/// <summary>
/// Time complexity: O(log(n)).
/// </summary>
public T ExtractMin()
{
if (heapForest.Head == null)
{
throw new Exception("Empty heap");
}
var minTree = heapForest.Head;
var current = heapForest.Head;
//find minimum tree
while (current.Next != null)
{
current = current.Next;
if (minTree.Data.Value.CompareTo(current.Data.Value) > 0)
{
minTree = current;
}
}
//remove tree root
heapForest.Delete(minTree);
var newHeapForest = new DoublyLinkedList <BinomialHeapNode <T> >();
//add removed roots children as new trees to forest
foreach (var child in minTree.Data.Children)
{
child.Parent = null;
newHeapForest.InsertLast(child);
}
mergeSortedForests(newHeapForest);
meld();
removeMapping(minTree.Data.Value, minTree.Data);
Count--;
return(minTree.Data.Value);
}
/// <summary>
/// Time complexity: O(1).
/// </summary>
internal void Union(DoublyLinkedList <T> newList)
{
if (Head == null)
{
Head = newList.Head;
Tail = newList.Tail;
return;
}
if (newList.Head == null)
{
return;
}
Head.Previous = newList.Tail;
newList.Tail.Next = Head;
Head = newList.Head;
}
/// <summary>
/// Shrink if needed
/// </summary>
private void shrink()
{
if (Math.Abs(filledBuckets - bucketSize * 0.3) < tolerance && bucketSize / 2 > initialBucketSize)
{
filledBuckets = 0;
//reduce array by half
var newBucketSize = bucketSize / 2;
var smallerArray = new DoublyLinkedList <HashSetNode <TV> > [newBucketSize];
for (int i = 0; i < bucketSize; i++)
{
var item = hashArray[i];
//hashcode changes when bucket size changes
if (item?.Head != null)
{
var current = item.Head;
//find new location for each item
while (current != null)
{
var next = current.Next;
var newIndex = Math.Abs(current.Data.Value.GetHashCode()) % newBucketSize;
if (smallerArray[newIndex] == null)
{
filledBuckets++;
smallerArray[newIndex] = new DoublyLinkedList <HashSetNode <TV> >();
}
smallerArray[newIndex].InsertFirst(current);
current = next;
}
}
}
hashArray = smallerArray;
}
}
/// <summary>
/// O(log(n)) complexity
/// </summary>
/// <returns></returns>
public T ExtractMax()
{
if (heapForest.Head == null)
{
throw new Exception("Empty heap");
}
var maxTree = heapForest.Head;
var current = heapForest.Head;
//find maximum tree
while (current.Next != null)
{
current = current.Next;
if (maxTree.Data.Value.CompareTo(current.Data.Value) < 0)
{
maxTree = current;
}
}
//remove tree root
heapForest.Delete(maxTree);
var newHeapForest = new DoublyLinkedList <BinomialHeapNode <T> >();
//add removed roots children as new trees to forest
foreach (var node in maxTree.Data.Children)
{
node.Parent = null;
newHeapForest.InsertLast(node);
}
MergeSortedForests(newHeapForest);
Meld();
Count--;
return(maxTree.Data.Value);
}
/// <summary>
/// Merges the given sorted forest to current sorted Forest
/// and returns the last inserted node (pointer required for update-key)
/// </summary>
private void mergeSortedForests(DoublyLinkedList <BinomialHeapNode <T> > newHeapForest)
{
var @new = newHeapForest.Head;
if (heapForest.Head == null)
{
heapForest = newHeapForest;
return;
}
var current = heapForest.Head;
//insert at right spot and move forward
while (@new != null && current != null)
{
if (current.Data.Degree < @new.Data.Degree)
{
current = current.Next;
}
else if (current.Data.Degree > @new.Data.Degree)
{
heapForest.InsertBefore(current, new DoublyLinkedListNode <BinomialHeapNode <T> >(@new.Data));
@new = @new.Next;
}
else
{
//equal
heapForest.InsertAfter(current, new DoublyLinkedListNode <BinomialHeapNode <T> >(@new.Data));
current = current.Next;
@new = @new.Next;
}
}
//copy left overs
while (@new != null)
{
heapForest.InsertAfter(heapForest.Tail, new DoublyLinkedListNode <BinomialHeapNode <T> >(@new.Data));
@new = @new.Next;
}
}