Package org.jheaps.tree

Class CostlessMeldPairingHeap<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 CostlessMeldPairingHeap<K,​V>
extends Object
implements MergeableAddressableHeap<K,​V>, Serializable
    The costless meld variant of the 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 implementation provides amortized O(1) time for findMin and insert, amortized O(log(n)) for deleteMin and delete and amortized O(loglog(n)) for the decreaseKey operation. The operation meld takes amortized zero time.

    This variant of the pairing heap is due to Amr Elmasry, described in detail in the following paper:

    • Amr Elmasry, Pairing Heaps with Costless Meld, In Proceedings of the 18th Annual European Symposium on Algorithms (ESA 2010), 183--193, 2010.

    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 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 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 the pairing 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:
    PairingHeap, FibonacciHeap, Serialized Form

    • Constructor Detail

      • CostlessMeldPairingHeap

        public CostlessMeldPairingHeap()
        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.

      • CostlessMeldPairingHeap

        public CostlessMeldPairingHeap​(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.