Class ReflectedHeap<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>
- Direct Known Subclasses:
ReflectedFibonacciHeap
,ReflectedPairingHeap
Comparator
provided at heap creation time, depending on which
constructor is used.
This class implements a general technique which uses two
MergeableAddressableHeap
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.
The running time bounds depend on the implementation of the underlying used heap. 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:
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Nested Class Summary
Nested ClassesModifier and TypeClassDescriptionprivate static class
private static class
Nested classes/interfaces inherited from interface org.jheaps.DoubleEndedAddressableHeap
DoubleEndedAddressableHeap.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 ReflectedHeap.ReflectedHandle<K,
V> A free element in case the size is oddprivate final AddressableHeap<K,
ReflectedHeap.HandleMap<K, V>> A maximum heapprivate final AddressableHeap<K,
ReflectedHeap.HandleMap<K, V>> A minimum heapprivate ReflectedHeap<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 static final long
private long
Size of the heap -
Constructor Summary
ConstructorsConstructorDescriptionReflectedHeap
(AddressableHeapFactory<K, ?> heapFactory) Constructs a new, empty heap, using the natural ordering of its keys.ReflectedHeap
(AddressableHeapFactory<K, ?> heapFactory, Comparator<? super K> comparator) Constructs a new, empty heap, ordered according to the given comparator. -
Method Summary
Modifier and TypeMethodDescriptionvoid
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
decreaseKey
(ReflectedHeap.ReflectedHandle<K, V> n, K newKey) Decrease the key of an element.private void
Delete an elementDelete and return an element with the maximum key.Delete and return an element with the minimum key.findMax()
Find an element with the maximum key.findMin()
Find an element with the minimum key.private void
increaseKey
(ReflectedHeap.ReflectedHandle<K, V> n, K newKey) Increase the key of an element.Insert a new element into the heap with a null value.Insert a new element into the heap.private void
insertPair
(ReflectedHeap.ReflectedHandle<K, V> handle1, ReflectedHeap.ReflectedHandle<K, V> handle2) Insert a pair of elements, one in the min heap and one in the max heap.boolean
isEmpty()
Returnstrue
if this heap is empty.void
meld
(MergeableDoubleEndedAddressableHeap<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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comparator
The comparator used to maintain order in this heap, or null if it uses the natural ordering of its keys. -
minHeap
A minimum heap -
maxHeap
A maximum heap -
free
A free element in case the size is odd -
size
private long sizeSize of the heap -
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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ReflectedHeap
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
.- Parameters:
heapFactory
- a factory for the underlying heap implementation- Throws:
NullPointerException
- if the heap factory is null
-
ReflectedHeap
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:
heapFactory
- a factory for the underlying heap implementationcomparator
- the comparator that will be used to order this heap. Ifnull
, the natural ordering of the keys will be used.- Throws:
NullPointerException
- if the heap factory is null
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Method Details
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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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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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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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insert
Insert a new element into the heap.- Specified by:
insert
in interfaceAddressableHeap<K,
V> - Specified by:
insert
in interfaceDoubleEndedAddressableHeap<K,
V> - Parameters:
key
- the element's keyvalue
- the element's value- Returns:
- a handle for the newly added element
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insert
Insert a new element into the heap with a null value.- Specified by:
insert
in interfaceAddressableHeap<K,
V> - Specified by:
insert
in interfaceDoubleEndedAddressableHeap<K,
V> - Parameters:
key
- the element's key- Returns:
- a handle for the newly added element
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findMin
Find an element with the minimum key.- Specified by:
findMin
in interfaceAddressableHeap<K,
V> - Specified by:
findMin
in interfaceDoubleEndedAddressableHeap<K,
V> - Returns:
- a handle to an element with minimum key
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findMax
Find an element with the maximum key.- Specified by:
findMax
in interfaceDoubleEndedAddressableHeap<K,
V> - Returns:
- an element with the maximum 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> - Specified by:
deleteMin
in interfaceDoubleEndedAddressableHeap<K,
V> - Returns:
- a handle to the deleted element with minimum key
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deleteMax
Delete and return an element with the maximum key. If multiple such elements exists, only one of them will be deleted.- Specified by:
deleteMax
in interfaceDoubleEndedAddressableHeap<K,
V> - Returns:
- the deleted element with the maximum 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.- Specified by:
meld
in interfaceMergeableDoubleEndedAddressableHeap<K,
V> - Parameters:
other
- a merge-able heap
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insertPair
private void insertPair(ReflectedHeap.ReflectedHandle<K, V> handle1, ReflectedHeap.ReflectedHandle<K, V> handle2) Insert a pair of elements, one in the min heap and one in the max heap.- Parameters:
handle1
- a handle to the first elementhandle2
- a handle to the second element
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delete
Delete an element- Parameters:
n
- a handle to the element
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decreaseKey
Decrease the key of an element.- Parameters:
n
- the elementnewKey
- the new key
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increaseKey
Increase the key of an element.- Parameters:
n
- the elementnewKey
- the new key
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