/// <inheritdoc cref="IHeap{TKey,TValue}.Remove"/>
public override TValue Remove(PairingHeapNode <TKey, TValue> node)
{
if (node == null)
{
throw new ArgumentNullException(nameof(node));
}
// Remove the node from its list of siblings. Merge all its children to form
// a new tree and merge that tree with the root.
var item = node.Value;
if (node == this.Root)
{
// Simplified case when we remove the root
this.Root = this.MergePairwisely(node.Child);
}
else
{
// The node is somewhere in the middle of the tree, so before we handle
// the child of the node, we also need to fix the list of siblings.
node.RemoveFromListOfSiblings();
// The only part left is the child of the node. As stated previously,
// we will simply merge it with the entire heap.
this.Root = this.Merge(this.Root, this.MergePairwisely(node.Child));
}
--this.count;
return(item);
}
/// <inheritdoc cref="IHeap{TKey,TValue}.Add"/>
public override PairingHeapNode <TKey, TValue> Add(TKey key, TValue value)
{
// Create a one-node tree for the specified item and merge it with this heap.
var tree = new PairingHeapNode <TKey, TValue>(key, value);
this.Root = this.Merge(this.Root, tree);
++this.count;
return(tree);
}
/// <inheritdoc cref="IHeap{TKey,TValue}.Merge"/>
public override void Merge(PairingHeap <TKey, TValue> other)
{
if (other == null)
{
throw new ArgumentNullException(nameof(other));
}
this.count += other.count;
this.Root = this.Merge(this.Root, other.Root);
}
/// <summary>
/// Performs a two-pass pairing over a list of siblings to form a single tree.
/// </summary>
/// <param name="node">The leftmost node (head) of the list to combine.</param>
private PairingHeapNode <TKey, TValue> MergePairwisely(PairingHeapNode <TKey, TValue> node)
{
if (node == null)
{
return(null);
}
PairingHeapNode <TKey, TValue> result, tail = null, next = node;
// The first pass is based on iterating left to right, merging trees pairwisely.
// We take two trees from the list, replace them by the result of merging, and
// consider two next trees. Note that after a pair of trees is merged, the formed
// tree is left for later. After this pass we will have ceiling(size / 2) trees.
// On the second pass, we will iterate back, so on the first pass we will maintain
// a temporary list structure for iterating through (during the second pass).
while (next != null)
{
// Take two trees from the list
var a = next;
var b = a.Next;
// Is there a tree to merge 'a' with?
if (b != null)
{
next = b.Next;
result = this.Merge(a, b);
// Maintain our temporary list for iterating in the second pass
result.Previous = tail;
tail = result;
}
else
{
a.Previous = tail;
tail = a;
break;
}
}
// On the second pass, iterate back (move right to left). Every time replace
// the rightmost tree with the result of merging it with its predecessor.
result = null;
while (tail != null)
{
next = tail.Previous;
result = this.Merge(result, tail);
tail = next;
}
// Return a reference to the root of the resulting tree
return(result);
}
/// <summary>
/// Merges two heaps and returns the root of the resulting heap.
/// </summary>
private PairingHeapNode <TKey, TValue> Merge(PairingHeapNode <TKey, TValue> a, PairingHeapNode <TKey, TValue> b)
{
// If merging occurs between a non-empty pairing heap and an empty
// pairing heap, merge just returns the non-empty pairing heap.
if (a == null)
{
return(b);
}
if (b == null)
{
return(a);
}
if (a == b)
{
return(a);
}
// If both pairing heaps are non-empty, the merge function returns
// a new heap where the smallest root of the two heaps is the root of
// the new combined heap and adds the other heap to the list of its children.
PairingHeapNode <TKey, TValue> parent, child;
if (this.Comparer.Compare(a.Key, b.Key) < 0)
{
parent = a;
child = b;
}
else
{
parent = b;
child = a;
}
// The smallest root will be the new leftmost child of the largest root.
// Thus, add it to the list of siblings and make a parent-child relation.
child.Next = parent.Child;
if (parent.Child != null)
{
parent.Child.Previous = child;
}
child.Previous = parent;
parent.Child = child;
// Roots have no siblings, so adjust the pointers accordingly.
parent.Next = null;
parent.Previous = null;
return(parent);
}
/// <inheritdoc cref="IHeap{TKey,TValue}.Update"/>
public override void Update(PairingHeapNode <TKey, TValue> node, TKey key)
{
if (node == null)
{
throw new ArgumentNullException(nameof(node));
}
var relation = this.Comparer.Compare(key, node.Key);
node.Key = key;
// If the new value is considered equal to the previous value, there is no need
// to fix the heap property, because it is already preserved.
if (relation == 0)
{
return;
}
if (relation < 0)
{
// In case the root gets a value that should be extracted from the heap even
// earlier, there is also no need to fix anything.
if (node == this.Root)
{
return;
}
node.RemoveFromListOfSiblings();
this.Root = this.Merge(this.Root, node);
return;
}
// In case the node was updated with a greater value, it is in the right spot.
// However, the heap property might be violated for all its children. For that
// reason we will merge them pairwisely to form a single tree and merge this
// tree with our heap.
var child = node.Child;
if (child == null)
{
return;
}
node.Child = null;
child.Previous = null; // TODO: this line might be not needed
var tree = this.MergePairwisely(child);
this.Root = this.Merge(this.Root, tree);
}
/// <summary>
/// Removes the node from its list of siblings. The child is not affected.
/// </summary>
public void RemoveFromListOfSiblings()
{
// Depending on whether the node is the leftmost node or not, we should
// update the 'child' pointer of the parent (for the leftmost node) or the
// 'next' pointer of the previous sibling (for other nodes).
if (this == this.Previous.Child)
{
this.Previous.Child = this.Next;
}
else
{
this.Previous.Next = this.Next;
}
// If the node is not the last element in the list of siblings, we also
// need to fix the 'previous' pointer of the next sibling.
if (this.Next != null)
{
this.Next.Previous = this.Previous;
}
}
