/// <summary>
/// Unites two disjoint sets given the root elements of the sets.
/// </summary>
/// <param name="xNode">The root of (the tree representing) the first set.</param>
/// <param name="yNode">The root of (the tree representing) the second set.</param>
/// <remarks><paramref name="xNode"/> and <paramref name="yNode"/> are assumed to
/// correspond to elements of different sets.</remarks>
private void Link(DisjointSetsNode <T> xNode, DisjointSetsNode <T> yNode)
{
DisjointSetsNode <T> parentNode, childNode;
if (xNode.Rank > yNode.Rank)
{
childNode = yNode;
parentNode = xNode;
}
else
{
childNode = xNode;
parentNode = yNode;
}
childNode.Parent = parentNode;
if (childNode.Rank == parentNode.Rank)
{
parentNode.Rank += 1;
}
// Swap nexts
var tempNode = parentNode.Next;
parentNode.Next = childNode.Next;
childNode.Next = tempNode;
}
public DisjointSetsNode(T x)
{
Element = x;
Parent = null;
Rank = 0;
Next = this;
}
/// <summary>
/// Inserts a singleton into the collection of disjoint sets.
/// </summary>
/// <param name="x">The element of the singleton to insert.</param>
/// <exception cref="ArgumentException"><paramref name="x"/> is already exists in the collection of disjoint sets.</exception>
public void MakeSet(T x)
{
if (dict.ContainsKey(x))
{
throw new ArgumentException($"The element {x} already exists in the collection of disjoint sets.", nameof(x));
}
var node = new DisjointSetsNode <T>(x);
dict[x] = node;
NumberOfSets++;
}