/// <summary>
/// Makes newChild a child of Node newParent.
/// O(1)
/// </summary>
private static void Link(FibonacciHeapNode <T, TKey> newChild, FibonacciHeapNode <T, TKey> newParent)
{
// remove newChild from root list of heap
newChild.Left.Right = newChild.Right;
newChild.Right.Left = newChild.Left;
// make newChild a child of newParent
newChild.Parent = newParent;
if (newParent.Child == null)
{
newParent.Child = newChild;
newChild.Right = newChild;
newChild.Left = newChild;
}
else
{
newChild.Left = newParent.Child;
newChild.Right = newParent.Child.Right;
newParent.Child.Right = newChild;
newChild.Right.Left = newChild;
}
// increase degree[newParent]
newParent.Degree++;
// set mark[newChild] false
newChild.Mark = false;
}
/// <summary>
/// The reverse of the link operation: removes newParent from the child list of newChild.
/// This method assumes that min is non-null.
/// Running time: O(1)
/// </summary>
private void Cut(FibonacciHeapNode <T, TKey> x, FibonacciHeapNode <T, TKey> y)
{
// remove newParent from childlist of newChild and decrement degree[newChild]
x.Left.Right = x.Right;
x.Right.Left = x.Left;
y.Degree--;
// reset newChild.child if necessary
if (y.Child == x)
{
y.Child = x.Right;
}
if (y.Degree == 0)
{
y.Child = null;
}
// add newParent to root list of heap
x.Left = _minNode;
x.Right = _minNode.Right;
_minNode.Right = x;
x.Right.Left = x;
// set parent[newParent] to nil
x.Parent = null;
// set mark[newParent] to false
x.Mark = false;
}
/// <summary>
/// Deletes a node from the heap.
/// O(log n)
/// </summary>
public void Delete(FibonacciHeapNode <T, TKey> x)
{
// make newParent as small as possible
DecreaseKey(x, _minKeyValue);
// remove the smallest, which decreases n also
RemoveMin();
}
/// <summary>
/// Removes the smalles node of the heap.
/// O(log n) amortized
/// </summary>
/// <returns></returns>
public FibonacciHeapNode <T, TKey> RemoveMin()
{
FibonacciHeapNode <T, TKey> minNode = _minNode;
if (minNode != null)
{
int numKids = minNode.Degree;
FibonacciHeapNode <T, TKey> oldMinChild = minNode.Child;
// for each child of minNode do...
while (numKids > 0)
{
FibonacciHeapNode <T, TKey> tempRight = oldMinChild.Right;
// remove oldMinChild from child list
oldMinChild.Left.Right = oldMinChild.Right;
oldMinChild.Right.Left = oldMinChild.Left;
// add oldMinChild to root list of heap
oldMinChild.Left = _minNode;
oldMinChild.Right = _minNode.Right;
_minNode.Right = oldMinChild;
oldMinChild.Right.Left = oldMinChild;
// set parent[oldMinChild] to null
oldMinChild.Parent = null;
oldMinChild = tempRight;
numKids--;
}
// remove minNode from root list of heap
minNode.Left.Right = minNode.Right;
minNode.Right.Left = minNode.Left;
if (minNode == minNode.Right)
{
_minNode = null;
}
else
{
_minNode = minNode.Right;
Consolidate();
}
// decrement size of heap
_nNodes--;
}
return(minNode);
}
/// <summary>
/// Decreses the key of a node.
/// O(1) amortized.
/// </summary>
public void DecreaseKey(FibonacciHeapNode <T, TKey> x, TKey k)
{
if (k.CompareTo(x.Key) > 0)
{
throw new ArgumentException("decreaseKey() got larger key value");
}
x.Key = k;
FibonacciHeapNode <T, TKey> y = x.Parent;
if ((y != null) && (x.Key.CompareTo(y.Key) < 0))
{
Cut(x, y);
CascadingCut(y);
}
if (x.Key.CompareTo(_minNode.Key) < 0)
{
_minNode = x;
}
}
/// <summary>
/// Performs a cascading cut operation. This cuts newChild from its parent and then
/// does the same for its parent, and so on up the tree.
/// </summary>
private void CascadingCut(FibonacciHeapNode <T, TKey> y)
{
FibonacciHeapNode <T, TKey> z = y.Parent;
// if there's a parent...
if (z != null)
{
// if newChild is unmarked, set it marked
if (!y.Mark)
{
y.Mark = true;
}
else
{
// it's marked, cut it from parent
Cut(y, z);
// cut its parent as well
CascadingCut(z);
}
}
}
/// <summary>
/// Inserts a new node with its key.
/// O(1)
/// </summary>
public void Insert(FibonacciHeapNode <T, TKey> node)
{
// concatenate node into min list
if (_minNode != null)
{
node.Left = _minNode;
node.Right = _minNode.Right;
_minNode.Right = node;
node.Right.Left = node;
if (node.Key.CompareTo(_minNode.Key) < 0)
{
_minNode = node;
}
}
else
{
_minNode = node;
}
_nNodes++;
}
/// <summary>
/// Removes all the elements from the heap.
/// </summary>
public void Clear()
{
_minNode = null;
_nNodes = 0;
}
private void Consolidate()
{
int arraySize = ((int)Math.Floor(Math.Log(_nNodes) * Constants.OneOverLogPhi)) + 1;
var array = new List <FibonacciHeapNode <T, TKey> >(arraySize);
// Initialize degree array
for (var i = 0; i < arraySize; i++)
{
array.Add(null);
}
// Find the number of root nodes.
var numRoots = 0;
FibonacciHeapNode <T, TKey> x = _minNode;
if (x != null)
{
numRoots++;
x = x.Right;
while (x != _minNode)
{
numRoots++;
x = x.Right;
}
}
// For each node in root list do...
while (numRoots > 0)
{
// Access this node's degree..
int d = x.Degree;
FibonacciHeapNode <T, TKey> next = x.Right;
// ..and see if there's another of the same degree.
for (;;)
{
FibonacciHeapNode <T, TKey> y = array[d];
if (y == null)
{
// Nope.
break;
}
// There is, make one of the nodes a child of the other.
// Do this based on the key value.
if (x.Key.CompareTo(y.Key) > 0)
{
FibonacciHeapNode <T, TKey> temp = y;
y = x;
x = temp;
}
// FibonacciHeapNode<T> newChild disappears from root list.
Link(y, x);
// We've handled this degree, go to next one.
array[d] = null;
d++;
}
// Save this node for later when we might encounter another
// of the same degree.
array[d] = x;
// Move forward through list.
x = next;
numRoots--;
}
// Set min to null (effectively losing the root list) and
// reconstruct the root list from the array entries in array[].
_minNode = null;
for (var i = 0; i < arraySize; i++)
{
FibonacciHeapNode <T, TKey> y = array[i];
if (y == null)
{
continue;
}
// We've got a live one, add it to root list.
if (_minNode != null)
{
// First remove node from root list.
y.Left.Right = y.Right;
y.Right.Left = y.Left;
// Now add to root list, again.
y.Left = _minNode;
y.Right = _minNode.Right;
_minNode.Right = y;
y.Right.Left = y;
// Check if this is a new min.
if (y.Key.CompareTo(_minNode.Key) < 0)
{
_minNode = y;
}
}
else
{
_minNode = y;
}
}
}
