Class CostlessMeldPairingHeap<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 findMin
and
insert
, amortized O(log(n)) for deleteMin
and delete
and amortized O(loglog(n)) for the decreaseKey
operation. The
operation meld
takes amortized zero time.
This variant of the pairing heap is due to Amr Elmasry, described in detail in the following paper:
- Amr Elmasry, Pairing Heaps with Costless Meld, In Proceedings of the 18th Annual European Symposium on Algorithms (ESA 2010), 183--193, 2010.
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 pairing 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 pairing 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 pairing 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:
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Nested Class Summary
Nested ClassesModifier and TypeClassDescription(package private) static class
Nested classes/interfaces inherited from interface org.jheaps.AddressableHeap
AddressableHeap.Handle<K,
V> -
Field Summary
FieldsModifier and TypeFieldDescriptionprivate 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 CostlessMeldPairingHeap.Node<K,
V>[] The decrease poolprivate Comparator
<CostlessMeldPairingHeap.Node<K, V>> Comparator for nodes in the decrease pool.private byte
Index of node with minimum key in the decrease pool.private byte
How many elements are valid in the decrease poolprivate static final int
Maximum length of decrease pool for long type.private CostlessMeldPairingHeap
<K, V> Used to reference the current heap or some other pairing heap in case of melding, so that handles remain valid even after a meld, without having to iterate over them.private CostlessMeldPairingHeap.Node
<K, V> The root of the pairing heapprivate static final long
private long
Size of the pairing heap -
Constructor Summary
ConstructorsConstructorDescriptionConstructs a new, empty heap, using the natural ordering of its keys.CostlessMeldPairingHeap
(Comparator<? super K> comparator) Constructs a new, empty heap, ordered according to the given comparator. -
Method Summary
Modifier and TypeMethodDescriptionprivate void
addPool
(CostlessMeldPairingHeap.Node<K, V> n, boolean updateMinimum) Append to decrease pool.void
clear()
Clear all the elements of the heap.private CostlessMeldPairingHeap.Node
<K, V> Two pass pair and compute root.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 CostlessMeldPairingHeap.Node
<K, V> Cut the children of a node and return the list.private void
Cut a node from its parent.private CostlessMeldPairingHeap.Node
<K, V> Cut the oldest child of a node.private void
decreaseKey
(CostlessMeldPairingHeap.Node<K, V> n, K newKey) private void
Delete a node.Delete and return an element with the minimum key.findMin()
Find an element with the minimum key.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 CostlessMeldPairingHeap.Node
<K, V> private void
linkInPlace
(CostlessMeldPairingHeap.Node<K, V> orphan, CostlessMeldPairingHeap.Node<K, V> n) Put an orphan node into the position of another node.private CostlessMeldPairingHeap.Node
<K, V> 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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DEFAULT_DECREASE_POOL_SIZE
private static final int DEFAULT_DECREASE_POOL_SIZEMaximum length of decrease pool for long type.- See Also:
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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. -
root
The root of the pairing heap -
size
private long sizeSize of the pairing heap -
decreasePool
The decrease pool -
decreasePoolSize
private byte decreasePoolSizeHow many elements are valid in the decrease pool -
decreasePoolMinPos
private byte decreasePoolMinPosIndex of node with minimum key in the decrease pool. Not existent if decreasePoolMin >= decreasePoolSize. -
decreasePoolComparator
Comparator for nodes in the decrease pool. Initialized lazily and used when sorting entries in the decrease pool. -
other
Used to reference the current heap or some other pairing 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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CostlessMeldPairingHeap
public CostlessMeldPairingHeap()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
. -
CostlessMeldPairingHeap
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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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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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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meld
Meld a heap into the current heap. After the operation theother
heap will be empty and will not permit further insertions. This operation takes amortized zero cost.- Specified by:
meld
in interfaceMergeableAddressableHeap<K,
V> - Parameters:
other
- a merge-able heap
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decreaseKey
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delete
Delete a node.- Parameters:
n
- the node
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consolidate
private void consolidate() -
addPool
Append to decrease pool. -
combine
Two pass pair and compute root. -
cutChildren
Cut the children of a node and return the list.- Parameters:
n
- the node- Returns:
- the first node in the children list
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cutOldestChild
Cut the oldest child of a node.- Parameters:
n
- the node- Returns:
- the oldest child of a node or null
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cutFromParent
Cut a node from its parent.- Parameters:
n
- the node
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linkInPlace
private void linkInPlace(CostlessMeldPairingHeap.Node<K, V> orphan, CostlessMeldPairingHeap.Node<K, V> n) Put an orphan node into the position of another node. The other node becomes an orphan.- Parameters:
orphan
- the orphan noden
- the node which will become an orphan
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link
private CostlessMeldPairingHeap.Node<K,V> link(CostlessMeldPairingHeap.Node<K, V> f, CostlessMeldPairingHeap.Node<K, V> s) -
linkWithComparator
private CostlessMeldPairingHeap.Node<K,V> linkWithComparator(CostlessMeldPairingHeap.Node<K, V> f, CostlessMeldPairingHeap.Node<K, V> s)
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