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package java.util;

import java.util.function.Consumer;
import java.util.function.Predicate;
import jdk.internal.access.SharedSecrets;
import jdk.internal.util.ArraysSupport;

An unbounded priority queue based on a priority heap. The elements of the priority queue are ordered according to their natural ordering, or by a Comparator provided at queue construction time, depending on which constructor is used. A priority queue does not permit null elements. A priority queue relying on natural ordering also does not permit insertion of non-comparable objects (doing so may result in ClassCastException). 
The head of this queue is the least element with respect to the specified ordering. If multiple elements are tied for least value, the head is one of those elements -- ties are broken arbitrarily. The queue retrieval operations poll, remove, peek, and element access the element at the head of the queue. 
A priority queue is unbounded, but has an internal
capacity governing the size of an array used to store the
elements on the queue.  It is always at least as large as the queue
size.  As elements are added to a priority queue, its capacity
grows automatically.  The details of the growth policy are not
specified.
This class and its iterator implement all of the
optional methods of the Collection and Iterator interfaces. The Iterator provided in method iterator() and the Spliterator provided in method spliterator() are not guaranteed to traverse the elements of the priority queue in any particular order. If you need ordered traversal, consider using Arrays.sort(pq.toArray()). 
Note that this implementation is not synchronized. Multiple threads should not access a PriorityQueue instance concurrently if any of the threads modifies the queue. Instead, use the thread-safe PriorityBlockingQueue class. 
Implementation note: this implementation provides O(log(n)) time for the enqueuing and dequeuing methods (offer, poll, remove() and add); linear time for the remove(Object) and contains(Object) methods; and constant time for the retrieval methods (peek, element, and size). 
This class is a member of the

Java Collections Framework.
Author:
Josh Bloch, Doug Lea
Type parameters:
<E> – the type of elements held in this queue
Since:
1.5/**
 * An unbounded priority {@linkplain Queue queue} based on a priority heap.
 * The elements of the priority queue are ordered according to their
 * {@linkplain Comparable natural ordering}, or by a {@link Comparator}
 * provided at queue construction time, depending on which constructor is
 * used.  A priority queue does not permit {@code null} elements.
 * A priority queue relying on natural ordering also does not permit
 * insertion of non-comparable objects (doing so may result in
 * {@code ClassCastException}).
 *
 * <p>The <em>head</em> of this queue is the <em>least</em> element
 * with respect to the specified ordering.  If multiple elements are
 * tied for least value, the head is one of those elements -- ties are
 * broken arbitrarily.  The queue retrieval operations {@code poll},
 * {@code remove}, {@code peek}, and {@code element} access the
 * element at the head of the queue.
 *
 * <p>A priority queue is unbounded, but has an internal
 * <i>capacity</i> governing the size of an array used to store the
 * elements on the queue.  It is always at least as large as the queue
 * size.  As elements are added to a priority queue, its capacity
 * grows automatically.  The details of the growth policy are not
 * specified.
 *
 * <p>This class and its iterator implement all of the
 * <em>optional</em> methods of the {@link Collection} and {@link
 * Iterator} interfaces.  The Iterator provided in method {@link
 * #iterator()} and the Spliterator provided in method {@link #spliterator()}
 * are <em>not</em> guaranteed to traverse the elements of
 * the priority queue in any particular order. If you need ordered
 * traversal, consider using {@code Arrays.sort(pq.toArray())}.
 *
 * <p><strong>Note that this implementation is not synchronized.</strong>
 * Multiple threads should not access a {@code PriorityQueue}
 * instance concurrently if any of the threads modifies the queue.
 * Instead, use the thread-safe {@link
 * java.util.concurrent.PriorityBlockingQueue} class.
 *
 * <p>Implementation note: this implementation provides
 * O(log(n)) time for the enqueuing and dequeuing methods
 * ({@code offer}, {@code poll}, {@code remove()} and {@code add});
 * linear time for the {@code remove(Object)} and {@code contains(Object)}
 * methods; and constant time for the retrieval methods
 * ({@code peek}, {@code element}, and {@code size}).
 *
 * <p>This class is a member of the
 * <a href="{@docRoot}/java.base/java/util/package-summary.html#CollectionsFramework">
 * Java Collections Framework</a>.
 *
 * @since 1.5
 * @author Josh Bloch, Doug Lea
 * @param <E> the type of elements held in this queue
 */
@SuppressWarnings("unchecked")
public class PriorityQueue<E> extends AbstractQueue<E>
    implements java.io.Serializable {

    private static final long serialVersionUID = -7720805057305804111L;

    private static final int DEFAULT_INITIAL_CAPACITY = 11;

    
Priority queue represented as a balanced binary heap: the two
children of queue[n] are queue[2*n+1] and queue[2*(n+1)].  The
priority queue is ordered by comparator, or by the elements'
natural ordering, if comparator is null: For each node n in the
heap and each descendant d of n, n <= d.  The element with the
lowest value is in queue[0], assuming the queue is nonempty.
/**
     * Priority queue represented as a balanced binary heap: the two
     * children of queue[n] are queue[2*n+1] and queue[2*(n+1)].  The
     * priority queue is ordered by comparator, or by the elements'
     * natural ordering, if comparator is null: For each node n in the
     * heap and each descendant d of n, n <= d.  The element with the
     * lowest value is in queue[0], assuming the queue is nonempty.
     */
    transient Object[] queue; // non-private to simplify nested class access

