Package org.jheaps.tree

Class SkewHeap<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>
    Direct Known Subclasses:
    LeftistHeap
    public class SkewHeap<K,​V>
extends java.lang.Object
implements MergeableAddressableHeap<K,​V>, java.io.Serializable
    Skew 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.

    Operations insert, deleteMin, and delete take amortized O(log(n)). Operation findMin is worst-case O(1). Note that a skew-heap does not efficiently support the operation decreaseKey which is amortized Ω(log(n)).

    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 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 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 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.

    See Also:
    Serialized Form

    • Field Detail

      • comparator

        protected 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

        protected long size
        Size of the heap

      • other

        protected SkewHeap<K,​V> other
        Used to reference the current heap or some other 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

      • SkewHeap

        public SkewHeap()
        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.

      • SkewHeap

        public SkewHeap​(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)
        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

      • 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

      • decreaseKey

        private void decreaseKey​(SkewHeap.Node<K,​V> n,
                         K newKey)

      • createNode

        protected SkewHeap.Node<K,​V> createNode​(K key,
                                              V value)
        Create a new node.
        Parameters:
        key - the key
        value - the value
        Returns:
        the newly created node

      • delete

        protected void delete​(SkewHeap.Node<K,​V> n)
        Delete a node from the heap.
        Parameters:
        n - the node

      • unlinkAndUnionChildren

        protected SkewHeap.Node<K,​V> unlinkAndUnionChildren​(SkewHeap.Node<K,​V> n)
        Unlink the two children of a node and union them forming a new tree.
        Parameters:
        n - the node
        Returns:
        the tree which is formed by the two children subtrees of the node

      • getParent

        protected SkewHeap.Node<K,​V> getParent​(SkewHeap.Node<K,​V> n)
        Get the parent node of a given node.
        Parameters:
        n - the node
        Returns:
        the parent of a node

      • unlinkRightChild

        protected SkewHeap.Node<K,​V> unlinkRightChild​(SkewHeap.Node<K,​V> n)
        Unlink the right child of a node.
        Parameters:
        n - the node
        Returns:
        the right child after unlinking

      • union

        protected SkewHeap.Node<K,​V> union​(SkewHeap.Node<K,​V> root1,
                                         SkewHeap.Node<K,​V> root2)
        Top-down union of two skew heaps.
        Parameters:
        root1 - the root of the first heap
        root2 - the root of the right heap
        Returns:
        the new root of the merged heap

      • unionWithComparator

        protected SkewHeap.Node<K,​V> unionWithComparator​(SkewHeap.Node<K,​V> root1,
                                                       SkewHeap.Node<K,​V> root2)
        Top-down union of two skew heaps with comparator.
        Parameters:
        root1 - the root of the first heap
        root2 - the root of the right heap
        Returns:
        the new root of the merged heap