Class HollowHeap<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:
    java.io.Serializable, AddressableHeap<K,​V>, MergeableAddressableHeap<K,​V>

    public class HollowHeap<K,​V>
    extends java.lang.Object
    implements MergeableAddressableHeap<K,​V>, java.io.Serializable
    Hollow 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 is the hollow heap described in detail in the following paper:

    • TD Hansen, H Kaplan, RE Tarjan and U Zwick. Hollow heaps. ACM Transactions on Algorithms (TALG), 13(3), 42, 2017.

    This implementation provides amortized O(1) time for operations that do not involve deleting an element such as insert, and decreaseKey. Operations deleteMin and delete are amortized O(log(n)). The operation meld is also amortized O(1).

    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 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.

    See Also:
    Serialized Form
    • Field Detail

      • AUX_BUCKET_ARRAY_SIZE

        private static final int AUX_BUCKET_ARRAY_SIZE
        Size of bucket array. Based on maximum rank.
        See Also:
        Constant Field Values
      • comparator

        private final java.util.Comparator<? super K> comparator
        The comparator used to maintain order in this heap, or null if it uses the natural ordering of its keys.
      • size

        private long size
        Size of the heap
      • nodes

        private long nodes
        Number of nodes (hollow or not). Useful for rebuilding.
      • other

        private HollowHeap<K,​V> other
        Used to reference the current heap or some other pairing heap in case of melding, so that handles remain valid even after a meld, without having to iterate over them. In order to avoid maintaining a full-fledged union-find data structure, we disallow a heap to be used in melding more than once. We use however, path-compression in case of cascading melds, that it, a handle moves from one heap to another and then another.
    • Constructor Detail

      • HollowHeap

        public HollowHeap()
        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.
      • HollowHeap

        public HollowHeap​(java.util.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 Detail

      • 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
        Throws:
        java.lang.IllegalStateException - if the heap has already been used in the right hand side of a meld
      • 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
        Throws:
        java.lang.IllegalStateException - if the heap has already been used in the right hand side of a meld
      • 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 java.util.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
      • meld

        public void meld​(MergeableAddressableHeap<K,​V> other)
        Meld a heap into the current heap. After the operation the other heap will be empty and will not permit further insertions.
        Specified by:
        meld in interface MergeableAddressableHeap<K,​V>
        Parameters:
        other - a merge-able heap
      • decreaseKey

        private void decreaseKey​(HollowHeap.Item<K,​V> e,
                                 K newKey)
        Decrease the key of an item.
        Parameters:
        n - the item
        newKey - the new key
      • delete

        private void delete​(HollowHeap.Item<K,​V> e)
        Delete an item
        Parameters:
        e - the item
      • doUnrankedLinks

        private void doUnrankedLinks​(int maxRank)