Class FibonacciHeap<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> MergeableAddressableHeap<K,
V>
Comparator
provided at heap
creation time, depending on which constructor is used.
This implementation provides amortized O(1) time for operations that do not
involve deleting an element such as insert
, and decreaseKey
.
Operation findMin
is worst-case O(1). Operations deleteMin
and delete
are amortized O(log(n)). The operation meld
is
also 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 Fibonacci 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 a Fibonacci 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 the Fibonacci 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.
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Nested Class Summary
Nested ClassesNested classes/interfaces inherited from interface org.jheaps.AddressableHeap
AddressableHeap.Handle<K,
V> -
Field Summary
FieldsModifier and TypeFieldDescriptionprivate FibonacciHeap.Node<K,
V>[] Auxiliary array for consolidationprivate static final int
Size of consolidation auxiliary array.private final Comparator
<? super K> The comparator used to maintain order in this heap, or null if it uses the natural ordering of its keys.private FibonacciHeap.Node
<K, V> The root with the minimum keyprotected FibonacciHeap
<K, V> Used to reference the current heap or some other heap in case of melding, so that handles remain valid even after a meld, without having to iterate over them.private int
Number of roots in the root listprivate static final long
private long
Size of the heap -
Constructor Summary
ConstructorsConstructorDescriptionConstructs a new, empty heap, using the natural ordering of its keys.FibonacciHeap
(Comparator<? super K> comparator) Constructs a new, empty heap, ordered according to the given comparator. -
Method Summary
Modifier and TypeMethodDescriptionprivate void
private void
void
clear()
Clear all the elements of the heap.Comparator
<? super K> Returns the comparator used to order the keys in this AddressableHeap, ornull
if this heap uses the natural ordering of its keys.private void
private void
cut
(FibonacciHeap.Node<K, V> x, FibonacciHeap.Node<K, V> y) private void
decreaseKey
(FibonacciHeap.Node<K, V> n, K newKey) private void
decreaseKeyWithComparator
(FibonacciHeap.Node<K, V> n, K newKey) Delete and return an element with the minimum key.findMin()
Find an element with the minimum key.private void
Insert a new element into the heap with a null value.Insert a new element into the heap.boolean
isEmpty()
Returnstrue
if this heap is empty.private void
link
(FibonacciHeap.Node<K, V> y, FibonacciHeap.Node<K, V> x) void
meld
(MergeableAddressableHeap<K, V> other) Meld a heap into the current heap.long
size()
Returns the number of elements in the heap.
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Field Details
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serialVersionUID
private static final long serialVersionUID- See Also:
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AUX_CONSOLIDATE_ARRAY_SIZE
private static final int AUX_CONSOLIDATE_ARRAY_SIZESize of consolidation auxiliary array. Computed for number of elements equal toLong.MAX_VALUE
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comparator
The comparator used to maintain order in this heap, or null if it uses the natural ordering of its keys. -
minRoot
The root with the minimum key -
roots
private int rootsNumber of roots in the root list -
size
private long sizeSize of the heap -
aux
Auxiliary array for consolidation -
other
Used to reference the current heap or some other heap in case of melding, so that handles remain valid even after a meld, without having to iterate over them. In order to avoid maintaining a full-fledged union-find data structure, we disallow a heap to be used in melding more than once. We use however, path-compression in case of cascading melds, that it, a handle moves from one heap to another and then another.
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Constructor Details
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FibonacciHeap
public FibonacciHeap()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
. -
FibonacciHeap
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.
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Method Details
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insert
Insert a new element into the heap.- Specified by:
insert
in interfaceAddressableHeap<K,
V> - Parameters:
key
- the element's keyvalue
- the element's value- Returns:
- a handle for the newly added element
- Throws:
IllegalStateException
- if the heap has already been used in the right hand side of a meld
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insert
Insert a new element into the heap with a null value.- Specified by:
insert
in interfaceAddressableHeap<K,
V> - Parameters:
key
- the element's key- Returns:
- a handle for the newly added element
- Throws:
IllegalStateException
- if the heap has already been used in the right hand side of a meld
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findMin
Find an element with the minimum key.- Specified by:
findMin
in interfaceAddressableHeap<K,
V> - Returns:
- a handle to an element with minimum key
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deleteMin
Delete and return an element with the minimum key. If multiple such elements exists, only one of them will be deleted. After the element is deleted the handle is invalidated and only methodAddressableHeap.Handle.getKey()
andAddressableHeap.Handle.getValue()
can be used.- Specified by:
deleteMin
in interfaceAddressableHeap<K,
V> - Returns:
- a handle to the deleted element with minimum key
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isEmpty
public boolean isEmpty()Returnstrue
if this heap is empty.- Specified by:
isEmpty
in interfaceAddressableHeap<K,
V> - Returns:
true
if this heap is empty,false
otherwise
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size
public long size()Returns the number of elements in the heap.- Specified by:
size
in interfaceAddressableHeap<K,
V> - Returns:
- the number of elements in the heap
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comparator
Returns the comparator used to order the keys in this AddressableHeap, ornull
if this heap uses the natural ordering of its keys.- Specified by:
comparator
in interfaceAddressableHeap<K,
V> - Returns:
- the comparator used to order the keys in this heap, or
null
if this addressable heap uses the natural ordering of its keys
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clear
public void clear()Clear all the elements of the heap. After calling this method all handles should be considered invalidated and the behavior of methodsAddressableHeap.Handle.decreaseKey(Object)
andAddressableHeap.Handle.delete()
is undefined.- Specified by:
clear
in interfaceAddressableHeap<K,
V>
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meld
Meld a heap into the current heap. After the operation theother
heap will be empty and will not permit further insertions.- Specified by:
meld
in interfaceMergeableAddressableHeap<K,
V> - Parameters:
other
- a merge-able heap
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decreaseKey
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decreaseKeyWithComparator
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forceDecreaseKeyToMinimum
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consolidate
private void consolidate() -
link
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cut
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cascadingCut
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addToRootList
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