    
The number of elements in the priority queue.
/**
     * The number of elements in the priority queue.
     */
    int size;

    
The comparator, or null if priority queue uses elements'
natural ordering.
/**
     * The comparator, or null if priority queue uses elements'
     * natural ordering.
     */
    private final Comparator<? super E> comparator;

    
The number of times this priority queue has been
structurally modified.  See AbstractList for gory details.
/**
     * The number of times this priority queue has been
     * <i>structurally modified</i>.  See AbstractList for gory details.
     */
    transient int modCount;     // non-private to simplify nested class access

    
Creates a PriorityQueue with the default initial capacity (11) that orders its elements according to their natural ordering. /**
     * Creates a {@code PriorityQueue} with the default initial
     * capacity (11) that orders its elements according to their
     * {@linkplain Comparable natural ordering}.
     */
    public PriorityQueue() {
        this(DEFAULT_INITIAL_CAPACITY, null);
    }

    
Creates a PriorityQueue with the specified initial capacity that orders its elements according to their natural ordering. 
Params:
initialCapacity – the initial capacity for this priority queue
Throws:
IllegalArgumentException – if initialCapacity is less than 1/**
     * Creates a {@code PriorityQueue} with the specified initial
     * capacity that orders its elements according to their
     * {@linkplain Comparable natural ordering}.
     *
     * @param initialCapacity the initial capacity for this priority queue
     * @throws IllegalArgumentException if {@code initialCapacity} is less
     *         than 1
     */
    public PriorityQueue(int initialCapacity) {
        this(initialCapacity, null);
    }

    
Creates a PriorityQueue with the default initial capacity and whose elements are ordered according to the specified comparator. 
Params:
comparator – the comparator that will be used to order this priority queue. If null, the 
        natural ordering of the elements will be used.
Since:
1.8/**
     * Creates a {@code PriorityQueue} with the default initial capacity and
     * whose elements are ordered according to the specified comparator.
     *
     * @param  comparator the comparator that will be used to order this
     *         priority queue.  If {@code null}, the {@linkplain Comparable
     *         natural ordering} of the elements will be used.
     * @since 1.8
     */
    public PriorityQueue(Comparator<? super E> comparator) {
        this(DEFAULT_INITIAL_CAPACITY, comparator);
    }

    
Creates a PriorityQueue with the specified initial capacity that orders its elements according to the specified comparator. 
Params:
initialCapacity – the initial capacity for this priority queue
comparator – the comparator that will be used to order this priority queue. If null, the 
        natural ordering of the elements will be used.
Throws:
IllegalArgumentException – if initialCapacity is less than 1/**
     * Creates a {@code PriorityQueue} with the specified initial capacity
     * that orders its elements according to the specified comparator.
     *
     * @param  initialCapacity the initial capacity for this priority queue
     * @param  comparator the comparator that will be used to order this
     *         priority queue.  If {@code null}, the {@linkplain Comparable
     *         natural ordering} of the elements will be used.
     * @throws IllegalArgumentException if {@code initialCapacity} is
     *         less than 1
     */
    public PriorityQueue(int initialCapacity,
                         Comparator<? super E> comparator) {
        // Note: This restriction of at least one is not actually needed,
        // but continues for 1.5 compatibility
        if (initialCapacity < 1)
            throw new IllegalArgumentException();
        this.queue = new Object[initialCapacity];
        this.comparator = comparator;
    }

    
Creates a PriorityQueue containing the elements in the specified collection. If the specified collection is an instance of a SortedSet or is another PriorityQueue, this priority queue will be ordered according to the same ordering. Otherwise, this priority queue will be ordered according to the natural ordering of its elements. 
Params:
c – the collection whose elements are to be placed
        into this priority queue
Throws:
ClassCastException – if elements of the specified collection
        cannot be compared to one another according to the priority
        queue's ordering
NullPointerException – if the specified collection or any
        of its elements are null/**
     * Creates a {@code PriorityQueue} containing the elements in the
     * specified collection.  If the specified collection is an instance of
     * a {@link SortedSet} or is another {@code PriorityQueue}, this
     * priority queue will be ordered according to the same ordering.
     * Otherwise, this priority queue will be ordered according to the
     * {@linkplain Comparable natural ordering} of its elements.
     *
     * @param  c the collection whose elements are to be placed
     *         into this priority queue
     * @throws ClassCastException if elements of the specified collection
     *         cannot be compared to one another according to the priority
     *         queue's ordering
     * @throws NullPointerException if the specified collection or any
     *         of its elements are null
     */
    public PriorityQueue(Collection<? extends E> c) {
        if (c instanceof SortedSet<?>) {
            SortedSet<? extends E> ss = (SortedSet<? extends E>) c;
            this.comparator = (Comparator<? super E>) ss.comparator();
            initElementsFromCollection(ss);
        }
        else if (c instanceof PriorityQueue<?>) {
            PriorityQueue<? extends E> pq = (PriorityQueue<? extends E>) c;
            this.comparator = (Comparator<? super E>) pq.comparator();
            initFromPriorityQueue(pq);
        }
        else {
            this.comparator = null;
            initFromCollection(c);
        }
    }

