/// <summary>
/// Updates the degree of a cell, cascading to update the degree of the
/// parents if necessary.
/// </summary>
/// <param name="cell">Cell to update.</param>
private void UpdateCellsDegree(
FibonacciHeapCell <TPriority, TValue> cell
)
{
Debug.Assert(cell != null);
Debug.Assert(cell.Children != null);
int oldDegree = cell.Degree;
cell.Degree = cell.Children.First is null
? 1
: cell.Children.Max(x => x.Degree) + 1;
if (oldDegree != cell.Degree)
{
if (
_degreeToCell.TryGetValue(
oldDegree,
out FibonacciHeapCell <TPriority, TValue> degreeMapValue
) &&
degreeMapValue == cell
)
{
_degreeToCell.Remove(oldDegree);
}
else if (cell.Parent != null)
{
UpdateCellsDegree(cell.Parent);
}
}
}
private FibonacciHeapCell <TPriority, TValue> ReduceCell([NotNull] ref FibonacciHeapCell <TPriority, TValue> cell)
{
FibonacciHeapCell <TPriority, TValue> nextCell = cell.Next;
while (_degreeToCell.TryGetValue(cell.Degree, out FibonacciHeapCell <TPriority, TValue> currentDegreeCell) &&
currentDegreeCell != cell)
{
_degreeToCell.Remove(cell.Degree);
if (PriorityComparison(currentDegreeCell.Priority, cell.Priority) * _directionMultiplier <= 0)
{
if (cell == nextCell)
{
nextCell = cell.Next;
}
ReduceCells(currentDegreeCell, cell);
cell = currentDegreeCell;
}
else
{
if (currentDegreeCell == nextCell)
{
nextCell = currentDegreeCell.Next;
}
ReduceCells(cell, currentDegreeCell);
}
}
return(nextCell);
}
/// <summary>
/// Merges the given <paramref name="heap"/> into this heap.
/// </summary>
/// <param name="heap">Heap to merge.</param>
/// <exception cref="Exception">If the heap is not in the same direction.</exception>
public void Merge(FibonacciHeap <TPriority, TValue> heap)
{
if (heap is null)
{
throw new ArgumentNullException(nameof(heap));
}
if (heap.Direction != Direction)
{
throw new InvalidOperationException("Heaps must go in the same direction when merging.");
}
if (heap.IsEmpty)
{
return;
}
bool isEmpty = IsEmpty;
_cells.MergeLists(heap._cells);
if (
isEmpty ||
PriorityComparison(
heap.Top.Priority,
Top.Priority
) *
_directionMultiplier
< 0
)
{
Top = heap.Top;
}
Count += heap.Count;
}
/// <summary>
/// Removes the given <paramref name="cell"/> from this cells list.
/// </summary>
/// <param name="cell">Cell to remove.</param>
internal void Remove(
FibonacciHeapCell <TPriority, TValue> cell
)
{
Debug.Assert(cell != null);
if (cell.Previous != null)
{
cell.Previous.Next = cell.Next;
}
else if (First == cell)
{
First = cell.Next;
}
if (cell.Next != null)
{
cell.Next.Previous = cell.Previous;
}
else if (_last == cell)
{
_last = cell.Previous;
}
cell.Next = null;
cell.Previous = null;
}
private void UpdateCellOppositeDirection([NotNull] FibonacciHeapCell <TPriority, TValue> cell, [NotNull] TPriority newKey)
{
cell.Priority = newKey;
if (cell.Children != null)
{
List <FibonacciHeapCell <TPriority, TValue> > toUpdate = null;
foreach (FibonacciHeapCell <TPriority, TValue> child in cell.Children)
{
if (PriorityComparison(cell.Priority, child.Priority) * _directionMultiplier > 0)
{
if (toUpdate is null)
{
toUpdate = new List <FibonacciHeapCell <TPriority, TValue> >();
}
toUpdate.Add(child);
}
}
if (toUpdate != null)
{
foreach (FibonacciHeapCell <TPriority, TValue> child in toUpdate)
{
cell.Marked = true;
cell.Children.Remove(child);
child.Parent = null;
child.Marked = false;
_cells.AddLast(child);
UpdateCellsDegree(cell);
}
}
}
UpdateNext();
}
private void ChangeKeyInternal(
FibonacciHeapCell <TPriority, TValue> cell,
// Null authorized if deleting the cell
TPriority newKey,
bool deletingCell
)
{
Debug.Assert(cell != null);
int delta = Math.Sign(PriorityComparison(cell.Priority, newKey));
if (delta == 0)
{
return;
}
if (delta == _directionMultiplier || deletingCell)
{
// New value is in the same direction as the heap
UpdateCellSameDirection(cell, newKey, deletingCell);
}
else
{
// Not removing a cell so the newKey must not be null
Debug.Assert(newKey != null);
// New value is in opposite direction of Heap, cut all children violating heap condition
UpdateCellOppositeDirection(cell, newKey);
}
}
/// <summary>
/// Enqueues an element in the heap.
