Class ReflectedFibonacciHeap<K,V>
- Type Parameters:
K
- the type of keys maintained by this heapV
- the type of values maintained by this heap
- All Implemented Interfaces:
Serializable
,AddressableHeap<K,
,V> DoubleEndedAddressableHeap<K,
,V> MergeableDoubleEndedAddressableHeap<K,
V>
Comparator
provided at heap creation time, depending on which
constructor is used.
This class implements a general technique which uses two
FibonacciHeap
s to implement a double ended heap, described in detail
in the following
paper:
- C. Makris, A. Tsakalidis, and K. Tsichlas. Reflected min-max heaps. Information Processing Letters, 86(4), 209--214, 2003.
This implementation provides amortized O(1) time for insert
,
findMin
, and findMax
. Operations decreaseKey
,
increaseKey
, deleteMin
, deleteMax
, and delete
are amortized O(log(n)). The operation meld
is amortized O(1).
All the above bounds, however, assume that the user does not perform cascading melds on heaps such as:
d.meld(e); c.meld(d); b.meld(c); a.meld(b);The above scenario, although efficiently supported by using union-find with path compression, invalidates the claimed bounds.
Note that the ordering maintained by a this heap, like any heap, and whether
or not an explicit comparator is provided, must be consistent with
equals
if this heap is to correctly implement the
AddressableHeap
interface. (See Comparable
or
Comparator
for a precise definition of consistent with
equals.) This is so because the AddressableHeap
interface is
defined in terms of the equals
operation, but this heap performs all
key comparisons using its compareTo
(or compare
) method, so
two keys that are deemed equal by this method are, from the standpoint of
this heap, equal. The behavior of a heap is well-defined even if its
ordering is inconsistent with equals
; it just fails to obey the
general contract of the AddressableHeap
interface.
Note that this implementation is not synchronized. If multiple threads access a heap concurrently, and at least one of the threads modifies the heap structurally, it must be synchronized externally. (A structural modification is any operation that adds or deletes one or more elements or changing the key of some element.) This is typically accomplished by synchronizing on some object that naturally encapsulates the heap.
- See Also:
-
Nested Class Summary
Nested ClassesNested classes/interfaces inherited from interface org.jheaps.DoubleEndedAddressableHeap
DoubleEndedAddressableHeap.Handle<K,
V> -
Field Summary
Fields -
Constructor Summary
ConstructorsConstructorDescriptionConstructs a new, empty heap, using the natural ordering of its keys.ReflectedFibonacciHeap
(Comparator<? super K> comparator) Constructs a new, empty heap, ordered according to the given comparator. -
Method Summary
-
Field Details
-
serialVersionUID
private static final long serialVersionUID- See Also:
-
-
Constructor Details
-
ReflectedFibonacciHeap
public ReflectedFibonacciHeap()Constructs a new, empty heap, using the natural ordering of its keys. All keys inserted into the heap must implement theComparable
interface. Furthermore, all such keys must be mutually comparable:k1.compareTo(k2)
must not throw aClassCastException
for any keysk1
andk2
in the heap. If the user attempts to put a key into the heap that violates this constraint (for example, the user attempts to put a string key into a heap whose keys are integers), theinsert(Object key)
call will throw aClassCastException
. -
ReflectedFibonacciHeap
Constructs a new, empty heap, ordered according to the given comparator. All keys inserted into the heap must be mutually comparable by the given comparator:comparator.compare(k1, k2)
must not throw aClassCastException
for any keysk1
andk2
in the heap. If the user attempts to put a key into the heap that violates this constraint, theinsert(Object key)
call will throw aClassCastException
.- Parameters:
comparator
- the comparator that will be used to order this heap. Ifnull
, the natural ordering of the keys will be used.
-