Package org.jheaps.array

Class DaryArrayAddressableHeap<K,V>

java.lang.Object
org.jheaps.array.DaryArrayAddressableHeap<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>
public class DaryArrayAddressableHeap<K,V> extends Object implements Serializable
An array based d-ary addressable heap. 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 implementation uses an array in order to store the elements. and automatically maintains the size of the array much like a Vector does, providing amortized O(log_d(n)) time cost for the insert and amortized O(d log_d(n)) for the deleteMin operation. Operation findMin, is a worst-case O(1) operation. Operations delete and decreaseKey take worst-case O(log(n)) time. The bounds are worst-case if the user initializes the heap with a capacity larger or equal to the total number of elements that are going to be inserted into the heap.

Constructing such a heap from an array of elements can be performed using the method heapify(int, Object[], Object[]) or heapify(int, Object[], Object[], Comparator) in linear time.

Note that the ordering maintained by a d-ary 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 a binary 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 d-ary 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.

Author:
Dimitrios Michail
See Also:

  • Field Details

    • DEFAULT_HEAP_CAPACITY

      public static final int DEFAULT_HEAP_CAPACITY
      Default initial capacity of the binary heap.
      See Also:

    • d

      protected int d
      Degree

    • NO_INDEX

      protected static final int NO_INDEX
      Denotes that a handle is not in the array
      See Also:

    • MAX_HEAP_CAPACITY

      protected static final int MAX_HEAP_CAPACITY
      The maximum heap capacity.
      See Also:

    • MIN_HEAP_CAPACITY

      protected static final int MIN_HEAP_CAPACITY
      The minimum heap capacity.
      See Also:

    • DOWNSIZING_MIN_HEAP_CAPACITY

      protected static final int DOWNSIZING_MIN_HEAP_CAPACITY
      Limit for the heap capacity when down-sizing.
      See Also:

    • comparator

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

    • array

      protected org.jheaps.array.AbstractArrayAddressableHeap<K,V>.org.jheaps.array.AbstractArrayAddressableHeap.ArrayHandle[] array
      The array use for representing the tree.

    • size

      protected int size
      Number of elements in the heap.

    • minCapacity

      protected final int minCapacity
      Minimum capacity due to initially requested capacity.

  • Constructor Details

    • DaryArrayAddressableHeap

      public DaryArrayAddressableHeap(int d)
      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.

      The initial capacity of the heap is DEFAULT_HEAP_CAPACITY and adjusts automatically based on the sequence of insertions and deletions.

      Parameters:
      d - the number of children of each node in the d-ary heap
      Throws:
      IllegalArgumentException - in case the number of children per node are less than 2

    • DaryArrayAddressableHeap

      public DaryArrayAddressableHeap(int d, int capacity)
      Constructs a new, empty heap, with a provided initial capacity 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.

      The initial capacity of the heap is provided by the user and is adjusted automatically based on the sequence of insertions and deletions. The capacity will never become smaller than the initial requested capacity.

      Parameters:
      d - the number of children of each node in the d-ary heap
      capacity - the initial heap capacity
      Throws:
      IllegalArgumentException - in case the number of children per node are less than 2

    • DaryArrayAddressableHeap

      public DaryArrayAddressableHeap(int d, 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.

      The initial capacity of the heap is DEFAULT_HEAP_CAPACITY and adjusts automatically based on the sequence of insertions and deletions.

      Parameters:
      d - the number of children of each node in the d-ary heap
      comparator - the comparator that will be used to order this heap. If null, the natural ordering of the keys will be used.
      Throws:
      IllegalArgumentException - in case the number of children per node are less than 2 *

    • DaryArrayAddressableHeap

      public DaryArrayAddressableHeap(int d, Comparator<? super K> comparator, int capacity)
      Constructs a new, empty heap, with a provided initial capacity 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.

      The initial capacity of the heap is provided by the user and is adjusted automatically based on the sequence of insertions and deletions. The capacity will never become smaller than the initial requested capacity.

      Parameters:
      d - the number of children of each node in the d-ary heap
      comparator - the comparator that will be used to order this heap. If null, the natural ordering of the keys will be used.
      capacity - the initial heap capacity
      Throws:
      IllegalArgumentException - in case the number of children per node are less than 2

  • Method Details

    • heapify

      public static <K, V> DaryArrayAddressableHeap<K,V> heapify(int d, K[] keys, V[] values)
      Create a heap from an array of elements. The elements of the array are not destroyed. The method has linear time complexity.
      Type Parameters:
      K - the type of keys maintained by the heap
      V - the type of values maintained by the heap
      Parameters:
      d - the number of children of the d-ary heap
      keys - an array of keys
      values - an array of values, can be null
      Returns:
      a d-ary heap
      Throws:
      IllegalArgumentException - in case the number of children per node are less than 2
      IllegalArgumentException - in case the keys array is null
      IllegalArgumentException - in case the values array has different length than the keys array

    • heapify

      public static <K, V> DaryArrayAddressableHeap<K,V> heapify(int d, K[] keys, V[] values, Comparator<? super K> comparator)
      Create a heap from an array of elements. The elements of the array are not destroyed. The method has linear time complexity.
      Type Parameters:
      K - the type of keys maintained by the heap
      V - the type of values maintained by the heap
      Parameters:
      d - the number of children of the d-ary heap
      keys - an array of keys
      values - an array of values, can be null
      comparator - the comparator to use
      Returns:
      a d-ary heap
      Throws:
      IllegalArgumentException - in case the number of children per node are less than 2
      IllegalArgumentException - in case the keys array is null
      IllegalArgumentException - in case the values array has different length than the keys array

    • handlesIterator

      public Iterator<AddressableHeap.Handle<K,V>> handlesIterator()
      Get an iterator for all handles currently in the heap. This method is especially useful when building a heap using the heapify method. Unspecified behavior will occur if the heap is modified while using this iterator.
      Returns:
      an iterator which will return all handles of the heap

    • ensureCapacity

      protected void ensureCapacity(int capacity)
      Ensure that the array representation has the necessary capacity.
      Parameters:
      capacity - the requested capacity

    • forceFixup

      protected void forceFixup(int k)

    • fixup

      protected void fixup(int k)

    • fixupWithComparator

      protected void fixupWithComparator(int k)

    • fixdown

      protected void fixdown(int k)

    • fixdownWithComparator

      protected void fixdownWithComparator(int k)

    • 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

    • 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>

    • 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

    • 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

    • checkCapacity

      protected final void checkCapacity(int capacity)