Class MinMaxBinaryArrayDoubleEndedHeap<K>
- Type Parameters:
K
- the type of keys maintained by this heap
- All Implemented Interfaces:
Serializable
,DoubleEndedHeap<K>
,Heap<K>
Comparator
provided at heap creation time, depending on which
constructor is used.
For details about the implementation see the following paper:
- M. D. Atkinson, J.-R. Sack, N. Santoro, and T. Strothotte. Min-max Heaps and Generalized Priority Queues. Commun. ACM, 29(10), 996--1000, 1986.
The implementation uses an array in order to store the elements and
automatically maintains the size of the array much like a
Vector
does, providing amortized O(log(n)) time cost for
the insert
, deleteMin
, and deleteMax
operations.
Operations findMin
and findMax
are worst-case O(1). The
bounds are worst-case if the user initializes the heap with a capacity larger
or equal to the total number of elements that are going to be inserted into
the heap.
Constructing such a heap from an array of elements can be performed using the
method heapify(Object[])
or heapify(Object[], Comparator)
in linear time.
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 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 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
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:
-
Field Summary
FieldsModifier and TypeFieldDescriptionstatic final int
Default initial capacity of the heap.private static final long
Fields inherited from class org.jheaps.array.AbstractArrayWeakHeap
array, comparator, DOWNSIZING_MIN_HEAP_CAPACITY, MAX_HEAP_CAPACITY, MIN_HEAP_CAPACITY, minCapacity, size
-
Constructor Summary
ConstructorsConstructorDescriptionConstructs a new, empty heap, using the natural ordering of its keys.MinMaxBinaryArrayDoubleEndedHeap
(int capacity) Constructs a new, empty heap, with a provided initial capacity using the natural ordering of its keys.MinMaxBinaryArrayDoubleEndedHeap
(Comparator<? super K> comparator) Constructs a new, empty heap, ordered according to the given comparator.MinMaxBinaryArrayDoubleEndedHeap
(Comparator<? super K> comparator, int capacity) Constructs a new, empty heap, with a provided initial capacity ordered according to the given comparator. -
Method Summary
Modifier and TypeMethodDescriptionDelete and return an element with the maximum key.protected void
ensureCapacity
(int capacity) Ensure that the array representation has the necessary capacity.findMax()
Find an element with the maximum key.protected void
fixdown
(int k) Downwards fix starting from a particular element.private void
fixdownMax
(int k) Downwards fix starting from a particular element at a maximum level.private void
fixdownMaxWithComparator
(int k) Downwards fix starting from a particular element at a maximum level.private void
fixdownMin
(int k) Downwards fix starting from a particular element at a minimum level.private void
fixdownMinWithComparator
(int k) Downwards fix starting from a particular element at a minimum level.protected void
fixdownWithComparator
(int k) Downwards fix starting from a particular element.protected void
fixup
(int k) Upwards fix starting from a particular elementprivate void
fixupMax
(int k) Upwards fix starting from a particular element at a maximum levelprivate void
fixupMaxWithComparator
(int k) Upwards fix starting from a particular element at a maximum level.private void
fixupMin
(int k) Upwards fix starting from a particular element at a minimum levelprivate void
fixupMinWithComparator
(int k) Upwards fix starting from a particular element at a minimum level.protected void
fixupWithComparator
(int k) Upwards fix starting from a particular elementstatic <K> MinMaxBinaryArrayDoubleEndedHeap<K>
heapify
(K[] array) Create a heap from an array of elements.static <K> MinMaxBinaryArrayDoubleEndedHeap<K>
heapify
(K[] array, Comparator<? super K> comparator) Create a heap from an array of elements.private int
maxChildOrGrandchild
(int k) Given a node at a maximum level, find its child or grandchild with the maximum key.private int
Given a node at a maximum level, find its child or grandchild with the maximum key.private int
minChildOrGrandchild
(int k) Given a node at a minimum level, find its child or grandchild with the minimum key.private int
Given a node at a minimum level, find its child or grandchild with the minimum key.(package private) boolean
onMinLevel
(int k) Return true if on a minimum level, false otherwise.Methods inherited from class org.jheaps.array.AbstractArrayHeap
deleteMin, findMin, initCapacity, insert
Methods inherited from class org.jheaps.array.AbstractArrayWeakHeap
checkCapacity, clear, comparator, isEmpty, size
-
Field Details
-
serialVersionUID
private static final long serialVersionUID- See Also:
-
DEFAULT_HEAP_CAPACITY
public static final int DEFAULT_HEAP_CAPACITYDefault initial capacity of the heap.- See Also:
-
-
Constructor Details
-
MinMaxBinaryArrayDoubleEndedHeap
public MinMaxBinaryArrayDoubleEndedHeap()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
.The initial capacity of the heap is
DEFAULT_HEAP_CAPACITY
and adjusts automatically based on the sequence of insertions and deletions. -
MinMaxBinaryArrayDoubleEndedHeap
public MinMaxBinaryArrayDoubleEndedHeap(int capacity) Constructs a new, empty heap, with a provided initial capacity 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
.The initial capacity of the heap is provided by the user and is adjusted automatically based on the sequence of insertions and deletions. The capacity will never become smaller than the initial requested capacity.
- Parameters:
capacity
- the initial heap capacity
-
MinMaxBinaryArrayDoubleEndedHeap
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
.The initial capacity of the heap is
DEFAULT_HEAP_CAPACITY
and adjusts automatically based on the sequence of insertions and deletions.- Parameters:
comparator
- the comparator that will be used to order this heap. Ifnull
, the natural ordering of the keys will be used.
