Class SkewHeap<K,V>
- java.lang.Object
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- org.jheaps.tree.SkewHeap<K,V>
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- Type Parameters:
K
- the type of keys maintained by this heapV
- the type of values maintained by this heap
- All Implemented Interfaces:
java.io.Serializable
,AddressableHeap<K,V>
,MergeableAddressableHeap<K,V>
- Direct Known Subclasses:
LeftistHeap
public class SkewHeap<K,V> extends java.lang.Object implements MergeableAddressableHeap<K,V>, java.io.Serializable
Skew heaps. The heap is sorted according to the natural ordering of its keys, or by aComparator
provided at heap creation time, depending on which constructor is used.Operations
insert
,deleteMin
, anddelete
take amortized O(log(n)). OperationfindMin
is worst-case O(1). Note that a skew-heap does not efficiently support the operationdecreaseKey
which is amortized Ω(log(n)).Note that the ordering maintained by 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 theHeap
interface. (SeeComparable
orComparator
for a precise definition of consistent with equals.) This is so because theHeap
interface is defined in terms of theequals
operation, but this heap performs all key comparisons using itscompareTo
(orcompare
) 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 withequals
; it just fails to obey the general contract of theHeap
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:
- Serialized Form
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Nested Class Summary
Nested Classes Modifier and Type Class Description (package private) static class
SkewHeap.Node<K,V>
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Nested classes/interfaces inherited from interface org.jheaps.AddressableHeap
AddressableHeap.Handle<K,V>
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Field Summary
Fields Modifier and Type Field Description protected java.util.Comparator<? super K>
comparator
The comparator used to maintain order in this heap, or null if it uses the natural ordering of its keys.protected SkewHeap<K,V>
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.protected SkewHeap.Node<K,V>
root
Root node of the heapprivate static long
serialVersionUID
protected long
size
Size of the heap
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description void
clear()
Clear all the elements of the heap.java.util.Comparator<? super K>
comparator()
Returns the comparator used to order the keys in this AddressableHeap, ornull
if this heap uses the natural ordering of its keys.protected SkewHeap.Node<K,V>
createNode(K key, V value)
Create a new node.private void
decreaseKey(SkewHeap.Node<K,V> n, K newKey)
protected void
delete(SkewHeap.Node<K,V> n)
Delete a node from the heap.AddressableHeap.Handle<K,V>
deleteMin()
Delete and return an element with the minimum key.AddressableHeap.Handle<K,V>
findMin()
Find an element with the minimum key.protected SkewHeap.Node<K,V>
getParent(SkewHeap.Node<K,V> n)
Get the parent node of a given node.AddressableHeap.Handle<K,V>
insert(K key)
Insert a new element into the heap with a null value.AddressableHeap.Handle<K,V>
insert(K key, V value)
Insert a new element into the heap.boolean
isEmpty()
Returnstrue
if this heap is empty.void
meld(MergeableAddressableHeap<K,V> other)
Meld a heap into the current heap.long
size()
Returns the number of elements in the heap.protected SkewHeap.Node<K,V>
union(SkewHeap.Node<K,V> root1, SkewHeap.Node<K,V> root2)
Top-down union of two skew heaps.protected SkewHeap.Node<K,V>
unionWithComparator(SkewHeap.Node<K,V> root1, SkewHeap.Node<K,V> root2)
Top-down union of two skew heaps with comparator.protected SkewHeap.Node<K,V>
unlinkAndUnionChildren(SkewHeap.Node<K,V> n)
Unlink the two children of a node and union them forming a new tree.protected SkewHeap.Node<K,V>
unlinkRightChild(SkewHeap.Node<K,V> n)
Unlink the right child of a node.
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Field Detail
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serialVersionUID
private static final long serialVersionUID
- See Also:
- Constant Field Values
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comparator
protected final java.util.Comparator<? super K> comparator
The comparator used to maintain order in this heap, or null if it uses the natural ordering of its keys.
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size
protected long size
Size of the heap
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root
protected SkewHeap.Node<K,V> root
Root node of the heap
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other
protected SkewHeap<K,V> 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 Detail
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SkewHeap
public SkewHeap()
Constructs a new, empty heap, using the natural ordering of its keys.All keys inserted into the heap must implement the
Comparable
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
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SkewHeap
public SkewHeap(java.util.Comparator<? super K> comparator)
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 Detail
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insert
public AddressableHeap.Handle<K,V> insert(K key)
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
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insert
public AddressableHeap.Handle<K,V> insert(K key, V value)
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
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findMin
public AddressableHeap.Handle<K,V> 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
public AddressableHeap.Handle<K,V> 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
public java.util.Comparator<? super K> 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
public void meld(MergeableAddressableHeap<K,V> other)
Description copied from interface:MergeableAddressableHeap
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
private void decreaseKey(SkewHeap.Node<K,V> n, K newKey)
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createNode
protected SkewHeap.Node<K,V> createNode(K key, V value)
Create a new node.- Parameters:
key
- the keyvalue
- the value- Returns:
- the newly created node
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delete
protected void delete(SkewHeap.Node<K,V> n)
Delete a node from the heap.- Parameters:
n
- the node
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unlinkAndUnionChildren
protected SkewHeap.Node<K,V> unlinkAndUnionChildren(SkewHeap.Node<K,V> n)
Unlink the two children of a node and union them forming a new tree.- Parameters:
n
- the node- Returns:
- the tree which is formed by the two children subtrees of the node
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getParent
protected SkewHeap.Node<K,V> getParent(SkewHeap.Node<K,V> n)
Get the parent node of a given node.- Parameters:
n
- the node- Returns:
- the parent of a node
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unlinkRightChild
protected SkewHeap.Node<K,V> unlinkRightChild(SkewHeap.Node<K,V> n)
Unlink the right child of a node.- Parameters:
n
- the node- Returns:
- the right child after unlinking
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union
protected SkewHeap.Node<K,V> union(SkewHeap.Node<K,V> root1, SkewHeap.Node<K,V> root2)
Top-down union of two skew heaps.- Parameters:
root1
- the root of the first heaproot2
- the root of the right heap- Returns:
- the new root of the merged heap
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unionWithComparator
protected SkewHeap.Node<K,V> unionWithComparator(SkewHeap.Node<K,V> root1, SkewHeap.Node<K,V> root2)
Top-down union of two skew heaps with comparator.- Parameters:
root1
- the root of the first heaproot2
- the root of the right heap- Returns:
- the new root of the merged heap
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