    
Creates a PriorityQueue containing the elements in the specified priority queue. This priority queue will be ordered according to the same ordering as the given priority queue. 
Params:
c – the priority queue whose elements are to be placed
        into this priority queue
Throws:
ClassCastException – if elements of c cannot be compared to one another according to c's ordering
NullPointerException – if the specified priority queue or any
        of its elements are null/**
     * Creates a {@code PriorityQueue} containing the elements in the
     * specified priority queue.  This priority queue will be
     * ordered according to the same ordering as the given priority
     * queue.
     *
     * @param  c the priority queue whose elements are to be placed
     *         into this priority queue
     * @throws ClassCastException if elements of {@code c} cannot be
     *         compared to one another according to {@code c}'s
     *         ordering
     * @throws NullPointerException if the specified priority queue or any
     *         of its elements are null
     */
    public PriorityQueue(PriorityQueue<? extends E> c) {
        this.comparator = (Comparator<? super E>) c.comparator();
        initFromPriorityQueue(c);
    }

    
Creates a PriorityQueue containing the elements in the specified sorted set. This priority queue will be ordered according to the same ordering as the given sorted set. 
Params:
c – the sorted set whose elements are to be placed
        into this priority queue
Throws:
ClassCastException – if elements of the specified sorted
        set cannot be compared to one another according to the
        sorted set's ordering
NullPointerException – if the specified sorted set or any
        of its elements are null/**
     * Creates a {@code PriorityQueue} containing the elements in the
     * specified sorted set.   This priority queue will be ordered
     * according to the same ordering as the given sorted set.
     *
     * @param  c the sorted set whose elements are to be placed
     *         into this priority queue
     * @throws ClassCastException if elements of the specified sorted
     *         set cannot be compared to one another according to the
     *         sorted set's ordering
     * @throws NullPointerException if the specified sorted set or any
     *         of its elements are null
     */
    public PriorityQueue(SortedSet<? extends E> c) {
        this.comparator = (Comparator<? super E>) c.comparator();
        initElementsFromCollection(c);
    }

    
Ensures that queue[0] exists, helping peek() and poll(). /** Ensures that queue[0] exists, helping peek() and poll(). */
    private static Object[] ensureNonEmpty(Object[] es) {
        return (es.length > 0) ? es : new Object[1];
    }

    private void initFromPriorityQueue(PriorityQueue<? extends E> c) {
        if (c.getClass() == PriorityQueue.class) {
            this.queue = ensureNonEmpty(c.toArray());
            this.size = c.size();
        } else {
            initFromCollection(c);
        }
    }

    private void initElementsFromCollection(Collection<? extends E> c) {
        Object[] es = c.toArray();
        int len = es.length;
        if (c.getClass() != ArrayList.class)
            es = Arrays.copyOf(es, len, Object[].class);
        if (len == 1 || this.comparator != null)
            for (Object e : es)
                if (e == null)
                    throw new NullPointerException();
        this.queue = ensureNonEmpty(es);
        this.size = len;
    }

    
Initializes queue array with elements from the given Collection.
Params:
c – the collection/**
     * Initializes queue array with elements from the given Collection.
     *
     * @param c the collection
     */
    private void initFromCollection(Collection<? extends E> c) {
        initElementsFromCollection(c);
        heapify();
    }

    
Increases the capacity of the array.
Params:
minCapacity – the desired minimum capacity/**
     * Increases the capacity of the array.
     *
     * @param minCapacity the desired minimum capacity
     */
    private void grow(int minCapacity) {
        int oldCapacity = queue.length;
        // Double size if small; else grow by 50%
        int newCapacity = ArraysSupport.newLength(oldCapacity,
                minCapacity - oldCapacity, /* minimum growth */
                oldCapacity < 64 ? oldCapacity + 2 : oldCapacity >> 1
                                           /* preferred growth */);
        queue = Arrays.copyOf(queue, newCapacity);
    }

    
Inserts the specified element into this priority queue.
Throws:
ClassCastException – if the specified element cannot be
        compared with elements currently in this priority queue
        according to the priority queue's ordering
NullPointerException – if the specified element is null
Returns:
true (as specified by Collection.add)/**
     * Inserts the specified element into this priority queue.
     *
     * @return {@code true} (as specified by {@link Collection#add})
     * @throws ClassCastException if the specified element cannot be
     *         compared with elements currently in this priority queue
     *         according to the priority queue's ordering
     * @throws NullPointerException if the specified element is null
     */
    public boolean add(E e) {
        return offer(e);
    }

