1 /*
   2  * Copyright (c) 2003, 2019, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
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   7  * published by the Free Software Foundation.  Oracle designates this
   8  * particular file as subject to the "Classpath" exception as provided
   9  * by Oracle in the LICENSE file that accompanied this code.
  10  *
  11  * This code is distributed in the hope that it will be useful, but WITHOUT
  12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14  * version 2 for more details (a copy is included in the LICENSE file that
  15  * accompanied this code).
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  23  * questions.
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  25 
  26 package java.util;
  27 
  28 import java.util.function.Consumer;
  29 import java.util.function.Predicate;
  30 import jdk.internal.access.SharedSecrets;
  31 import jdk.internal.util.ArraysSupport;
  32 
  33 /**
  34  * An unbounded priority {@linkplain Queue queue} based on a priority heap.
  35  * The elements of the priority queue are ordered according to their
  36  * {@linkplain Comparable natural ordering}, or by a {@link Comparator}
  37  * provided at queue construction time, depending on which constructor is
  38  * used.  A priority queue does not permit {@code null} elements.
  39  * A priority queue relying on natural ordering also does not permit
  40  * insertion of non-comparable objects (doing so may result in
  41  * {@code ClassCastException}).
  42  *
  43  * <p>The <em>head</em> of this queue is the <em>least</em> element
  44  * with respect to the specified ordering.  If multiple elements are
  45  * tied for least value, the head is one of those elements -- ties are
  46  * broken arbitrarily.  The queue retrieval operations {@code poll},
  47  * {@code remove}, {@code peek}, and {@code element} access the
  48  * element at the head of the queue.
  49  *
  50  * <p>A priority queue is unbounded, but has an internal
  51  * <i>capacity</i> governing the size of an array used to store the
  52  * elements on the queue.  It is always at least as large as the queue
  53  * size.  As elements are added to a priority queue, its capacity
  54  * grows automatically.  The details of the growth policy are not
  55  * specified.
  56  *
  57  * <p>This class and its iterator implement all of the
  58  * <em>optional</em> methods of the {@link Collection} and {@link
  59  * Iterator} interfaces.  The Iterator provided in method {@link
  60  * #iterator()} and the Spliterator provided in method {@link #spliterator()}
  61  * are <em>not</em> guaranteed to traverse the elements of
  62  * the priority queue in any particular order. If you need ordered
  63  * traversal, consider using {@code Arrays.sort(pq.toArray())}.
  64  *
  65  * <p><strong>Note that this implementation is not synchronized.</strong>
  66  * Multiple threads should not access a {@code PriorityQueue}
  67  * instance concurrently if any of the threads modifies the queue.
  68  * Instead, use the thread-safe {@link
  69  * java.util.concurrent.PriorityBlockingQueue} class.
  70  *
  71  * <p>Implementation note: this implementation provides
  72  * O(log(n)) time for the enqueuing and dequeuing methods
  73  * ({@code offer}, {@code poll}, {@code remove()} and {@code add});
  74  * linear time for the {@code remove(Object)} and {@code contains(Object)}
  75  * methods; and constant time for the retrieval methods
  76  * ({@code peek}, {@code element}, and {@code size}).
  77  *
  78  * <p>This class is a member of the
  79  * <a href="{@docRoot}/java.base/java/util/package-summary.html#CollectionsFramework">
  80  * Java Collections Framework</a>.
  81  *
  82  * @since 1.5
  83  * @author Josh Bloch, Doug Lea
  84  * @param <E> the type of elements held in this queue
  85  */
  86 @SuppressWarnings("unchecked")
  87 public class PriorityQueue<E> extends AbstractQueue<E>
  88     implements java.io.Serializable {
  89 
  90     private static final long serialVersionUID = -7720805057305804111L;
  91 
  92     private static final int DEFAULT_INITIAL_CAPACITY = 11;
  93 
  94     /**
  95      * Priority queue represented as a balanced binary heap: the two
  96      * children of queue[n] are queue[2*n+1] and queue[2*(n+1)].  The
  97      * priority queue is ordered by comparator, or by the elements'
  98      * natural ordering, if comparator is null: For each node n in the
  99      * heap and each descendant d of n, n <= d.  The element with the
 100      * lowest value is in queue[0], assuming the queue is nonempty.
