Class SkewHeap<K,V>

java.lang.Object
org.jheaps.tree.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:
Serializable, AddressableHeap<K,V>, MergeableAddressableHeap<K,V>
Direct Known Subclasses:
LeftistHeap

public class SkewHeap<K,V> extends Object implements MergeableAddressableHeap<K,V>, 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:
  • Field Details

    • serialVersionUID

      private static final long serialVersionUID
      See Also:
    • comparator

      protected final 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
    • root

      protected SkewHeap.Node<K,V> root
      Root node 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 Details

    • 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(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

    • 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
    • findMin

      public AddressableHeap.Handle<K,V> findMin()
      Find an element with the minimum key.
      Specified by:
      findMin in interface AddressableHeap<K,V>
      Returns:
      a handle to an element with minimum key
    • deleteMin

      public AddressableHeap.Handle<K,V> deleteMin()
      Delete and return an element with the minimum key. If multiple such elements exists, only one of them will be deleted. After the element is deleted the handle is invalidated and only method AddressableHeap.Handle.getKey() and AddressableHeap.Handle.getValue() can be used.
      Specified by:
      deleteMin in interface AddressableHeap<K,V>
      Returns:
      a handle to the deleted element with minimum key
    • 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 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
    • clear

      public void clear()
      Clear all the elements of the heap. After calling this method all handles should be considered invalidated and the behavior of methods AddressableHeap.Handle.decreaseKey(Object) and AddressableHeap.Handle.delete() is undefined.
      Specified by:
      clear in interface AddressableHeap<K,V>
    • meld

      public void meld(MergeableAddressableHeap<K,V> other)
      Description copied from interface: MergeableAddressableHeap
      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(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