    
Inserts the specified element into this priority queue.
Throws:
ClassCastException – if the specified element cannot be
        compared with elements currently in this priority queue
        according to the priority queue's ordering
NullPointerException – if the specified element is null
Returns:
true (as specified by Queue.offer)/**
     * Inserts the specified element into this priority queue.
     *
     * @return {@code true} (as specified by {@link Queue#offer})
     * @throws ClassCastException if the specified element cannot be
     *         compared with elements currently in this priority queue
     *         according to the priority queue's ordering
     * @throws NullPointerException if the specified element is null
     */
    public boolean offer(E e) {
        if (e == null)
            throw new NullPointerException();
        modCount++;
        int i = size;
        if (i >= queue.length)
            grow(i + 1);
        siftUp(i, e);
        size = i + 1;
        return true;
    }

    public E peek() {
        return (E) queue[0];
    }

    private int indexOf(Object o) {
        if (o != null) {
            final Object[] es = queue;
            for (int i = 0, n = size; i < n; i++)
                if (o.equals(es[i]))
                    return i;
        }
        return -1;
    }

    
Removes a single instance of the specified element from this queue, if it is present. More formally, removes an element e such that o.equals(e), if this queue contains one or more such elements. Returns true if and only if this queue contained the specified element (or equivalently, if this queue changed as a result of the call). 
Params:
o – element to be removed from this queue, if present
Returns:
true if this queue changed as a result of the call/**
     * Removes a single instance of the specified element from this queue,
     * if it is present.  More formally, removes an element {@code e} such
     * that {@code o.equals(e)}, if this queue contains one or more such
     * elements.  Returns {@code true} if and only if this queue contained
     * the specified element (or equivalently, if this queue changed as a
     * result of the call).
     *
     * @param o element to be removed from this queue, if present
     * @return {@code true} if this queue changed as a result of the call
     */
    public boolean remove(Object o) {
        int i = indexOf(o);
        if (i == -1)
            return false;
        else {
            removeAt(i);
            return true;
        }
    }

    
Identity-based version for use in Itr.remove.
Params:
o – element to be removed from this queue, if present/**
     * Identity-based version for use in Itr.remove.
     *
     * @param o element to be removed from this queue, if present
     */
    void removeEq(Object o) {
        final Object[] es = queue;
        for (int i = 0, n = size; i < n; i++) {
            if (o == es[i]) {
                removeAt(i);
                break;
            }
        }
    }

    
Returns true if this queue contains the specified element. More formally, returns true if and only if this queue contains at least one element e such that o.equals(e). 
Params:
o – object to be checked for containment in this queue
Returns:
true if this queue contains the specified element/**
     * Returns {@code true} if this queue contains the specified element.
     * More formally, returns {@code true} if and only if this queue contains
     * at least one element {@code e} such that {@code o.equals(e)}.
     *
     * @param o object to be checked for containment in this queue
     * @return {@code true} if this queue contains the specified element
     */
    public boolean contains(Object o) {
        return indexOf(o) >= 0;
    }

    
Returns an array containing all of the elements in this queue.
The elements are in no particular order.
The returned array will be "safe" in that no references to it are
maintained by this queue.  (In other words, this method must allocate
a new array).  The caller is thus free to modify the returned array.
This method acts as bridge between array-based and collection-based
APIs.
Returns:
an array containing all of the elements in this queue/**
     * Returns an array containing all of the elements in this queue.
     * The elements are in no particular order.
     *
     * <p>The returned array will be "safe" in that no references to it are
     * maintained by this queue.  (In other words, this method must allocate
     * a new array).  The caller is thus free to modify the returned array.
     *
     * <p>This method acts as bridge between array-based and collection-based
     * APIs.
     *
     * @return an array containing all of the elements in this queue
     */
    public Object[] toArray() {
        return Arrays.copyOf(queue, size);
    }