/// </summary>
/// <param name="priority">Value priority.</param>
/// <param name="value">Value to add.</param>
public FibonacciHeapCell <TPriority, TValue> Enqueue(
TPriority priority,
TValue value
)
{
if (priority == null)
{
throw new ArgumentNullException(nameof(priority));
}
var newCell = new FibonacciHeapCell <TPriority, TValue>
{
Priority = priority,
Value = value,
Marked = false,
Children = new FibonacciHeapLinkedList <TPriority, TValue>(),
Degree = 1,
Next = null,
Previous = null,
Parent = null,
Removed = false
};
// We don't do any book keeping or maintenance of the heap on Enqueue,
// We just add this cell to the end of the list of Heaps, updating the Next if required
_cells.AddLast(newCell);
if (Top is null || PriorityComparison(newCell.Priority, Top.Priority) * _directionMultiplier < 0)
{
Top = newCell;
}
++Count;
return(newCell);
}
public CellLevel(
FibonacciHeapCell <TPriority, TValue> cell,
int level
)
{
Cell = cell;
Level = level;
}
/// <summary>
/// Changes the priority of the given <paramref name="cell"/>.
/// </summary>
/// <param name="cell">Cell to update the priority.</param>
/// <param name="newPriority">New priority.</param>
public void ChangeKey([NotNull] FibonacciHeapCell <TPriority, TValue> cell, [NotNull] TPriority newPriority)
{
if (cell is null)
{
throw new ArgumentNullException(nameof(cell));
}
ChangeKeyInternal(cell, newPriority, false);
}
/// <summary>
/// Deletes the given <paramref name="cell"/> from this heap.
/// </summary>
/// <param name="cell">Cell to delete.</param>
public void Delete([NotNull] FibonacciHeapCell <TPriority, TValue> cell)
{
if (cell is null)
{
throw new ArgumentNullException(nameof(cell));
}
ChangeKeyInternal(cell, default(TPriority), true);
Dequeue();
}
IEnumerator <FibonacciHeapCell <TPriority, TValue> > GetEnumerator()
{
FibonacciHeapCell <TPriority, TValue> current = First;
while (current != null)
{
yield return(current);
current = current.Next;
}
}
public TVertex Dequeue()
{
FibonacciHeapCell <TDistance, TVertex> cell = _heap.Top;
if (cell is null)
{
throw new InvalidOperationException("Queue is empty.");
}
_heap.Dequeue();
return(cell.Value);
}
private void CompressHeap()
{
FibonacciHeapCell <TPriority, TValue> cell = _cells.First;
while (cell != null)
{
var nextCell = ReduceCell(ref cell);
_degreeToCell[cell.Degree] = cell;
cell = nextCell;
}
}
private void UpdateCellSameDirection(
[NotNull] FibonacciHeapCell <TPriority, TValue> cell,
[CanBeNull] TPriority newKey,
bool deletingCell)
{
cell.Priority = newKey;
FibonacciHeapCell <TPriority, TValue> parentCell = cell.Parent;
if (parentCell != null &&
(PriorityComparison(newKey, parentCell.Priority) * _directionMultiplier < 0 || deletingCell))
{
cell.Marked = false;
// ReSharper disable once PossibleNullReferenceException
// Justification: parentCell must have children because child has parentCell as Parent.
