private void ExtractTree(FibonacciHeapNode <TE, TP> node)
{
FibonacciHeapNode <TE, TP> parent = node.Parent;
// Extract
node.Parent = null;
parent.Children = node.LeftSibling ?? node.RightSibling;
if (node.LeftSibling != null)
{
node.LeftSibling.RightSibling = node.RightSibling;
}
if (node.RightSibling != null)
{
node.RightSibling.LeftSibling = node.LeftSibling;
}
node.LeftSibling = null;
node.RightSibling = null;
// Move to root tree list
Append(Root, node);
// If the parent had already lost a child extract it too
if (parent != null)
{
if (parent.HasLostAChild)
{
parent.HasLostAChild = false;
ExtractTree(parent);
}
else
{
parent.HasLostAChild = true;
}
}
}
public HashSet <FibonacciHeapNode <TE, TP> > GetAllSiblings()
{
HashSet <FibonacciHeapNode <TE, TP> > siblings = new HashSet <FibonacciHeapNode <TE, TP> >
{
this
};
// Find siblings
FibonacciHeapNode <TE, TP> leftIterator = LeftSibling;
FibonacciHeapNode <TE, TP> rightIterator = RightSibling;
// Enumerate siblings on the left
while (leftIterator != null)
{
siblings.Add(leftIterator);
leftIterator = leftIterator.LeftSibling;
}
// Enumerate siblings on the right
while (rightIterator != null)
{
siblings.Add(rightIterator);
rightIterator = rightIterator.RightSibling;
}
return(siblings);
}
public FibonacciHeapNode <TE, TP> GetMinimumNodeAmongSibglings()
{
FibonacciHeapNode <TE, TP> minimumNode = this;
// Find minimum
FibonacciHeapNode <TE, TP> leftIterator = LeftSibling;
FibonacciHeapNode <TE, TP> rightIterator = RightSibling;
// Look for a smaller node on the left
while (leftIterator != null)
{
if (leftIterator.IsSmallerThan(minimumNode))
{
minimumNode = leftIterator;
}
leftIterator = leftIterator.LeftSibling;
}
// Look for a smaller node on the right
while (rightIterator != null)
{
if (rightIterator.IsSmallerThan(minimumNode))
{
minimumNode = rightIterator;
}
rightIterator = rightIterator.RightSibling;
}
// Done return smallest node found
return(minimumNode);
}
private FibonacciHeapNode <TE, TP> MergeInto(FibonacciHeapNode <TE, TP> root, FibonacciHeapNode <TE, TP> tree)
{
// Extract tree to merge from its siblings
if (tree.LeftSibling != null)
{
tree.LeftSibling.RightSibling = tree.RightSibling;
}
if (tree.RightSibling != null)
{
tree.RightSibling.LeftSibling = tree.LeftSibling;
}
tree.LeftSibling = null;
tree.RightSibling = null;
// Merge tree into children of root
if (root.Children == null)
{
root.Children = tree;
}
else
{
Append(root.Children, tree);
}
tree.Parent = root;
// Return the resulting heap
return(root);
}
private void ConsolidateTrees()
{
if (Root != null)
{
// Keep track of which trees have which rank
Dictionary <int, FibonacciHeapNode <TE, TP> > RankRoots = new Dictionary <int, FibonacciHeapNode <TE, TP> >();
// Check each tree
foreach (FibonacciHeapNode <TE, TP> node in Root.GetAllSiblings())
{
FibonacciHeapNode <TE, TP> newTreeRoot = node;
int rank = newTreeRoot.GetRank();
// If there is already a tree with the same rank, merge them
while (RankRoots.ContainsKey(rank))
{
FibonacciHeapNode <TE, TP> nodeToLink = RankRoots[rank];
RankRoots.Remove(rank);
newTreeRoot = MergeHeaps(newTreeRoot, nodeToLink);
rank = newTreeRoot.GetRank();
}
// The tree - newly merged or not - is currently the only known tree with that rank
RankRoots.Add(rank, newTreeRoot);
}
}
}
private void Append(FibonacciHeapNode <TE, TP> heap1, FibonacciHeapNode <TE, TP> heap2)
{
var rightEdge = heap1.GetRightmostSibling();
var leftEdge = heap2.GetLeftmostSibling();
rightEdge.RightSibling = leftEdge;
leftEdge.LeftSibling = rightEdge;
}
public (TE, TP) ExtractMinimum()
{
if (Empty)
{
throw new InvalidOperationException("Heap is empty.");
}
// Step 1 - remove minimum element
// Get minimum node and set root pointer to one of it's siblings (could be null if there are none)
FibonacciHeapNode <TE, TP> minimumNode = Root;
Root = minimumNode.LeftSibling ?? minimumNode.RightSibling;
// Connect siblings, if any
if (minimumNode.LeftSibling != null)
{
minimumNode.LeftSibling.RightSibling = minimumNode.RightSibling;
}
if (minimumNode.RightSibling != null)
{
minimumNode.RightSibling.LeftSibling = minimumNode.LeftSibling;
}
// Merge children into root tree list
if (minimumNode.Children != null)
{
minimumNode.Children.Parent = null;
// In case the root pointer was null, set it to a child
if (Root == null)
{
Root = minimumNode.Children;
}
// If not merge the children into the root tree list
else
{
Append(Root, minimumNode.Children);
}
}
// Step 2 - update minimum element if needed
if (Root != null)
{
Root = Root.GetMinimumNodeAmongSibglings();
}
// Step 3 - consolidate trees
ConsolidateTrees();
// Update count
Count--;
// Done, return minimum
return(minimumNode.Element, minimumNode.Priority);
}
public FibonacciHeapNode <TE, TP> GetRightmostSibling()
{
FibonacciHeapNode <TE, TP> iterator = this;
while (iterator.RightSibling != null)
{
iterator = iterator.RightSibling;
}
return(iterator);
}
private FibonacciHeapNode <TE, TP> MergeHeaps(FibonacciHeapNode <TE, TP> heap1, FibonacciHeapNode <TE, TP> heap2)
{
if (heap1.IsSmallerThan(heap2))
{
return(MergeInto(heap1, heap2));
}
else
{
return(MergeInto(heap2, heap1));
}
}
public void DecreaseKey(TE element, TP priority)
{
FibonacciHeapNode <TE, TP> node = GetNode(element);
node.Priority = priority;
// If the heap order is violated, extract the subtree and move it to the main tree list
if (node.Parent != null && node.IsSmallerThan(node.Parent))
{
ExtractTree(node);
}
Root = Root.GetMinimumNodeAmongSibglings();
}
public void Insert(TE element, TP priority)
{
var newNode = new FibonacciHeapNode <TE, TP>(element, priority);
if (Empty)
{
Root = newNode;
}
else
{
Append(Root, newNode);
if (newNode.IsSmallerThan(Root))
{
Root = newNode;
}
}
Count++;
}
public bool IsSmallerThan(FibonacciHeapNode <TE, TP> node)
{
return(Priority.CompareTo(node.Priority) == -1);
}