Package org.jheaps.array

Class 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:
    Serialized Form

    • Field Detail

      • DEFAULT_HEAP_CAPACITY

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

    • Constructor Detail

      • 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 Detail

      • 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

      • 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>