    
Returns an array containing all of the elements in this queue; the
runtime type of the returned array is that of the specified array.
The returned array elements are in no particular order.
If the queue fits in the specified array, it is returned therein.
Otherwise, a new array is allocated with the runtime type of the
specified array and the size of this queue.
If the queue fits in the specified array with room to spare (i.e., the array has more elements than the queue), the element in the array immediately following the end of the collection is set to null. 
Like the toArray() method, this method acts as bridge between array-based and collection-based APIs. Further, this method allows precise control over the runtime type of the output array, and may, under certain circumstances, be used to save allocation costs. 
Suppose x is a queue known to contain only strings. The following code can be used to dump the queue into a newly allocated array of String: 
 String[] y = x.toArray(new String[0]);
 Note that toArray(new Object[0]) is identical in function to toArray(). 
Params:
a – the array into which the elements of the queue are to
         be stored, if it is big enough; otherwise, a new array of the
         same runtime type is allocated for this purpose.
Throws:
ArrayStoreException – if the runtime type of the specified array
        is not a supertype of the runtime type of every element in
        this queue
NullPointerException – if the specified array is null
Returns:
an array containing all of the elements in this queue/**
     * Returns an array containing all of the elements in this queue; the
     * runtime type of the returned array is that of the specified array.
     * The returned array elements are in no particular order.
     * If the queue fits in the specified array, it is returned therein.
     * Otherwise, a new array is allocated with the runtime type of the
     * specified array and the size of this queue.
     *
     * <p>If the queue fits in the specified array with room to spare
     * (i.e., the array has more elements than the queue), the element in
     * the array immediately following the end of the collection is set to
     * {@code null}.
     *
     * <p>Like the {@link #toArray()} method, this method acts as bridge between
     * array-based and collection-based APIs.  Further, this method allows
     * precise control over the runtime type of the output array, and may,
     * under certain circumstances, be used to save allocation costs.
     *
     * <p>Suppose {@code x} is a queue known to contain only strings.
     * The following code can be used to dump the queue into a newly
     * allocated array of {@code String}:
     *
     * <pre> {@code String[] y = x.toArray(new String[0]);}</pre>
     *
     * Note that {@code toArray(new Object[0])} is identical in function to
     * {@code toArray()}.
     *
     * @param a the array into which the elements of the queue are to
     *          be stored, if it is big enough; otherwise, a new array of the
     *          same runtime type is allocated for this purpose.
     * @return an array containing all of the elements in this queue
     * @throws ArrayStoreException if the runtime type of the specified array
     *         is not a supertype of the runtime type of every element in
     *         this queue
     * @throws NullPointerException if the specified array is null
     */
    public <T> T[] toArray(T[] a) {
        final int size = this.size;
        if (a.length < size)
            // Make a new array of a's runtime type, but my contents:
            return (T[]) Arrays.copyOf(queue, size, a.getClass());
        System.arraycopy(queue, 0, a, 0, size);
        if (a.length > size)
            a[size] = null;
        return a;
    }

    
Returns an iterator over the elements in this queue. The iterator
does not return the elements in any particular order.
Returns:
an iterator over the elements in this queue/**
     * Returns an iterator over the elements in this queue. The iterator
     * does not return the elements in any particular order.
     *
     * @return an iterator over the elements in this queue
     */
    public Iterator<E> iterator() {
        return new Itr();
    }

    private final class Itr implements Iterator<E> {
        
Index (into queue array) of element to be returned by
subsequent call to next.
/**
         * Index (into queue array) of element to be returned by
         * subsequent call to next.
         */
        private int cursor;

        
Index of element returned by most recent call to next,
unless that element came from the forgetMeNot list.
Set to -1 if element is deleted by a call to remove.
/**
         * Index of element returned by most recent call to next,
         * unless that element came from the forgetMeNot list.
         * Set to -1 if element is deleted by a call to remove.
         */
        private int lastRet = -1;

        
A queue of elements that were moved from the unvisited portion of
the heap into the visited portion as a result of "unlucky" element
removals during the iteration.  (Unlucky element removals are those
that require a siftup instead of a siftdown.)  We must visit all of
the elements in this list to complete the iteration.  We do this
after we've completed the "normal" iteration.
We expect that most iterations, even those involving removals,
will not need to store elements in this field.
/**
         * A queue of elements that were moved from the unvisited portion of
         * the heap into the visited portion as a result of "unlucky" element
         * removals during the iteration.  (Unlucky element removals are those
         * that require a siftup instead of a siftdown.)  We must visit all of
         * the elements in this list to complete the iteration.  We do this
         * after we've completed the "normal" iteration.
         *
         * We expect that most iterations, even those involving removals,
         * will not need to store elements in this field.
         */
        private ArrayDeque<E> forgetMeNot;

        
Element returned by the most recent call to next iff that
element was drawn from the forgetMeNot list.
/**
         * Element returned by the most recent call to next iff that
         * element was drawn from the forgetMeNot list.
         */
        private E lastRetElt;

        
The modCount value that the iterator believes that the backing
Queue should have.  If this expectation is violated, the iterator
has detected concurrent modification.
/**
         * The modCount value that the iterator believes that the backing
         * Queue should have.  If this expectation is violated, the iterator
         * has detected concurrent modification.
         */
        private int expectedModCount = modCount;

        Itr() {}                        // prevent access constructor creation

        public boolean hasNext() {
            return cursor < size ||
                (forgetMeNot != null && !forgetMeNot.isEmpty());
        }

        public E next() {
            if (expectedModCount != modCount)
                throw new ConcurrentModificationException();
            if (cursor < size)
                return (E) queue[lastRet = cursor++];
            if (forgetMeNot != null) {
                lastRet = -1;
                lastRetElt = forgetMeNot.poll();
                if (lastRetElt != null)
                    return lastRetElt;
            }
            throw new NoSuchElementException();
        }

        public void remove() {
            if (expectedModCount != modCount)
                throw new ConcurrentModificationException();
            if (lastRet != -1) {
                E moved = PriorityQueue.this.removeAt(lastRet);
                lastRet = -1;
                if (moved == null)
                    cursor--;
                else {
                    if (forgetMeNot == null)
                        forgetMeNot = new ArrayDeque<>();
                    forgetMeNot.add(moved);
                }
            } else if (lastRetElt != null) {
                PriorityQueue.this.removeEq(lastRetElt);
                lastRetElt = null;
            } else {
                throw new IllegalStateException();
            }
            expectedModCount = modCount;
        }
    }

