Class BinaryTreeSoftHeap<K>
- Type Parameters:
K
- the type of keys maintained by this heap
- All Implemented Interfaces:
Serializable
,Heap<K>
,MergeableHeap<K>
Comparator
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 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 the Heap
interface. (See Comparable
or Comparator
for a precise
definition of consistent with equals.) This is so because the
Heap
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 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
Heap
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
(package private) static class
(package private) static class
(package private) static class
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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 final int
Tree nodes with less or equal than this rank will have no corrupted keys.(package private) final BinaryTreeSoftHeap.RootList
<K> The root list, in non-decreasing rank order.private static final long
private long
Size of the heap.private static final long[]
Already computed values for target sizes. -
Constructor Summary
ConstructorsConstructorDescriptionBinaryTreeSoftHeap
(double errorRate) Constructs a new, empty heap, using the natural ordering of its keys.BinaryTreeSoftHeap
(double errorRate, 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 this heap.private BinaryTreeSoftHeap.TreeNode
<K> Combine two trees into a new tree.Comparator
<? super K> Returns the comparator used to order the keys in this heap, ornull
if this heap uses the natural ordering of its keys.Delete and return an element with the minimum key.findMin()
Find an element with the minimum key.void
Insert a key into the heap.boolean
isEmpty()
Returnstrue
if this heap is empty.void
meld
(MergeableHeap<K> other) Meld a heap into the current heap.private void
Merge a list into the root list.private void
Sift elements from children nodes until the current node has enough elements in its list.long
size()
Returns the number of elements in this heap.private long
targetSize
(int rank) Compute the target size for a particular rank.private void
Update all suffix minimum pointers for a node and all its predecessors in the root list.
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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. -
TARGET_SIZE
private static final long[] TARGET_SIZEAlready computed values for target sizes. -
rankLimit
private final int rankLimitTree nodes with less or equal than this rank will have no corrupted keys. -
rootList
The root list, in non-decreasing rank order. -
size
private long sizeSize of the heap.
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Constructor Details
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BinaryTreeSoftHeap
public BinaryTreeSoftHeap(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:
IllegalArgumentException
- if the error rate is less or equal to zeroIllegalArgumentException
- if the error rate is greater or equal to one
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BinaryTreeSoftHeap
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:
IllegalArgumentException
- if the error rate is less or equal to zeroIllegalArgumentException
- if the error rate is greater or equal to one
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Method Details
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isEmpty
public boolean isEmpty()Returnstrue
if this heap is empty. -
size
public long size()Returns the number of elements in this heap. -
comparator
Returns the comparator used to order the keys in this heap, ornull
if this heap uses the natural ordering of its keys.- Specified by:
comparator
in interfaceHeap<K>
- Returns:
- the comparator used to order the keys in this heap, or
null
if this heap uses the natural ordering of its keys
-
clear
public void clear()Clear all the elements of this heap. -
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 interfaceMergeableHeap<K>
- Parameters:
other
- a merge-able heap- Throws:
IllegalArgumentException
- ifother
has a different error rate
-
insert
Insert a key into the heap. -
findMin
Find an element with the minimum key. -
deleteMin
Delete and return an element with the minimum key. If multiple such elements exists, only one of them will be deleted. -
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
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 BinaryTreeSoftHeap.TreeNode<K> combine(BinaryTreeSoftHeap.TreeNode<K> x, BinaryTreeSoftHeap.TreeNode<K> 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
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(BinaryTreeSoftHeap.RootListNode<K> head, BinaryTreeSoftHeap.RootListNode<K> 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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