Package org.jheaps.array

Class BinaryArrayWeakHeap<K>

  • Type Parameters:
    K - the type of keys maintained by this heap
    All Implemented Interfaces:
    java.io.Serializable, Heap<K>
    Direct Known Subclasses:
    BinaryArrayBulkInsertWeakHeap
    public class BinaryArrayWeakHeap<K>
extends AbstractArrayWeakHeap<K>
implements java.io.Serializable
    An array based binary weak 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.

    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

      • reverse

        protected java.util.BitSet reverse
        Reverse bits

    • Constructor Detail

      • BinaryArrayWeakHeap

        public BinaryArrayWeakHeap()
        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.

      • BinaryArrayWeakHeap

        public BinaryArrayWeakHeap​(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

      • BinaryArrayWeakHeap

        public BinaryArrayWeakHeap​(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.

        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.

      • BinaryArrayWeakHeap

        public BinaryArrayWeakHeap​(java.util.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> BinaryArrayWeakHeap<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 heap
        Throws:
        java.lang.IllegalArgumentException - in case the array is null

      • heapify

        public static <K> BinaryArrayWeakHeap<K> heapify​(K[] array,
                                                 java.util.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 heap
        Throws:
        java.lang.IllegalArgumentException - in case the array is null

      • findMin

        public K findMin()
        Find an element with the minimum key.
        Specified by:
        findMin in interface Heap<K>
        Returns:
        an element with the minimum key

      • insert

        public void insert​(K key)
        Insert a key into the heap.
        Specified by:
        insert in interface Heap<K>
        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.
        Specified by:
        deleteMin in interface Heap<K>
        Returns:
        the deleted element with the minimum key

      • ensureCapacity

        protected void ensureCapacity​(int capacity)
        Ensure that the array representation has the necessary capacity.
        Specified by:
        ensureCapacity in class AbstractArrayWeakHeap<K>
        Parameters:
        capacity - the requested capacity

      • dancestor

        protected int dancestor​(int j)
        Return the distinguished ancestor of an element.
        Parameters:
        j - the element
        Returns:
        the distinguished ancestor of the element

      • join

        protected boolean join​(int i,
                       int j)
        Join two weak heaps into one.
        Parameters:
        i - root of the first weak heap
        j - root of the second weak heap
        Returns:
        true if already a weak heap, false if a flip was needed

      • joinWithComparator

        protected boolean joinWithComparator​(int i,
                                     int j)
        Join two weak heaps into one.
        Parameters:
        i - root of the first weak heap
        j - root of the second weak heap
        Returns:
        true if already a weak heap, false if a flip was needed

      • fixup

        protected void fixup​(int j)
        Description copied from class: AbstractArrayWeakHeap
        Upwards fix starting from a particular element
        Specified by:
        fixup in class AbstractArrayWeakHeap<K>
        Parameters:
        j - the index of the starting element

      • fixupWithComparator

        protected void fixupWithComparator​(int j)
        Description copied from class: AbstractArrayWeakHeap
        Upwards fix starting from a particular element. Performs comparisons using the comparator.
        Specified by:
        fixupWithComparator in class AbstractArrayWeakHeap<K>
        Parameters:
        j - the index of the starting element

      • fixdown

        protected void fixdown​(int j)
        Description copied from class: AbstractArrayWeakHeap
        Downwards fix starting from a particular element
        Specified by:
        fixdown in class AbstractArrayWeakHeap<K>
        Parameters:
        j - the index of the starting element

      • fixdownWithComparator

        protected void fixdownWithComparator​(int j)
        Description copied from class: AbstractArrayWeakHeap
        Downwards fix starting from a particular element. Performs comparisons using the comparator.
        Specified by:
        fixdownWithComparator in class AbstractArrayWeakHeap<K>
        Parameters:
        j - the index of the starting element