/// <summary>
/// Inserts an element into the heap.
/// </summary>
/// <param name="item">The element to insert into the heap.</param>
/// <returns>The pointer to the inserted element.</returns>
public ElementPointer Insert(T item)
{
var result = new OptimizedChildSiblingTreeNode <T>(item);
this._head = this._head == null ? result : this.Meld(result, this._head);
return(new(result));
}
/// <summary>
/// Destructively merges another heap.
/// </summary>
/// <param name="heap">Another heap with elements to add to this heap.</param>
/// <remarks><paramref name="heap"/> is emptied in the process.</remarks>
public void Merge(PairingHeap <T> heap)
{
if (heap._head == null)
{
return;
}
this._head = this._head == null ? heap._head : this.Meld(heap._head, this._head);
heap._head = null;
}
private OptimizedChildSiblingTreeNode <T> Meld(OptimizedChildSiblingTreeNode <T> head1, OptimizedChildSiblingTreeNode <T> head2)
{
if (this._comparer.Compare(head1.Value, head2.Value) < 0)
{
MeldInto(head1, head2);
return(head1);
}
else
{
MeldInto(head2, head1);
return(head2);
}
/// <summary>
/// Extracts a minimum element from the heap.
/// </summary>
/// <param name="result">A minimum element that was contained in the heap.</param>
/// <returns><c>true</c> if an element was removed from the heap; otherwise, <c>false</c>.</returns>
public bool TryExtractMinimum([MaybeNullWhen(false)] out T result)
{
if (this._head == null)
{
result = default;
return(false);
}
result = this._head.Value;
this._head = this.MergePairs(this._head.FirstChild);
return(true);
}
private OptimizedChildSiblingTreeNode <T>?MergePairs(OptimizedChildSiblingTreeNode <T>?firstChild)
{
if (firstChild == null)
{
return(null);
}
var last = PassOne(firstChild);
var result = PassTwo(last);
result.LeftSiblingOrParent = null;
result.RightSibling = null;
return(result);
OptimizedChildSiblingTreeNode <T> PassOne(OptimizedChildSiblingTreeNode <T> current)
{
OptimizedChildSiblingTreeNode <T>?previous = null;
while (current.RightSibling != null)
{
var other = current.RightSibling;
var next = other.RightSibling;
var melded = this.Meld(current, other);
melded.LeftSiblingOrParent = previous;
if (next == null)
{
return(melded);
}
previous = melded;
current = next;
}
current.LeftSiblingOrParent = previous;
return(current);
}
OptimizedChildSiblingTreeNode <T> PassTwo(OptimizedChildSiblingTreeNode <T> current)
{
var merging = current.LeftSiblingOrParent;
while (merging != null)
{
var next = merging.LeftSiblingOrParent;
current = this.Meld(current, merging);
merging = next;
}
return(current);
}
}
static void MeldInto(OptimizedChildSiblingTreeNode <T> parent, OptimizedChildSiblingTreeNode <T> child)
{
child.LeftSiblingOrParent = parent;
var oldFirstChild = parent.FirstChild;
if (oldFirstChild != null)
{
oldFirstChild.LeftSiblingOrParent = child;
}
child.RightSibling = oldFirstChild;
parent.FirstChild = child;
}
private static void Cut(OptimizedChildSiblingTreeNode <T> node)
{
var reference = node.LeftSiblingOrParent !;
if (reference.FirstChild == node)
{
reference.FirstChild = node.RightSibling;
}
else
{
Debug.Assert(reference.RightSibling == node);
reference.RightSibling = node.RightSibling;
}
}
/// <summary>
/// Decreases the element inside a specified element pointer.
/// </summary>
/// <param name="element">The pointer to the element to decrease.</param>
/// <param name="item">The new element.</param>
/// <remarks>It is undefined behavior to increase the element.</remarks>
public void Decrease(ElementPointer element, T item)
{
Debug.Assert(this._head != null);
var node = element.Node;
if (this._head == node)
{
node.Value = item;
return;
}
Cut(node);
node.LeftSiblingOrParent = null;
node.RightSibling = null;
node.Value = item;
this._head = this.Meld(this._head !, node);
}
/// <summary>
/// Removes an element from the heap.
/// </summary>
/// <param name="element">The pointer to the element to be removed.</param>
public void Remove(ElementPointer element)
{
Debug.Assert(this._head != null);
var node = element.Node;
if (this._head == node)
{
this._head = this.MergePairs(this._head.FirstChild);
return;
}
Cut(node);
if (node.FirstChild != null)
{
this._head = this.Meld(this._head !, this.MergePairs(node.FirstChild));
}
}
internal ElementPointer(OptimizedChildSiblingTreeNode <T> node)
{
this._node = node;
}