Package org.jheaps.tree

Class PurePairingHeap<K,V>

java.lang.Object
org.jheaps.tree.PurePairingHeap<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>, MergeableAddressableHeap<K,V>
public class PurePairingHeap<K,V> extends Object implements MergeableAddressableHeap<K,V>, Serializable
Pure 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.

The pure pairing heap is a simplification of the PairingHeap due to Tarjan and Xu, described in detail in the following paper:

  • Robert E. Tarjan and Xiaoyang Xu, Pure Pairing Heaps, arXiv:2607.23118, 2026.
A standard pairing heap performs a deleteMin using a pairing pass followed by an assembly pass which links together all the winners of the pairing pass into a single tree. The pure pairing heap instead eliminates the assembly pass entirely: during its single pairing pass it keeps track of the winner of minimum key, and once the pass is complete, it simply makes that winner the new root and re-parents every other surviving winner as one of its children. Despite being simpler than the standard pairing heap, the pure pairing heap achieves the same amortized bounds as the more complicated multipass pairing heap.

This implementation provides amortized O(log(n)) time cost for the deleteMin operation, amortized O(loglog(n)) time cost for the decreaseKey operation, and amortized O(1) time cost for the insert and meld operations. Operation findMin, is a worst-case O(1) operation.

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 pure pairing 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 a pure 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 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:

  • Constructor Details

    • PurePairingHeap

      public PurePairingHeap()
      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.

    • PurePairingHeap

      public PurePairingHeap(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.

  • Method Details