Class BinaryTreeSoftAddressableHeap<K,V>
- java.lang.Object
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- org.jheaps.tree.BinaryTreeSoftAddressableHeap<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>
public class BinaryTreeSoftAddressableHeap<K,V> extends java.lang.Object implements MergeableAddressableHeap<K,V>, java.io.Serializable
A binary tree soft addressable heap. 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.If n elements are inserted into a soft heap, then up to εn of the elements still contained in the heap, for a given error parameter ε, may be corrupted, i.e., have their keys artificially increased. In exchange for allowing these corruptions, each soft heap operation is performed in O(log 1/ε) amortized time. Note that n here is the number of elements inserted into the heaps, not the current number of elements in the heap which may be considerably smaller. Moreover the user has no control on which elements may be corrupted.
This variant of the soft heap is due to Kaplan and Zwick, described in detail in the following paper:
- Haim Kaplan and Uri Zwick, A simpler implementation and analysis of Chazelle's Soft Heaps, In Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2009), 477--485, 2009.
Note that the operation
decreaseKey()
always throws anUnsupportedOperationException
as a soft heap does not support such an operation.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 soft 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 a pairing heap performs all key comparisons using itscompareTo
(orcompare
) method, so two keys that are deemed equal by this method are, from the standpoint of the 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
BinaryTreeSoftAddressableHeap.RootList<K,V>
(package private) static class
BinaryTreeSoftAddressableHeap.RootListNode<K,V>
(package private) static class
BinaryTreeSoftAddressableHeap.SoftHandle<K,V>
(package private) static class
BinaryTreeSoftAddressableHeap.TreeNode<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 private 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.private BinaryTreeSoftAddressableHeap<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.private int
rankLimit
Tree nodes with less or equal than this rank will have no corrupted keys.(package private) BinaryTreeSoftAddressableHeap.RootList<K,V>
rootList
The root list, in non-decreasing rank order.private static long
serialVersionUID
private long
size
Size of the heap.private static long[]
TARGET_SIZE
Already computed values for target sizes.
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Constructor Summary
Constructors Constructor Description BinaryTreeSoftAddressableHeap(double errorRate)
Constructs a new, empty heap, using the natural ordering of its keys.BinaryTreeSoftAddressableHeap(double errorRate, java.util.Comparator<? super K> comparator)
Constructs a new, empty heap, ordered according to the given comparator.
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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.private BinaryTreeSoftAddressableHeap.TreeNode<K,V>
combine(BinaryTreeSoftAddressableHeap.TreeNode<K,V> x, BinaryTreeSoftAddressableHeap.TreeNode<K,V> y)
Combine two trees into a new tree.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.private void
delete(BinaryTreeSoftAddressableHeap.RootListNode<K,V> n)
Delete a node from the root list.private void
delete(BinaryTreeSoftAddressableHeap.SoftHandle<K,V> n)
Delete an element.AddressableHeap.Handle<K,V>
deleteMin()
Delete and return an element with the minimum key.BinaryTreeSoftAddressableHeap.SoftHandle<K,V>
findMin()
Find an element with the minimum key.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.private void
mergeInto(BinaryTreeSoftAddressableHeap.RootListNode<K,V> head, BinaryTreeSoftAddressableHeap.RootListNode<K,V> tail)
Merge a list into the root list.private void
sift(BinaryTreeSoftAddressableHeap.TreeNode<K,V> x)
Sift elements from children nodes until the current node has enough elements in its list.long
size()
Returns the number of elements in the heap.private long
targetSize(int rank)
Compute the target size for a particular rank.private void
updateSuffixMin(BinaryTreeSoftAddressableHeap.RootListNode<K,V> t)
Update all suffix minimum pointers for a node and all its predecessors in the root list.
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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
private 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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TARGET_SIZE
private static final long[] TARGET_SIZE
Already computed values for target sizes.
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rankLimit
private final int rankLimit
Tree nodes with less or equal than this rank will have no corrupted keys.
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rootList
final BinaryTreeSoftAddressableHeap.RootList<K,V> rootList
The root list, in non-decreasing rank order.
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size
private long size
Size of the heap.
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other
private BinaryTreeSoftAddressableHeap<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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BinaryTreeSoftAddressableHeap
public BinaryTreeSoftAddressableHeap(double errorRate)
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:
errorRate
- the error rate- Throws:
java.lang.IllegalArgumentException
- if the error rate is less or equal to zerojava.lang.IllegalArgumentException
- if the error rate is greater or equal to one
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BinaryTreeSoftAddressableHeap
public BinaryTreeSoftAddressableHeap(double errorRate, 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:
errorRate
- the error ratecomparator
- the comparator that will be used to order this heap. Ifnull
, the natural ordering of the keys will be used.- Throws:
java.lang.IllegalArgumentException
- if the error rate is less or equal to zerojava.lang.IllegalArgumentException
- if the error rate is greater or equal to one
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Method Detail
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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)
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- Throws:
java.lang.IllegalArgumentException
- ifother
has a different error rate
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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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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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findMin
public BinaryTreeSoftAddressableHeap.SoftHandle<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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targetSize
private long targetSize(int rank)
Compute the target size for a particular rank.- Parameters:
rank
- the rank- Returns:
- the target size
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sift
private void sift(BinaryTreeSoftAddressableHeap.TreeNode<K,V> x)
Sift elements from children nodes until the current node has enough elements in its list.- Parameters:
x
- the node
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combine
private BinaryTreeSoftAddressableHeap.TreeNode<K,V> combine(BinaryTreeSoftAddressableHeap.TreeNode<K,V> x, BinaryTreeSoftAddressableHeap.TreeNode<K,V> y)
Combine two trees into a new tree.- Parameters:
x
- the first treey
- the second tree- Returns:
- the combined tree
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updateSuffixMin
private void updateSuffixMin(BinaryTreeSoftAddressableHeap.RootListNode<K,V> t)
Update all suffix minimum pointers for a node and all its predecessors in the root list.- Parameters:
t
- the node
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mergeInto
private void mergeInto(BinaryTreeSoftAddressableHeap.RootListNode<K,V> head, BinaryTreeSoftAddressableHeap.RootListNode<K,V> tail)
Merge a list into the root list. Assumes that the two lists are sorted in non-decreasing order of rank.- Parameters:
head
- the list headtail
- the list tail
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delete
private void delete(BinaryTreeSoftAddressableHeap.RootListNode<K,V> n)
Delete a node from the root list.- Parameters:
n
- the node
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delete
private void delete(BinaryTreeSoftAddressableHeap.SoftHandle<K,V> n)
Delete an element.- Parameters:
n
- the element to delete
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