 101      */
 102     transient Object[] queue; // non-private to simplify nested class access
 103 
 104     /**
 105      * The number of elements in the priority queue.
 106      */
 107     int size;
 108 
 109     /**
 110      * The comparator, or null if priority queue uses elements'
 111      * natural ordering.
 112      */
 113     private final Comparator<? super E> comparator;
 114 
 115     /**
 116      * The number of times this priority queue has been
 117      * <i>structurally modified</i>.  See AbstractList for gory details.
 118      */
 119     transient int modCount;     // non-private to simplify nested class access
 120 
 121     /**
 122      * Creates a {@code PriorityQueue} with the default initial
 123      * capacity (11) that orders its elements according to their
 124      * {@linkplain Comparable natural ordering}.
 125      */
 126     public PriorityQueue() {
 127         this(DEFAULT_INITIAL_CAPACITY, null);
 128     }
 129 
 130     /**
 131      * Creates a {@code PriorityQueue} with the specified initial
 132      * capacity that orders its elements according to their
 133      * {@linkplain Comparable natural ordering}.
 134      *
 135      * @param initialCapacity the initial capacity for this priority queue
 136      * @throws IllegalArgumentException if {@code initialCapacity} is less
 137      *         than 1
 138      */
 139     public PriorityQueue(int initialCapacity) {
 140         this(initialCapacity, null);
 141     }
 142 
 143     /**
 144      * Creates a {@code PriorityQueue} with the default initial capacity and
 145      * whose elements are ordered according to the specified comparator.
 146      *
 147      * @param  comparator the comparator that will be used to order this
 148      *         priority queue.  If {@code null}, the {@linkplain Comparable
 149      *         natural ordering} of the elements will be used.
 150      * @since 1.8
 151      */
 152     public PriorityQueue(Comparator<? super E> comparator) {
 153         this(DEFAULT_INITIAL_CAPACITY, comparator);
 154     }
 155 
 156     /**
 157      * Creates a {@code PriorityQueue} with the specified initial capacity
 158      * that orders its elements according to the specified comparator.
 159      *
 160      * @param  initialCapacity the initial capacity for this priority queue
 161      * @param  comparator the comparator that will be used to order this
 162      *         priority queue.  If {@code null}, the {@linkplain Comparable
 163      *         natural ordering} of the elements will be used.
 164      * @throws IllegalArgumentException if {@code initialCapacity} is
 165      *         less than 1
 166      */
 167     public PriorityQueue(int initialCapacity,
 168                          Comparator<? super E> comparator) {
 169         // Note: This restriction of at least one is not actually needed,
 170         // but continues for 1.5 compatibility
 171         if (initialCapacity < 1)
 172             throw new IllegalArgumentException();
 173         this.queue = new Object[initialCapacity];
 174         this.comparator = comparator;
 175     }
 176 
 177     /**
 178      * Creates a {@code PriorityQueue} containing the elements in the
 179      * specified collection.  If the specified collection is an instance of
 180      * a {@link SortedSet} or is another {@code PriorityQueue}, this
 181      * priority queue will be ordered according to the same ordering.
 182      * Otherwise, this priority queue will be ordered according to the
 183      * {@linkplain Comparable natural ordering} of its elements.