    public int size() {
        return size;
    }

    
Removes all of the elements from this priority queue.
The queue will be empty after this call returns.
/**
     * Removes all of the elements from this priority queue.
     * The queue will be empty after this call returns.
     */
    public void clear() {
        modCount++;
        final Object[] es = queue;
        for (int i = 0, n = size; i < n; i++)
            es[i] = null;
        size = 0;
    }

    public E poll() {
        final Object[] es;
        final E result;

        if ((result = (E) ((es = queue)[0])) != null) {
            modCount++;
            final int n;
            final E x = (E) es[(n = --size)];
            es[n] = null;
            if (n > 0) {
                final Comparator<? super E> cmp;
                if ((cmp = comparator) == null)
                    siftDownComparable(0, x, es, n);
                else
                    siftDownUsingComparator(0, x, es, n, cmp);
            }
        }
        return result;
    }

    
Removes the ith element from queue.
Normally this method leaves the elements at up to i-1,
inclusive, untouched.  Under these circumstances, it returns
null.  Occasionally, in order to maintain the heap invariant,
it must swap a later element of the list with one earlier than
i.  Under these circumstances, this method returns the element
that was previously at the end of the list and is now at some
position before i. This fact is used by iterator.remove so as to
avoid missing traversing elements.
/**
     * Removes the ith element from queue.
     *
     * Normally this method leaves the elements at up to i-1,
     * inclusive, untouched.  Under these circumstances, it returns
     * null.  Occasionally, in order to maintain the heap invariant,
     * it must swap a later element of the list with one earlier than
     * i.  Under these circumstances, this method returns the element
     * that was previously at the end of the list and is now at some
     * position before i. This fact is used by iterator.remove so as to
     * avoid missing traversing elements.
     */
    E removeAt(int i) {
        // assert i >= 0 && i < size;
        final Object[] es = queue;
        modCount++;
        int s = --size;
        if (s == i) // removed last element
            es[i] = null;
        else {
            E moved = (E) es[s];
            es[s] = null;
            siftDown(i, moved);
            if (es[i] == moved) {
                siftUp(i, moved);
                if (es[i] != moved)
                    return moved;
            }
        }
        return null;
    }

    
Inserts item x at position k, maintaining heap invariant by
promoting x up the tree until it is greater than or equal to
its parent, or is the root.
To simplify and speed up coercions and comparisons, the
Comparable and Comparator versions are separated into different
methods that are otherwise identical. (Similarly for siftDown.)
Params:
k – the position to fill
x – the item to insert/**
     * Inserts item x at position k, maintaining heap invariant by
     * promoting x up the tree until it is greater than or equal to
     * its parent, or is the root.
     *
     * To simplify and speed up coercions and comparisons, the
     * Comparable and Comparator versions are separated into different
     * methods that are otherwise identical. (Similarly for siftDown.)
     *
     * @param k the position to fill
     * @param x the item to insert
     */
    private void siftUp(int k, E x) {
        if (comparator != null)
            siftUpUsingComparator(k, x, queue, comparator);
        else
            siftUpComparable(k, x, queue);
    }

    private static <T> void siftUpComparable(int k, T x, Object[] es) {
        Comparable<? super T> key = (Comparable<? super T>) x;
        while (k > 0) {
            int parent = (k - 1) >>> 1;
            Object e = es[parent];
            if (key.compareTo((T) e) >= 0)
                break;
            es[k] = e;
            k = parent;
        }
        es[k] = key;
    }

    private static <T> void siftUpUsingComparator(
        int k, T x, Object[] es, Comparator<? super T> cmp) {
        while (k > 0) {
            int parent = (k - 1) >>> 1;
            Object e = es[parent];
            if (cmp.compare(x, (T) e) >= 0)
                break;
            es[k] = e;
            k = parent;
        }
        es[k] = x;
    }

    
Inserts item x at position k, maintaining heap invariant by
demoting x down the tree repeatedly until it is less than or
equal to its children or is a leaf.
Params:
k – the position to fill
x – the item to insert/**
     * Inserts item x at position k, maintaining heap invariant by
     * demoting x down the tree repeatedly until it is less than or
     * equal to its children or is a leaf.
     *
     * @param k the position to fill
     * @param x the item to insert
     */
    private void siftDown(int k, E x) {
        if (comparator != null)
            siftDownUsingComparator(k, x, queue, size, comparator);
        else
            siftDownComparable(k, x, queue, size);
    }

    private static <T> void siftDownComparable(int k, T x, Object[] es, int n) {
        // assert n > 0;
        Comparable<? super T> key = (Comparable<? super T>)x;
        int half = n >>> 1;           // loop while a non-leaf
        while (k < half) {
            int child = (k << 1) + 1; // assume left child is least
            Object c = es[child];
            int right = child + 1;
            if (right < n &&
                ((Comparable<? super T>) c).compareTo((T) es[right]) > 0)
                c = es[child = right];
            if (key.compareTo((T) c) <= 0)
                break;
            es[k] = c;
            k = child;
        }
        es[k] = key;
    }

    private static <T> void siftDownUsingComparator(
        int k, T x, Object[] es, int n, Comparator<? super T> cmp) {
        // assert n > 0;
        int half = n >>> 1;
        while (k < half) {
            int child = (k << 1) + 1;
            Object c = es[child];
            int right = child + 1;
            if (right < n && cmp.compare((T) c, (T) es[right]) > 0)
                c = es[child = right];
            if (cmp.compare(x, (T) c) <= 0)
                break;
            es[k] = c;
            k = child;
        }
        es[k] = x;
    }

