Package org.jheaps.array

Class BinaryArrayHeap<K>

java.lang.Object
org.jheaps.array.BinaryArrayHeap<K>
Type Parameters:
K - the type of keys maintained by this heap
All Implemented Interfaces:
Serializable, Heap<K>
public class BinaryArrayHeap<K> extends Object
An array based binary 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(n)) time cost for the insert and deleteMin operations. Operation findMin, is a worst-case O(1) operation. 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(Object[]) or heapify(Object[], Comparator) in linear time.

Note that the ordering maintained by a binary 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 binary 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 Summary

    Fields
    Modifier and Type
    Field
    Description
    protected K[]
    array
    The array used for representing the heap.
    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.
    static final int
    DEFAULT_HEAP_CAPACITY
    Default initial capacity of the binary heap.
    protected static final int
    DOWNSIZING_MIN_HEAP_CAPACITY
    Limit for the heap capacity when down-sizing.
    protected static final int
    MAX_HEAP_CAPACITY
    The maximum heap capacity.
    protected static final int
    MIN_HEAP_CAPACITY
    The minimum heap capacity.
    protected final int
    minCapacity
    Minimum capacity due to initially requested capacity.
    protected int
    size
    Number of elements in the heap.

  • Constructor Summary

    Constructors
    Constructor
    Description
    BinaryArrayHeap()
    Constructs a new, empty heap, using the natural ordering of its keys.
    BinaryArrayHeap(int capacity)
    Constructs a new, empty heap, with a provided initial capacity using the natural ordering of its keys.
    BinaryArrayHeap(Comparator<? super K> comparator)
    Constructs a new, empty heap, ordered according to the given comparator.
    BinaryArrayHeap(Comparator<? super K> comparator, int capacity)
    Constructs a new, empty heap, with a provided initial capacity ordered according to the given comparator.

  • Method Summary

    Modifier and Type
    Method
    Description
    protected final void
    checkCapacity(int capacity)
    Check that a capacity is valid.
    void
    clear()
    Clear all the elements of this heap.
    Comparator<? super K>
    comparator()
    Returns the comparator used to order the keys in this heap, or null if this heap uses the natural ordering of its keys.
    K
    deleteMin()
    Delete and return an element with the minimum key.
    protected void
    ensureCapacity(int capacity)
    Ensure that the array representation has the necessary capacity.
    K
    findMin()
    Find an element with the minimum key.
    protected void
    fixdown(int k)
    Downwards fix starting from a particular element
    protected void
    fixdownWithComparator(int k)
    Downwards fix starting from a particular element.
    protected void
    fixup(int k)
    Upwards fix starting from a particular element
    protected void
    fixupWithComparator(int k)
    Upwards fix starting from a particular element.
    static <K> BinaryArrayHeap<K>
    heapify(K[] array)
    Create a heap from an array of elements.
    static <K> BinaryArrayHeap<K>
    heapify(K[] array, Comparator<? super K> comparator)
    Create a heap from an array of elements.
    protected void
    initCapacity(int capacity)
    Initialize the array representation
    void
    insert(K key)
    Insert a key into the heap.
    boolean
    isEmpty()
    Returns true if this heap is empty.
    long
    size()
    Returns the number of elements in this heap.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • DEFAULT_HEAP_CAPACITY

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

    • array

      protected K[] array
      The array used for representing the heap.

    • size

      protected int size
      Number of elements in the heap.

    • minCapacity

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

  • Constructor Details

    • BinaryArrayHeap

      public BinaryArrayHeap()
      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.

    • BinaryArrayHeap

      public BinaryArrayHeap(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:
      capacity - the initial heap capacity

    • BinaryArrayHeap

      public BinaryArrayHeap(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:
      comparator - the comparator that will be used to order this heap. If null, the natural ordering of the keys will be used.

    • BinaryArrayHeap

      public BinaryArrayHeap(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:
      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

  • Method Details

    • heapify

      public static <K> BinaryArrayHeap<K> heapify(K[] array)
      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
      Parameters:
      array - an array of elements
      Returns:
      a binary heap
      Throws:
      IllegalArgumentException - in case the array is null

    • heapify

      public static <K> BinaryArrayHeap<K> heapify(K[] array, 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
      Parameters:
      array - an array of elements
      comparator - the comparator to use
      Returns:
      a binary heap
      Throws:
      IllegalArgumentException - in case the array is null

    • ensureCapacity

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

    • fixup

      protected void fixup(int k)
      Upwards fix starting from a particular element
      Parameters:
      k - the index of the starting element

    • fixupWithComparator

      protected void fixupWithComparator(int k)
      Upwards fix starting from a particular element. Performs comparisons using the comparator.
      Parameters:
      k - the index of the starting element

    • fixdown

      protected void fixdown(int k)
      Downwards fix starting from a particular element
      Parameters:
      k - the index of the starting element

    • fixdownWithComparator

      protected void fixdownWithComparator(int k)
      Downwards fix starting from a particular element. Performs comparisons using the comparator.
      Parameters:
      k - the index of the starting element

    • initCapacity

      protected void initCapacity(int capacity)
      Initialize the array representation
      Parameters:
      capacity - the capacity

    • findMin

      public K findMin()
      Find an element with the minimum key.
      Returns:
      an element with the minimum key

    • insert

      public void insert(K key)
      Insert a key into the heap.
      Parameters:
      key - the key to insert

    • deleteMin

      public K deleteMin()
      Delete and return an element with the minimum key. If multiple such elements exists, only one of them will be deleted.
      Returns:
      the deleted element with the minimum key

    • isEmpty

      public boolean isEmpty()
      Returns true if this heap is empty.
      Specified by:
      isEmpty in interface Heap<K>
      Returns:
      true if this heap is empty, false otherwise

    • size

      public long size()
      Returns the number of elements in this heap.
      Specified by:
      size in interface Heap<K>
      Returns:
      the number of elements in this heap

    • comparator

      public Comparator<? super K> comparator()
      Returns the comparator used to order the keys in this heap, or null if this heap uses the natural ordering of its keys.
      Specified by:
      comparator in interface Heap<K>
      Returns:
      the comparator used to order the keys in this heap, or null if this heap uses the natural ordering of its keys

    • clear

      public void clear()
      Clear all the elements of this heap.
      Specified by:
      clear in interface Heap<K>

    • checkCapacity

      protected final void checkCapacity(int capacity)
      Check that a capacity is valid.
      Parameters:
      capacity - the capacity
      Throws:
      IllegalArgumentException - if the capacity is negative or more than the maximum array size