org.jheaps.tree

Class ReflectedPairingHeap<K,V>

java.lang.Object

org.jheaps.tree.ReflectedHeap<K,V>

org.jheaps.tree.ReflectedPairingHeap<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>, DoubleEndedAddressableHeap<K,V>, MergeableDoubleEndedAddressableHeap<K,V>

public class ReflectedPairingHeap<K,V>
extends ReflectedHeap<K,V>

Reflected double ended heaps based on pairing heaps. 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.

This class implements a general technique which uses two PairingHeaps to implement a double ended heap, described in detail in the following paper:

• C. Makris, A. Tsakalidis, and K. Tsichlas. Reflected min-max heaps. Information Processing Letters, 86(4), 209--214, 2003.

This implementation provides amortized O(log(n)) time cost for the insert, deleteMin, deleteMax, decreaseKey, increaseKey, and delete operations. findMin and findMax are worst-case O(1) operations. The operation meld is amortized O(log(n)).

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 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 AddressableHeap interface. (See Comparable or Comparator for a precise definition of consistent with equals.) This is so because the AddressableHeap 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 AddressableHeap 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.DoubleEndedAddressableHeap

DoubleEndedAddressableHeap.Handle<K,V>

Constructor Summary

Constructors

Constructor and Description
ReflectedPairingHeap() Constructs a new, empty heap, using the natural ordering of its keys.
ReflectedPairingHeap(Comparator<? super K> comparator) Constructs a new, empty heap, ordered according to the given comparator.

Method Summary

Methods inherited from class org.jheaps.tree.ReflectedHeap

clear, comparator, deleteMax, deleteMin, findMax, findMin, insert, insert, isEmpty, meld, size

Methods inherited from class java.lang.Object

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

Constructor Detail

ReflectedPairingHeap

public ReflectedPairingHeap()

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.

ReflectedPairingHeap

public ReflectedPairingHeap(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.

Parameters:

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