 184      *
 185      * @param  c the collection whose elements are to be placed
 186      *         into this priority queue
 187      * @throws ClassCastException if elements of the specified collection
 188      *         cannot be compared to one another according to the priority
 189      *         queue's ordering
 190      * @throws NullPointerException if the specified collection or any
 191      *         of its elements are null
 192      */
 193     public PriorityQueue(Collection<? extends E> c) {
 194         if (c instanceof SortedSet<?>) {
 195             SortedSet<? extends E> ss = (SortedSet<? extends E>) c;
 196             this.comparator = (Comparator<? super E>) ss.comparator();
 197             initElementsFromCollection(ss);
 198         }
 199         else if (c instanceof PriorityQueue<?>) {
 200             PriorityQueue<? extends E> pq = (PriorityQueue<? extends E>) c;
 201             this.comparator = (Comparator<? super E>) pq.comparator();
 202             initFromPriorityQueue(pq);
 203         }
 204         else {
 205             this.comparator = null;
 206             initFromCollection(c);
 207         }
 208     }
 209 
 210     /**
 211      * Creates a {@code PriorityQueue} containing the elements in the
 212      * specified priority queue.  This priority queue will be
 213      * ordered according to the same ordering as the given priority
 214      * queue.
 215      *
 216      * @param  c the priority queue whose elements are to be placed
 217      *         into this priority queue
 218      * @throws ClassCastException if elements of {@code c} cannot be
 219      *         compared to one another according to {@code c}'s
 220      *         ordering
 221      * @throws NullPointerException if the specified priority queue or any
 222      *         of its elements are null
 223      */
 224     public PriorityQueue(PriorityQueue<? extends E> c) {
 225         this.comparator = (Comparator<? super E>) c.comparator();
 226         initFromPriorityQueue(c);
 227     }
 228 
 229     /**
 230      * Creates a {@code PriorityQueue} containing the elements in the
 231      * specified sorted set.   This priority queue will be ordered
 232      * according to the same ordering as the given sorted set.
 233      *
 234      * @param  c the sorted set whose elements are to be placed
 235      *         into this priority queue
 236      * @throws ClassCastException if elements of the specified sorted
 237      *         set cannot be compared to one another according to the
 238      *         sorted set's ordering
 239      * @throws NullPointerException if the specified sorted set or any
 240      *         of its elements are null
 241      */
 242     public PriorityQueue(SortedSet<? extends E> c) {
 243         this.comparator = (Comparator<? super E>) c.comparator();
 244         initElementsFromCollection(c);
 245     }
 246 
 247     /** Ensures that queue[0] exists, helping peek() and poll(). */
 248     private static Object[] ensureNonEmpty(Object[] es) {
 249         return (es.length > 0) ? es : new Object[1];
 250     }
 251 
 252     private void initFromPriorityQueue(PriorityQueue<? extends E> c) {
 253         if (c.getClass() == PriorityQueue.class) {
 254             this.queue = ensureNonEmpty(c.toArray());
 255             this.size = c.size();
 256         } else {
 257             initFromCollection(c);
 258         }
 259     }
 260 
 261     private void initElementsFromCollection(Collection<? extends E> c) {
 262         Object[] es = c.toArray();
 263         int len = es.length;
 264         // If c.toArray incorrectly doesn't return Object[], copy it.
 265         if (es.getClass() != Object[].class)
 266             es = Arrays.copyOf(es, len, Object[].class);
 267         if (len == 1 || this.comparator != null)
 268             for (Object e : es)
 269                 if (e == null)
 270                     throw new NullPointerException();
 271         this.queue = ensureNonEmpty(es);
 272         this.size = len;
 273     }
 274 
 275     /**
 276      * Initializes queue array with elements from the given Collection.
 277      *
 278      * @param c the collection
 279      */
 280     private void initFromCollection(Collection<? extends E> c) {
 281         initElementsFromCollection(c);
 282         heapify();
 283     }
 284 
 285     /**
 286      * Increases the capacity of the array.
 287      *
 288      * @param minCapacity the desired minimum capacity
 289      */
 290     private void grow(int minCapacity) {
 291         int oldCapacity = queue.length;
 292         // Double size if small; else grow by 50%
 293         int newCapacity = ArraysSupport.newLength(oldCapacity,
 294                 minCapacity - oldCapacity, /* minimum growth */
 295                 oldCapacity < 64 ? oldCapacity + 2 : oldCapacity >> 1
 296                                            /* preferred growth */);
 297         queue = Arrays.copyOf(queue, newCapacity);
 298     }
 299 
 300     /**
 301      * Inserts the specified element into this priority queue.
