/// <summary>
/// Remove x from the child list of y.
/// </summary>
/// <param name="x">A child of y we just decreased the value of.</param>
/// <param name="y">The now former parent of x.</param>
protected void Cut(FHeapNode <T> x, FHeapNode <T> y)
{
if (MinItem == null)
{
throw new InvalidOperationException("Heap malformed");
}
if (y.Degree == 1)
{
y.Child = null;
MinItem.AddRight(x);
}
else if (y.Degree > 1)
{
x.Remove();
}
else
{
throw new InvalidOperationException("Heap malformed");
}
y.Degree--;
x.Mark = false;
x.Parent = null;
}
/// <summary>
/// Return the MinItem and remove it from the heap.
/// </summary>
/// <remarks>
/// This function (with all of its helper functions) is the most complicated
/// part of the Fibonacci Heap. However, it can be broken down into a few steps.
/// <list type="number">
/// <item>
/// Add the children of MinItem to the root list. Either one of these children,
/// or another of the items in the root list is a candidate to become the new
/// MinItem.
/// </item>
/// <item>
/// Remove the MinItem from the root list and appoint a new MinItem temporarily.
/// </item>
/// <item>
/// <see cref="Consolidate" /> what's left
/// of the heap.
/// </item>
/// </list>
/// </remarks>
/// <returns>The minimum item from the heap.</returns>
public T Pop()
{
FHeapNode <T>?z = null;
if (MinItem == null)
{
throw new InvalidOperationException("Heap is empty!");
}
z = MinItem;
// Since z is leaving the heap, add its children to the root list
if (z.Child != null)
{
foreach (var x in SiblingIterator(z.Child))
{
x.Parent = null;
}
// This effectively adds each child x to the root list
z.ConcatenateRight(z.Child);
}
if (Count == 1)
{
MinItem = null;
Count = 0;
return(z.Key);
}
// Temporarily reassign MinItem to an arbitrary item in the root
// list
MinItem = MinItem.Right;
// Remove the old MinItem from the root list altogether
z.Remove();
// Consolidate the heap
Consolidate();
Count -= 1;
return(z.Key);
}
/// <summary>
/// Make y a child of x.
/// </summary>
/// <param name="y">A node to become the child of x.</param>
/// <param name="x">A node to become the parent of y.</param>
private void FibHeapLink(FHeapNode <T> y, FHeapNode <T> x)
{
y.Remove();
x.AddChild(y);
y.Mark = false;
}