-
MinMaxBinaryArrayDoubleEndedHeap
Constructs a new, empty heap, with a provided initial capacity 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
.The initial capacity of the heap is provided by the user and is adjusted automatically based on the sequence of insertions and deletions.The capacity will never become smaller than the initial requested capacity.
- Parameters:
comparator
- the comparator that will be used to order this heap. Ifnull
, the natural ordering of the keys will be used.capacity
- the initial heap capacity
-
-
Method Details
-
heapify
Create a heap from an array of elements. The elements of the array are not destroyed. The method has linear time complexity.- Type Parameters:
K
- the type of keys maintained by the heap- Parameters:
array
- an array of elements- Returns:
- a heap
- Throws:
IllegalArgumentException
- in case the array is null
-
heapify
public static <K> MinMaxBinaryArrayDoubleEndedHeap<K> heapify(K[] array, Comparator<? super K> comparator) Create a heap from an array of elements. The elements of the array are not destroyed. The method has linear time complexity.- Type Parameters:
K
- the type of keys maintained by the heap- Parameters:
array
- an array of elementscomparator
- the comparator to use- Returns:
- a heap
- Throws:
IllegalArgumentException
- in case the array is null
-
ensureCapacity
protected void ensureCapacity(int capacity) Ensure that the array representation has the necessary capacity.- Specified by:
ensureCapacity
in classAbstractArrayWeakHeap<K>
- Parameters:
capacity
- the requested capacity
-
findMax
Find an element with the maximum key.- Specified by:
findMax
in interfaceDoubleEndedHeap<K>
- Returns:
- an element with the maximum key
-
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 interfaceDoubleEndedHeap<K>
- Returns:
- the deleted element with the maximum key
-
fixup
protected void fixup(int k) Upwards fix starting from a particular element- Specified by:
fixup
in classAbstractArrayWeakHeap<K>
- Parameters:
k
- the index of the starting element
-
fixupWithComparator
protected void fixupWithComparator(int k) Upwards fix starting from a particular element- Specified by:
fixupWithComparator
in classAbstractArrayWeakHeap<K>
- Parameters:
k
- the index of the starting element
-
fixupMin
private void fixupMin(int k) Upwards fix starting from a particular element at a minimum level- Parameters:
k
- the index of the starting element
-
fixupMinWithComparator
private void fixupMinWithComparator(int k) Upwards fix starting from a particular element at a minimum level. Performs comparisons using the comparator.- Parameters:
k
- the index of the starting element
-
fixupMax
private void fixupMax(int k) Upwards fix starting from a particular element at a maximum level- Parameters:
k
- the index of the starting element
-
fixupMaxWithComparator
private void fixupMaxWithComparator(int k) Upwards fix starting from a particular element at a maximum level. Performs comparisons using the comparator.- Parameters:
k
- the index of the starting element
-
fixdown
protected void fixdown(int k) Downwards fix starting from a particular element.- Specified by:
fixdown
in classAbstractArrayWeakHeap<K>
- Parameters:
k
- the index of the starting element
-
fixdownWithComparator
protected void fixdownWithComparator(int k) Downwards fix starting from a particular element. Performs comparisons using the comparator.- Specified by:
fixdownWithComparator
in classAbstractArrayWeakHeap<K>
- Parameters:
k
- the index of the starting element
-
fixdownMin
private void fixdownMin(int k) Downwards fix starting from a particular element at a minimum level.- Parameters:
k
- the index of the starting element
-
fixdownMinWithComparator
private void fixdownMinWithComparator(int k) Downwards fix starting from a particular element at a minimum level. Performs comparisons using the comparator.- Parameters:
k
- the index of the starting element
-
fixdownMax
private void fixdownMax(int k) Downwards fix starting from a particular element at a maximum level.- Parameters:
k
- the index of the starting element
-
fixdownMaxWithComparator
private void fixdownMaxWithComparator(int k) Downwards fix starting from a particular element at a maximum level. Performs comparisons using the comparator.- Parameters:
k
- the index of the starting element
-
onMinLevel
boolean onMinLevel(int k) Return true if on a minimum level, false otherwise.- Parameters:
k
- the element- Returns:
- true if on a minimum level, false otherwise
-
maxChildOrGrandchild
private int maxChildOrGrandchild(int k) Given a node at a maximum level, find its child or grandchild with the maximum key. This method should not be called for a node which has no children.- Parameters:
k
- a node at a maximum level- Returns:
- the child or grandchild with a maximum key, or undefined if there are no children
-
maxChildOrGrandchildWithComparator
private int maxChildOrGrandchildWithComparator(int k) Given a node at a maximum level, find its child or grandchild with the maximum key. This method should not be called for a node which has no children.- Parameters:
k
- a node at a maximum level- Returns:
- the child or grandchild with a maximum key, or undefined if there are no children
-
minChildOrGrandchild
private int minChildOrGrandchild(int k) Given a node at a minimum level, find its child or grandchild with the minimum key. This method should not be called for a node which has no children.- Parameters:
k
- a node at a minimum level- Returns:
- the child or grandchild with a minimum key, or undefined if there are no children
-
minChildOrGrandchildWithComparator
private int minChildOrGrandchildWithComparator(int k) Given a node at a minimum level, find its child or grandchild with the minimum key. This method should not be called for a node which has no children.- Parameters:
k
- a node at a minimum level- Returns:
- the child or grandchild with a minimum key, or undefined if there are no children
-