 302      *
 303      * @return {@code true} (as specified by {@link Collection#add})
 304      * @throws ClassCastException if the specified element cannot be
 305      *         compared with elements currently in this priority queue
 306      *         according to the priority queue's ordering
 307      * @throws NullPointerException if the specified element is null
 308      */
 309     public boolean add(E e) {
 310         return offer(e);
 311     }
 312 
 313     /**
 314      * Inserts the specified element into this priority queue.
 315      *
 316      * @return {@code true} (as specified by {@link Queue#offer})
 317      * @throws ClassCastException if the specified element cannot be
 318      *         compared with elements currently in this priority queue
 319      *         according to the priority queue's ordering
 320      * @throws NullPointerException if the specified element is null
 321      */
 322     public boolean offer(E e) {
 323         if (e == null)
 324             throw new NullPointerException();
 325         modCount++;
 326         int i = size;
 327         if (i >= queue.length)
 328             grow(i + 1);
 329         siftUp(i, e);
 330         size = i + 1;
 331         return true;
 332     }
 333 
 334     public E peek() {
 335         return (E) queue[0];
 336     }
 337 
 338     private int indexOf(Object o) {
 339         if (o != null) {
 340             final Object[] es = queue;
 341             for (int i = 0, n = size; i < n; i++)
 342                 if (o.equals(es[i]))
 343                     return i;
 344         }
 345         return -1;
 346     }
 347 
 348     /**
 349      * Removes a single instance of the specified element from this queue,
 350      * if it is present.  More formally, removes an element {@code e} such
 351      * that {@code o.equals(e)}, if this queue contains one or more such
 352      * elements.  Returns {@code true} if and only if this queue contained
 353      * the specified element (or equivalently, if this queue changed as a
 354      * result of the call).
 355      *
 356      * @param o element to be removed from this queue, if present
 357      * @return {@code true} if this queue changed as a result of the call
 358      */
 359     public boolean remove(Object o) {
 360         int i = indexOf(o);
 361         if (i == -1)
 362             return false;
 363         else {
 364             removeAt(i);
 365             return true;
 366         }
 367     }
 368 
 369     /**
 370      * Identity-based version for use in Itr.remove.
 371      *
 372      * @param o element to be removed from this queue, if present
 373      */
 374     void removeEq(Object o) {
 375         final Object[] es = queue;
 376         for (int i = 0, n = size; i < n; i++) {
 377             if (o == es[i]) {
 378                 removeAt(i);
 379                 break;
 380             }
 381         }
 382     }
 383 
 384     /**
 385      * Returns {@code true} if this queue contains the specified element.
 386      * More formally, returns {@code true} if and only if this queue contains
 387      * at least one element {@code e} such that {@code o.equals(e)}.
 388      *
 389      * @param o object to be checked for containment in this queue
 390      * @return {@code true} if this queue contains the specified element
 391      */
 392     public boolean contains(Object o) {
 393         return indexOf(o) >= 0;
 394     }
 395 
 396     /**
 397      * Returns an array containing all of the elements in this queue.
 398      * The elements are in no particular order.
 399      *
 400      * <p>The returned array will be "safe" in that no references to it are
 401      * maintained by this queue.  (In other words, this method must allocate
 402      * a new array).  The caller is thus free to modify the returned array.
 403      *
 404      * <p>This method acts as bridge between array-based and collection-based
 405      * APIs.
 406      *
 407      * @return an array containing all of the elements in this queue
 408      */
 409     public Object[] toArray() {
 410         return Arrays.copyOf(queue, size);
 411     }
 412 
 413     /**
 414      * Returns an array containing all of the elements in this queue; the
 415      * runtime type of the returned array is that of the specified array.
 416      * The returned array elements are in no particular order.
 417      * If the queue fits in the specified array, it is returned therein.
 418      * Otherwise, a new array is allocated with the runtime type of the
 419      * specified array and the size of this queue.
 420      *
 421      * <p>If the queue fits in the specified array with room to spare
 422      * (i.e., the array has more elements than the queue), the element in
 423      * the array immediately following the end of the collection is set to
 424      * {@code null}.
