinedPartition = P1 + P2;
ds.Join(v, u);
Partitions[ds.FindSet(u) - 1] = JoinedPartition;
ClustersSet.Remove(P1);
ClustersSet.Remove(P2);
ClustersSet.Add(JoinedPartition);
}
if (--TerminateIndex == 1)
{
break; // Gives it some room.
}
}
return(ClustersSet);
}