parentCell.Children.Remove(cell);
UpdateCellsDegree(parentCell);
cell.Parent = null;
_cells.AddLast(cell);
// This loop is the cascading cut, we continue to cut
// ancestors of the cell reduced until we hit a root
// or we found an unmarked ancestor
while (parentCell.Marked && parentCell.Parent != null)
{
// ReSharper disable once PossibleNullReferenceException
// Justification: parentCell must have children because child has parentCell as Parent.
parentCell.Parent.Children.Remove(parentCell);
UpdateCellsDegree(parentCell);
parentCell.Marked = false;
_cells.AddLast(parentCell);
FibonacciHeapCell <TPriority, TValue> currentParent = parentCell;
parentCell = parentCell.Parent;
currentParent.Parent = null;
}
if (parentCell.Parent != null)
{
// We mark this cell to note that it had a child
// cut from it before
parentCell.Marked = true;
}
}
// Update next
if (deletingCell || PriorityComparison(newKey, Top.Priority) * _directionMultiplier < 0)
{
Top = cell;
}
}
/// <summary>
/// Updates the Next pointer, maintaining the heap
/// by folding duplicate heap degrees into each other.
/// Takes O(log(N)) time amortized.
/// </summary>
private void UpdateNext()
{
CompressHeap();
FibonacciHeapCell <TPriority, TValue> cell = _cells.First;
Top = cell;
while (cell != null)
{
if (PriorityComparison(cell.Priority, Top.Priority) * _directionMultiplier < 0)
{
Top = cell;
}
cell = cell.Next;
}
}
/// <summary>
/// Adds the given <paramref name="cell"/> at the end of this cells list.
/// </summary>
/// <param name="cell">Cell to add.</param>
internal void AddLast([NotNull] FibonacciHeapCell <TPriority, TValue> cell)
{
Debug.Assert(cell != null);
if (_last != null)
{
_last.Next = cell;
}
cell.Previous = _last;
_last = cell;
if (First is null)
{
First = cell;
}
}
/// <summary>
/// Given two cells, adds the child cell as a child of the parent cell.
/// </summary>
/// <param name="parentCell">Parent cell.</param>
/// <param name="childCell">Child cell.</param>
private void ReduceCells(
[NotNull] FibonacciHeapCell <TPriority, TValue> parentCell,
[NotNull] FibonacciHeapCell <TPriority, TValue> childCell)
{
Debug.Assert(parentCell != null);
Debug.Assert(parentCell.Children != null);
Debug.Assert(childCell != null);
_cells.Remove(childCell);
parentCell.Children.AddLast(childCell);
childCell.Parent = parentCell;
childCell.Marked = false;
if (parentCell.Degree == childCell.Degree)
{
parentCell.Degree += 1;
}
}
/// <inheritdoc />
public IEnumerator <KeyValuePair <TPriority, TValue> > GetEnumerator()
{
var tempHeap = new FibonacciHeap <TPriority, TValue>(Direction, PriorityComparison);
var cellsStack = new Stack <FibonacciHeapCell <TPriority, TValue> >();
_cells.ForEach(x => cellsStack.Push(x));
while (cellsStack.Count > 0)
{
FibonacciHeapCell <TPriority, TValue> topCell = cellsStack.Peek();
tempHeap.Enqueue(topCell.Priority, topCell.Value);
cellsStack.Pop();
topCell.Children?.ForEach(x => cellsStack.Push(x));
}
while (!tempHeap.IsEmpty)
{
yield return(tempHeap.Top.ToKeyValuePair());
tempHeap.Dequeue();
}
}
/// <summary>
/// Merges the given <paramref name="cells"/> at the end of this cells list.
/// </summary>
/// <param name="cells">Cells to merge.</param>
internal void MergeLists([NotNull] FibonacciHeapLinkedList <TPriority, TValue> cells)
{
Debug.Assert(cells != null);
if (cells.First is null)
{
return;
}
if (_last != null)
{
_last.Next = cells.First;
}
cells.First.Previous = _last;
_last = cells._last;
if (First is null)
{
First = cells.First;
}
}
internal FibonacciHeapLinkedList()
{
First = null;
_last = null;
}