 425      *
 426      * <p>Like the {@link #toArray()} method, this method acts as bridge between
 427      * array-based and collection-based APIs.  Further, this method allows
 428      * precise control over the runtime type of the output array, and may,
 429      * under certain circumstances, be used to save allocation costs.
 430      *
 431      * <p>Suppose {@code x} is a queue known to contain only strings.
 432      * The following code can be used to dump the queue into a newly
 433      * allocated array of {@code String}:
 434      *
 435      * <pre> {@code String[] y = x.toArray(new String[0]);}</pre>
 436      *
 437      * Note that {@code toArray(new Object[0])} is identical in function to
 438      * {@code toArray()}.
 439      *
 440      * @param a the array into which the elements of the queue are to
 441      *          be stored, if it is big enough; otherwise, a new array of the
 442      *          same runtime type is allocated for this purpose.
 443      * @return an array containing all of the elements in this queue
 444      * @throws ArrayStoreException if the runtime type of the specified array
 445      *         is not a supertype of the runtime type of every element in
 446      *         this queue
 447      * @throws NullPointerException if the specified array is null
 448      */
 449     public <T> T[] toArray(T[] a) {
 450         final int size = this.size;
 451         if (a.length < size)
 452             // Make a new array of a's runtime type, but my contents:
 453             return (T[]) Arrays.copyOf(queue, size, a.getClass());
 454         System.arraycopy(queue, 0, a, 0, size);
 455         if (a.length > size)
 456             a[size] = null;
 457         return a;
 458     }
 459 
 460     /**
 461      * Returns an iterator over the elements in this queue. The iterator
 462      * does not return the elements in any particular order.
 463      *
 464      * @return an iterator over the elements in this queue
 465      */
 466     public Iterator<E> iterator() {
 467         return new Itr();
 468     }
 469 
 470     private final class Itr implements Iterator<E> {
 471         /**
 472          * Index (into queue array) of element to be returned by
 473          * subsequent call to next.
 474          */
 475         private int cursor;
 476 
 477         /**
 478          * Index of element returned by most recent call to next,
 479          * unless that element came from the forgetMeNot list.
 480          * Set to -1 if element is deleted by a call to remove.
 481          */
 482         private int lastRet = -1;
 483 
 484         /**
 485          * A queue of elements that were moved from the unvisited portion of
 486          * the heap into the visited portion as a result of "unlucky" element
 487          * removals during the iteration.  (Unlucky element removals are those
 488          * that require a siftup instead of a siftdown.)  We must visit all of
 489          * the elements in this list to complete the iteration.  We do this
 490          * after we've completed the "normal" iteration.
 491          *
 492          * We expect that most iterations, even those involving removals,
 493          * will not need to store elements in this field.
 494          */
 495         private ArrayDeque<E> forgetMeNot;
 496 
 497         /**
 498          * Element returned by the most recent call to next iff that
 499          * element was drawn from the forgetMeNot list.
 500          */
 501         private E lastRetElt;
 502 
 503         /**
 504          * The modCount value that the iterator believes that the backing
 505          * Queue should have.  If this expectation is violated, the iterator
 506          * has detected concurrent modification.
