Class MinMaxBinaryArrayDoubleEndedHeap<K>

  • Type Parameters:
    K - the type of keys maintained by this heap
    All Implemented Interfaces:
    java.io.Serializable, DoubleEndedHeap<K>, Heap<K>

    public class MinMaxBinaryArrayDoubleEndedHeap<K>
    extends AbstractArrayHeap<K>
    implements DoubleEndedHeap<K>, java.io.Serializable
    An array based binary MinMax 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.

    For details about the implementation see the following paper:

    • M. D. Atkinson, J.-R. Sack, N. Santoro, and T. Strothotte. Min-max Heaps and Generalized Priority Queues. Commun. ACM, 29(10), 996--1000, 1986.

    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, deleteMin, and deleteMax operations. Operations findMin and findMax are worst-case O(1). 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 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:
    Serialized Form
    • Field Detail

      • DEFAULT_HEAP_CAPACITY

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

      • MinMaxBinaryArrayDoubleEndedHeap

        public MinMaxBinaryArrayDoubleEndedHeap()
        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.

      • MinMaxBinaryArrayDoubleEndedHeap

        public MinMaxBinaryArrayDoubleEndedHeap​(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
      • MinMaxBinaryArrayDoubleEndedHeap

        public MinMaxBinaryArrayDoubleEndedHeap​(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.
      • MinMaxBinaryArrayDoubleEndedHeap

        public MinMaxBinaryArrayDoubleEndedHeap​(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> MinMaxBinaryArrayDoubleEndedHeap<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> MinMaxBinaryArrayDoubleEndedHeap<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
      • 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
      • findMax

        public K findMax()
        Find an element with the maximum key.
        Specified by:
        findMax in interface DoubleEndedHeap<K>
        Returns:
        an element with the maximum key
      • deleteMax

        public K deleteMax()
        Delete and return an element with the maximum key. If multiple such elements exists, only one of them will be deleted.
        Specified by:
        deleteMax in interface DoubleEndedHeap<K>
        Returns:
        the deleted element with the maximum key
      • fixup

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

        protected void fixupWithComparator​(int k)
        Upwards fix starting from a particular element
        Specified by:
        fixupWithComparator in class AbstractArrayWeakHeap<K>
        Parameters:
        k - the index of the starting element
      • fixupMin

        private void fixupMin​(int k)
        Upwards fix starting from a particular element at a minimum level
        Parameters:
        k - the index of the starting element
      • fixupMinWithComparator

        private void fixupMinWithComparator​(int k)
        Upwards fix starting from a particular element at a minimum level. Performs comparisons using the comparator.
        Parameters:
        k - the index of the starting element
      • fixupMax

        private void fixupMax​(int k)
        Upwards fix starting from a particular element at a maximum level
        Parameters:
        k - the index of the starting element
      • fixupMaxWithComparator

        private void fixupMaxWithComparator​(int k)
        Upwards fix starting from a particular element at a maximum level. 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.
        Specified by:
        fixdown in class AbstractArrayWeakHeap<K>
        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.
        Specified by:
        fixdownWithComparator in class AbstractArrayWeakHeap<K>
        Parameters:
        k - the index of the starting element
      • fixdownMin

        private void fixdownMin​(int k)
        Downwards fix starting from a particular element at a minimum level.
        Parameters:
        k - the index of the starting element
      • fixdownMinWithComparator

        private void fixdownMinWithComparator​(int k)
        Downwards fix starting from a particular element at a minimum level. Performs comparisons using the comparator.
        Parameters:
        k - the index of the starting element
      • fixdownMax

        private void fixdownMax​(int k)
        Downwards fix starting from a particular element at a maximum level.
        Parameters:
        k - the index of the starting element
      • fixdownMaxWithComparator

        private void fixdownMaxWithComparator​(int k)
        Downwards fix starting from a particular element at a maximum level. Performs comparisons using the comparator.
        Parameters:
        k - the index of the starting element
      • onMinLevel

        boolean onMinLevel​(int k)
        Return true if on a minimum level, false otherwise.
        Parameters:
        k - the element
        Returns:
        true if on a minimum level, false otherwise
      • maxChildOrGrandchild

        private int maxChildOrGrandchild​(int k)
        Given a node at a maximum level, find its child or grandchild with the maximum key. This method should not be called for a node which has no children.
        Parameters:
        k - a node at a maximum level
        Returns:
        the child or grandchild with a maximum key, or undefined if there are no children
      • maxChildOrGrandchildWithComparator

        private int maxChildOrGrandchildWithComparator​(int k)
        Given a node at a maximum level, find its child or grandchild with the maximum key. This method should not be called for a node which has no children.
        Parameters:
        k - a node at a maximum level
        Returns:
        the child or grandchild with a maximum key, or undefined if there are no children
      • minChildOrGrandchild

        private int minChildOrGrandchild​(int k)
        Given a node at a minimum level, find its child or grandchild with the minimum key. This method should not be called for a node which has no children.
        Parameters:
        k - a node at a minimum level
        Returns:
        the child or grandchild with a minimum key, or undefined if there are no children
      • minChildOrGrandchildWithComparator

        private int minChildOrGrandchildWithComparator​(int k)
        Given a node at a minimum level, find its child or grandchild with the minimum key. This method should not be called for a node which has no children.
        Parameters:
        k - a node at a minimum level
        Returns:
        the child or grandchild with a minimum key, or undefined if there are no children