    
Establishes the heap invariant (described above) in the entire tree,
assuming nothing about the order of the elements prior to the call.
This classic algorithm due to Floyd (1964) is known to be O(size).
/**
     * Establishes the heap invariant (described above) in the entire tree,
     * assuming nothing about the order of the elements prior to the call.
     * This classic algorithm due to Floyd (1964) is known to be O(size).
     */
    private void heapify() {
        final Object[] es = queue;
        int n = size, i = (n >>> 1) - 1;
        final Comparator<? super E> cmp;
        if ((cmp = comparator) == null)
            for (; i >= 0; i--)
                siftDownComparable(i, (E) es[i], es, n);
        else
            for (; i >= 0; i--)
                siftDownUsingComparator(i, (E) es[i], es, n, cmp);
    }

    
Returns the comparator used to order the elements in this queue, or null if this queue is sorted according to the natural ordering of its elements. 
Returns:
the comparator used to order this queue, or null if this queue is sorted according to the natural ordering of its elements/**
     * Returns the comparator used to order the elements in this
     * queue, or {@code null} if this queue is sorted according to
     * the {@linkplain Comparable natural ordering} of its elements.
     *
     * @return the comparator used to order this queue, or
     *         {@code null} if this queue is sorted according to the
     *         natural ordering of its elements
     */
    public Comparator<? super E> comparator() {
        return comparator;
    }

    
Saves this queue to a stream (that is, serializes it).
Params:
s – the stream
Throws:
IOException – if an I/O error occurs
@serialData
The length of the array backing the instance is emitted (int), followed by all of its elements (each an Object) in the proper order./**
     * Saves this queue to a stream (that is, serializes it).
     *
     * @param s the stream
     * @throws java.io.IOException if an I/O error occurs
     * @serialData The length of the array backing the instance is
     *             emitted (int), followed by all of its elements
     *             (each an {@code Object}) in the proper order.
     */
    private void writeObject(java.io.ObjectOutputStream s)
        throws java.io.IOException {
        // Write out element count, and any hidden stuff
        s.defaultWriteObject();

        // Write out array length, for compatibility with 1.5 version
        s.writeInt(Math.max(2, size + 1));

        // Write out all elements in the "proper order".
        final Object[] es = queue;
        for (int i = 0, n = size; i < n; i++)
            s.writeObject(es[i]);
    }

    
Reconstitutes the PriorityQueue instance from a stream (that is, deserializes it). 
Params:
s – the stream
Throws:
ClassNotFoundException – if the class of a serialized object
        could not be found
IOException – if an I/O error occurs/**
     * Reconstitutes the {@code PriorityQueue} instance from a stream
     * (that is, deserializes it).
     *
     * @param s the stream
     * @throws ClassNotFoundException if the class of a serialized object
     *         could not be found
     * @throws java.io.IOException if an I/O error occurs
     */
    private void readObject(java.io.ObjectInputStream s)
        throws java.io.IOException, ClassNotFoundException {
        // Read in size, and any hidden stuff
        s.defaultReadObject();

        // Read in (and discard) array length
        s.readInt();

        SharedSecrets.getJavaObjectInputStreamAccess().checkArray(s, Object[].class, size);
        final Object[] es = queue = new Object[Math.max(size, 1)];

        // Read in all elements.
        for (int i = 0, n = size; i < n; i++)
            es[i] = s.readObject();

        // Elements are guaranteed to be in "proper order", but the
        // spec has never explained what that might be.
        heapify();
    }

    
Creates a late-binding
and fail-fast Spliterator over the elements in this queue. The spliterator does not traverse elements in any particular order (the ORDERED characteristic is not reported). 
The Spliterator reports Spliterator.SIZED, Spliterator.SUBSIZED, and Spliterator.NONNULL. Overriding implementations should document the reporting of additional characteristic values. 
Returns:
a Spliterator over the elements in this queue
Since:
1.8/**
     * Creates a <em><a href="Spliterator.html#binding">late-binding</a></em>
     * and <em>fail-fast</em> {@link Spliterator} over the elements in this
     * queue. The spliterator does not traverse elements in any particular order
     * (the {@link Spliterator#ORDERED ORDERED} characteristic is not reported).
     *
     * <p>The {@code Spliterator} reports {@link Spliterator#SIZED},
     * {@link Spliterator#SUBSIZED}, and {@link Spliterator#NONNULL}.
     * Overriding implementations should document the reporting of additional
     * characteristic values.
     *
     * @return a {@code Spliterator} over the elements in this queue
     * @since 1.8
     */
    public final Spliterator<E> spliterator() {
        return new PriorityQueueSpliterator(0, -1, 0);
    }

    final class PriorityQueueSpliterator implements Spliterator<E> {
        private int index;            // current index, modified on advance/split
        private int fence;            // -1 until first use
        private int expectedModCount; // initialized when fence set

