org.jheaps.array

Class DaryArrayAddressableHeap<K,V>

java.lang.Object

org.jheaps.array.DaryArrayAddressableHeap<K,V>

Type Parameters:

K - the type of keys maintained by this heap

V - the type of values maintained by this heap

All Implemented Interfaces:

Serializable, AddressableHeap<K,V>

public class DaryArrayAddressableHeap<K,V>
extends Object
implements Serializable

An array based d-ary addressable 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. Operations delete and decreaseKey take worst-case O(log(n)) time. 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[], Object[]) or heapify(int, Object[], 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 binary 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

Nested Class Summary

Nested classes/interfaces inherited from interface org.jheaps.AddressableHeap

AddressableHeap.Handle<K,V>

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor and Description
DaryArrayAddressableHeap(int d) Constructs a new, empty heap, using the natural ordering of its keys.
DaryArrayAddressableHeap(int d, Comparator<? super K> comparator) Constructs a new, empty heap, ordered according to the given comparator.
DaryArrayAddressableHeap(int d, Comparator<? super K> comparator, int capacity) Constructs a new, empty heap, with a provided initial capacity ordered according to the given comparator.
DaryArrayAddressableHeap(int d, int capacity) Constructs a new, empty heap, with a provided initial capacity using the natural ordering of its keys.

Method Summary

Modifier and Type	Method and Description
void	clear() Clear all the elements of the heap.
Comparator<? super K>	comparator() Returns the comparator used to order the keys in this AddressableHeap, or null if this heap uses the natural ordering of its keys.
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.
static <K,V> DaryArrayAddressableHeap<K,V>	heapify(int d, K[] keys, V[] values) Create a heap from an array of elements.
static <K,V> DaryArrayAddressableHeap<K,V>	heapify(int d, K[] keys, V[] values, Comparator<? super K> comparator) Create a heap from an array of elements.
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() Returns true if this heap is empty.
long	size() Returns the number of elements in the 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 binary heap.

See Also:

Constant Field Values

Constructor Detail

DaryArrayAddressableHeap

public DaryArrayAddressableHeap(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

DaryArrayAddressableHeap

public DaryArrayAddressableHeap(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

DaryArrayAddressableHeap

public DaryArrayAddressableHeap(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 *

DaryArrayAddressableHeap

public DaryArrayAddressableHeap(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,V> DaryArrayAddressableHeap<K,V> heapify(int d,
                                                          K[] keys,
                                                          V[] values)

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

V - the type of values maintained by the heap

Parameters:

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

keys - an array of keys

values - an array of values, can be null

Returns:

a d-ary heap

Throws:

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

IllegalArgumentException - in case the keys array is null

IllegalArgumentException - in case the values array has different length than the keys array

heapify

public static <K,V> DaryArrayAddressableHeap<K,V> heapify(int d,
                                                          K[] keys,
                                                          V[] values,
                                                          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

V - the type of values maintained by the heap

Parameters:

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

keys - an array of keys

values - an array of values, can be null

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 keys array is null

IllegalArgumentException - in case the values array has different length than the keys array

findMin

public AddressableHeap.Handle<K,V> findMin()

Find an element with the minimum key.

Specified by:

findMin in interface AddressableHeap<K,V>

Returns:

a handle to an element with minimum key

isEmpty

public boolean isEmpty()

Returns true if this heap is empty.

Specified by:

isEmpty in interface AddressableHeap<K,V>

Returns:

true if this heap is empty, false otherwise

size

public long size()

Returns the number of elements in the heap.

Specified by:

size in interface AddressableHeap<K,V>

Returns:

the number of elements in the heap

comparator

public Comparator<? super K> comparator()

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

Specified by:

comparator in interface AddressableHeap<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

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 methods AddressableHeap.Handle.decreaseKey(Object) and AddressableHeap.Handle.delete() is undefined.

Specified by:

clear in interface AddressableHeap<K,V>

insert

public AddressableHeap.Handle<K,V> insert(K key)

Insert a new element into the heap with a null value.

Specified by:

insert in interface AddressableHeap<K,V>

Parameters:

key - the element's key

Returns:

a handle for the newly added element

insert

public AddressableHeap.Handle<K,V> insert(K key,
                                          V value)

Insert a new element into the heap.

Specified by:

insert in interface AddressableHeap<K,V>

Parameters:

key - the element's key

value - the element's value

Returns:

a handle for the newly added element

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 method AddressableHeap.Handle.getKey() and AddressableHeap.Handle.getValue() can be used.

Specified by:

deleteMin in interface AddressableHeap<K,V>

Returns:

a handle to the deleted element with minimum key