 507          */
 508         private int expectedModCount = modCount;
 509 
 510         Itr() {}                        // prevent access constructor creation
 511 
 512         public boolean hasNext() {
 513             return cursor < size ||
 514                 (forgetMeNot != null && !forgetMeNot.isEmpty());
 515         }
 516 
 517         public E next() {
 518             if (expectedModCount != modCount)
 519                 throw new ConcurrentModificationException();
 520             if (cursor < size)
 521                 return (E) queue[lastRet = cursor++];
 522             if (forgetMeNot != null) {
 523                 lastRet = -1;
 524                 lastRetElt = forgetMeNot.poll();
 525                 if (lastRetElt != null)
 526                     return lastRetElt;
 527             }
 528             throw new NoSuchElementException();
 529         }
 530 
 531         public void remove() {
 532             if (expectedModCount != modCount)
 533                 throw new ConcurrentModificationException();
 534             if (lastRet != -1) {
 535                 E moved = PriorityQueue.this.removeAt(lastRet);
 536                 lastRet = -1;
 537                 if (moved == null)
 538                     cursor--;
 539                 else {
 540                     if (forgetMeNot == null)
 541                         forgetMeNot = new ArrayDeque<>();
 542                     forgetMeNot.add(moved);
 543                 }
 544             } else if (lastRetElt != null) {
 545                 PriorityQueue.this.removeEq(lastRetElt);
 546                 lastRetElt = null;
 547             } else {
 548                 throw new IllegalStateException();
 549             }
 550             expectedModCount = modCount;
 551         }
 552     }
 553 
 554     public int size() {
 555         return size;
 556     }
 557 
 558     /**
 559      * Removes all of the elements from this priority queue.
 560      * The queue will be empty after this call returns.
 561      */
 562     public void clear() {
 563         modCount++;
 564         final Object[] es = queue;
 565         for (int i = 0, n = size; i < n; i++)
 566             es[i] = null;
 567         size = 0;
 568     }
 569 
 570     public E poll() {
 571         final Object[] es;
 572         final E result;
 573 
 574         if ((result = (E) ((es = queue)[0])) != null) {
 575             modCount++;
 576             final int n;
 577             final E x = (E) es[(n = --size)];
 578             es[n] = null;
 579             if (n > 0) {
 580                 final Comparator<? super E> cmp;
 581                 if ((cmp = comparator) == null)
 582                     siftDownComparable(0, x, es, n);
 583                 else
 584                     siftDownUsingComparator(0, x, es, n, cmp);
 585             }
 586         }
 587         return result;
 588     }
 589 
 590     /**
 591      * Removes the ith element from queue.
 592      *
 593      * Normally this method leaves the elements at up to i-1,
 594      * inclusive, untouched.  Under these circumstances, it returns
 595      * null.  Occasionally, in order to maintain the heap invariant,
 596      * it must swap a later element of the list with one earlier than
 597      * i.  Under these circumstances, this method returns the element
 598      * that was previously at the end of the list and is now at some
 599      * position before i. This fact is used by iterator.remove so as to
 600      * avoid missing traversing elements.
 601      */
 602     E removeAt(int i) {
 603         // assert i >= 0 && i < size;
 604         final Object[] es = queue;
 605         modCount++;
 606         int s = --size;
 607         if (s == i) // removed last element
 608             es[i] = null;
 609         else {
 610             E moved = (E) es[s];
 611             es[s] = null;
 612             siftDown(i, moved);
 613             if (es[i] == moved) {
 614                 siftUp(i, moved);
 615                 if (es[i] != moved)
 616                     return moved;
 617             }
 618         }
 619         return null;
 620     }
 621 
 622     /**
 623      * Inserts item x at position k, maintaining heap invariant by
 624      * promoting x up the tree until it is greater than or equal to
 625      * its parent, or is the root.
 626      *
 627      * To simplify and speed up coercions and comparisons, the
 628      * Comparable and Comparator versions are separated into different
 629      * methods that are otherwise identical. (Similarly for siftDown.)
 630      *
 631      * @param k the position to fill
 632      * @param x the item to insert
 633      */
 634     private void siftUp(int k, E x) {
 635         if (comparator != null)
 636             siftUpUsingComparator(k, x, queue, comparator);
 637         else
 638             siftUpComparable(k, x, queue);
 639     }
 640 
 641     private static <T> void siftUpComparable(int k, T x, Object[] es) {
 642         Comparable<? super T> key = (Comparable<? super T>) x;
 643         while (k > 0) {
 644             int parent = (k - 1) >>> 1;
 645             Object e = es[parent];
 646             if (key.compareTo((T) e) >= 0)
 647                 break;
 648             es[k] = e;
 649             k = parent;
 650         }
 651         es[k] = key;
 652     }
 653 
 654     private static <T> void siftUpUsingComparator(
 655         int k, T x, Object[] es, Comparator<? super T> cmp) {
 656         while (k > 0) {
 657             int parent = (k - 1) >>> 1;
 658             Object e = es[parent];
 659             if (cmp.compare(x, (T) e) >= 0)
 660                 break;
 661             es[k] = e;
 662             k = parent;
 663         }
 664         es[k] = x;
 665     }
 666 
 667     /**
 668      * Inserts item x at position k, maintaining heap invariant by
 669      * demoting x down the tree repeatedly until it is less than or
 670      * equal to its children or is a leaf.