        
Creates new spliterator covering the given range. /** Creates new spliterator covering the given range. */
        PriorityQueueSpliterator(int origin, int fence, int expectedModCount) {
            this.index = origin;
            this.fence = fence;
            this.expectedModCount = expectedModCount;
        }

        private int getFence() { // initialize fence to size on first use
            int hi;
            if ((hi = fence) < 0) {
                expectedModCount = modCount;
                hi = fence = size;
            }
            return hi;
        }

        public PriorityQueueSpliterator trySplit() {
            int hi = getFence(), lo = index, mid = (lo + hi) >>> 1;
            return (lo >= mid) ? null :
                new PriorityQueueSpliterator(lo, index = mid, expectedModCount);
        }

        public void forEachRemaining(Consumer<? super E> action) {
            if (action == null)
                throw new NullPointerException();
            if (fence < 0) { fence = size; expectedModCount = modCount; }
            final Object[] es = queue;
            int i, hi; E e;
            for (i = index, index = hi = fence; i < hi; i++) {
                if ((e = (E) es[i]) == null)
                    break;      // must be CME
                action.accept(e);
            }
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
        }

        public boolean tryAdvance(Consumer<? super E> action) {
            if (action == null)
                throw new NullPointerException();
            if (fence < 0) { fence = size; expectedModCount = modCount; }
            int i;
            if ((i = index) < fence) {
                index = i + 1;
                E e;
                if ((e = (E) queue[i]) == null
                    || modCount != expectedModCount)
                    throw new ConcurrentModificationException();
                action.accept(e);
                return true;
            }
            return false;
        }

        public long estimateSize() {
            return getFence() - index;
        }

        public int characteristics() {
            return Spliterator.SIZED | Spliterator.SUBSIZED | Spliterator.NONNULL;
        }
    }

    
Throws:
NullPointerException – {@inheritDoc}/**
     * @throws NullPointerException {@inheritDoc}
     */
    public boolean removeIf(Predicate<? super E> filter) {
        Objects.requireNonNull(filter);
        return bulkRemove(filter);
    }

    
Throws:
NullPointerException – {@inheritDoc}/**
     * @throws NullPointerException {@inheritDoc}
     */
    public boolean removeAll(Collection<?> c) {
        Objects.requireNonNull(c);
        return bulkRemove(e -> c.contains(e));
    }

    
Throws:
NullPointerException – {@inheritDoc}/**
     * @throws NullPointerException {@inheritDoc}
     */
    public boolean retainAll(Collection<?> c) {
        Objects.requireNonNull(c);
        return bulkRemove(e -> !c.contains(e));
    }

    // A tiny bit set implementation

    private static long[] nBits(int n) {
        return new long[((n - 1) >> 6) + 1];
    }
    private static void setBit(long[] bits, int i) {
        bits[i >> 6] |= 1L << i;
    }
    private static boolean isClear(long[] bits, int i) {
        return (bits[i >> 6] & (1L << i)) == 0;
    }

    
Implementation of bulk remove methods. /** Implementation of bulk remove methods. */
    private boolean bulkRemove(Predicate<? super E> filter) {
        final int expectedModCount = ++modCount;
        final Object[] es = queue;
        final int end = size;
        int i;
        // Optimize for initial run of survivors
        for (i = 0; i < end && !filter.test((E) es[i]); i++)
            ;
        if (i >= end) {
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
            return false;
        }
        // Tolerate predicates that reentrantly access the collection for
        // read (but writers still get CME), so traverse once to find
        // elements to delete, a second pass to physically expunge.
        final int beg = i;
        final long[] deathRow = nBits(end - beg);
        deathRow[0] = 1L;   // set bit 0
        for (i = beg + 1; i < end; i++)
            if (filter.test((E) es[i]))
                setBit(deathRow, i - beg);
        if (modCount != expectedModCount)
            throw new ConcurrentModificationException();
        int w = beg;
        for (i = beg; i < end; i++)
            if (isClear(deathRow, i - beg))
                es[w++] = es[i];
        for (i = size = w; i < end; i++)
            es[i] = null;
        heapify();
        return true;
    }

    
Throws:
NullPointerException – {@inheritDoc}/**
     * @throws NullPointerException {@inheritDoc}
     */
    public void forEach(Consumer<? super E> action) {
        Objects.requireNonNull(action);
        final int expectedModCount = modCount;
        final Object[] es = queue;
        for (int i = 0, n = size; i < n; i++)
            action.accept((E) es[i]);
        if (expectedModCount != modCount)
            throw new ConcurrentModificationException();
    }
}