Package org.jheaps.array

Class DaryArrayHeap<K>

java.lang.Object

org.jheaps.array.DaryArrayHeap<K>

Type Parameters:

K - the type of keys maintained by this heap

All Implemented Interfaces:

Serializable, Heap<K>

public class DaryArrayHeap<K>
extends Object

An array based d-ary heap. The heap is sorted according to the natural ordering of its keys, or by a Comparator provided at heap creation time, depending on which constructor is used.

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_d(n)) time cost for the insert and amortized O(d log_d(n)) for the deleteMin operation. Operation findMin, is a worst-case O(1) operation. 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(int, Object[]) or heapify(int, Object[], Comparator) in linear time.

Note that the ordering maintained by a d-ary 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 d-ary 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 d-ary 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.

Author:

Dimitrios Michail

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static int	DEFAULT_HEAP_CAPACITY	Default initial capacity of the heap.

Constructor Summary

Constructors

Constructor	Description
DaryArrayHeap(int d)	Constructs a new, empty heap, using the natural ordering of its keys.
DaryArrayHeap(int d, int capacity)	Constructs a new, empty heap, with a provided initial capacity using the natural ordering of its keys.
DaryArrayHeap(int d, Comparator<? super K> comparator)	Constructs a new, empty heap, ordered according to the given comparator.
DaryArrayHeap(int d, 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 Type	Method	Description
void	clear()	Clear all the elements of this heap.
Comparator<? super K>	comparator()	Returns the comparator used to order the keys in this heap, or null if this heap uses the natural ordering of its keys.
K	deleteMin()	Delete and return an element with the minimum key.
K	findMin()	Find an element with the minimum key.
static <K> DaryArrayHeap<K>	heapify(int d, K[] array)	Create a heap from an array of elements.
static <K> DaryArrayHeap<K>	heapify(int d, K[] array, Comparator<? super K> comparator)	Create a heap from an array of elements.
void	insert(K key)	Insert a key into the heap.
boolean	isEmpty()	Returns true if this heap is empty.
long	size()	Returns the number of elements in this heap.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

DEFAULT_HEAP_CAPACITY

public static final int DEFAULT_HEAP_CAPACITY

Default initial capacity of the heap.

See Also:

Constant Field Values

Constructor Detail

DaryArrayHeap

public DaryArrayHeap(int d)

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 a ClassCastException for any keys k1 and k2 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), the insert(Object key) call will throw a ClassCastException.

The initial capacity of the heap is DEFAULT_HEAP_CAPACITY and adjusts automatically based on the sequence of insertions and deletions.

Parameters:

d - the number of children of each node in the d-ary heap

Throws:

IllegalArgumentException - in case the number of children per node are less than 2

DaryArrayHeap

public DaryArrayHeap(int d,
                     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 a ClassCastException for any keys k1 and k2 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), the insert(Object key) call will throw a ClassCastException.

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:

d - the number of children of each node in the d-ary heap

capacity - the initial heap capacity

Throws:

IllegalArgumentException - in case the number of children per node are less than 2

DaryArrayHeap

public DaryArrayHeap(int d,
                     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 a ClassCastException for any keys k1 and k2 in the heap. If the user attempts to put a key into the heap that violates this constraint, the insert(Object key) call will throw a ClassCastException.

The initial capacity of the heap is DEFAULT_HEAP_CAPACITY and adjusts automatically based on the sequence of insertions and deletions.

Parameters:

d - the number of children of each node in the d-ary heap

comparator - the comparator that will be used to order this heap. If null, the natural ordering of the keys will be used.

Throws:

IllegalArgumentException - in case the number of children per node are less than 2

DaryArrayHeap

public DaryArrayHeap(int d,
                     Comparator<? super K> comparator,
                     int capacity)

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 a ClassCastException for any keys k1 and k2 in the heap. If the user attempts to put a key into the heap that violates this constraint, the insert(Object key) call will throw a ClassCastException.

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:

d - the number of children of each node in the d-ary heap

comparator - the comparator that will be used to order this heap. If null, the natural ordering of the keys will be used.

capacity - the initial heap capacity

Throws:

IllegalArgumentException - in case the number of children per node are less than 2

Method Detail

heapify

public static <K> DaryArrayHeap<K> heapify(int d,
                                           K[] array)

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:

d - the number of children of the d-ary heap

array - an array of elements

Returns:

a d-ary heap

Throws:

IllegalArgumentException - in case the number of children per node are less than 2

IllegalArgumentException - in case the array is null

heapify

public static <K> DaryArrayHeap<K> heapify(int d,
                                           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:

d - the number of children of the d-ary heap

array - an array of elements

comparator - the comparator to use

Returns:

a d-ary heap

Throws:

IllegalArgumentException - in case the number of children per node are less than 2

IllegalArgumentException - in case the array is null

findMin

public K findMin()

Find an element with the minimum key.

Returns:

an element with the minimum key

insert

public void insert(K key)

Insert a key into the heap.

Parameters:

key - the key to insert

deleteMin

public K deleteMin()

Delete and return an element with the minimum key. If multiple such elements exists, only one of them will be deleted.

Returns:

the deleted element with the minimum key

isEmpty

public boolean isEmpty()

Returns true if this heap is empty.

Specified by:

isEmpty in interface Heap<K>

Returns:

true if this heap is empty, false otherwise

size

public long size()

Returns the number of elements in this heap.

Specified by:

size in interface Heap<K>

Returns:

the number of elements in this heap

comparator

public Comparator<? super K> comparator()

Returns the comparator used to order the keys in this heap, or null if this heap uses the natural ordering of its keys.

Specified by:

comparator in interface Heap<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.

Specified by:

clear in interface Heap<K>