 671      *
 672      * @param k the position to fill
 673      * @param x the item to insert
 674      */
 675     private void siftDown(int k, E x) {
 676         if (comparator != null)
 677             siftDownUsingComparator(k, x, queue, size, comparator);
 678         else
 679             siftDownComparable(k, x, queue, size);
 680     }
 681 
 682     private static <T> void siftDownComparable(int k, T x, Object[] es, int n) {
 683         // assert n > 0;
 684         Comparable<? super T> key = (Comparable<? super T>)x;
 685         int half = n >>> 1;           // loop while a non-leaf
 686         while (k < half) {
 687             int child = (k << 1) + 1; // assume left child is least
 688             Object c = es[child];
 689             int right = child + 1;
 690             if (right < n &&
 691                 ((Comparable<? super T>) c).compareTo((T) es[right]) > 0)
 692                 c = es[child = right];
 693             if (key.compareTo((T) c) <= 0)
 694                 break;
 695             es[k] = c;
 696             k = child;
 697         }
 698         es[k] = key;
 699     }
 700 
 701     private static <T> void siftDownUsingComparator(
 702         int k, T x, Object[] es, int n, Comparator<? super T> cmp) {
 703         // assert n > 0;
 704         int half = n >>> 1;
 705         while (k < half) {
 706             int child = (k << 1) + 1;
 707             Object c = es[child];
 708             int right = child + 1;
 709             if (right < n && cmp.compare((T) c, (T) es[right]) > 0)
 710                 c = es[child = right];
 711             if (cmp.compare(x, (T) c) <= 0)
 712                 break;
 713             es[k] = c;
 714             k = child;
 715         }
 716         es[k] = x;
 717     }
 718 
 719     /**
 720      * Establishes the heap invariant (described above) in the entire tree,
 721      * assuming nothing about the order of the elements prior to the call.
 722      * This classic algorithm due to Floyd (1964) is known to be O(size).
 723      */
 724     private void heapify() {
 725         final Object[] es = queue;
 726         int n = size, i = (n >>> 1) - 1;
 727         final Comparator<? super E> cmp;
 728         if ((cmp = comparator) == null)
 729             for (; i >= 0; i--)
 730                 siftDownComparable(i, (E) es[i], es, n);
 731         else
 732             for (; i >= 0; i--)
 733                 siftDownUsingComparator(i, (E) es[i], es, n, cmp);
 734     }
 735 
 736     /**
 737      * Returns the comparator used to order the elements in this
 738      * queue, or {@code null} if this queue is sorted according to
 739      * the {@linkplain Comparable natural ordering} of its elements.
 740      *
 741      * @return the comparator used to order this queue, or
 742      *         {@code null} if this queue is sorted according to the
 743      *         natural ordering of its elements
 744      */
 745     public Comparator<? super E> comparator() {
 746         return comparator;
 747     }
 748 
 749     /**
 750      * Saves this queue to a stream (that is, serializes it).
 751      *
 752      * @param s the stream
 753      * @throws java.io.IOException if an I/O error occurs
 754      * @serialData The length of the array backing the instance is
 755      *             emitted (int), followed by all of its elements
 756      *             (each an {@code Object}) in the proper order.
 757      */
 758     private void writeObject(java.io.ObjectOutputStream s)
 759         throws java.io.IOException {
 760         // Write out element count, and any hidden stuff
 761         s.defaultWriteObject();
 762 
 763         // Write out array length, for compatibility with 1.5 version
 764         s.writeInt(Math.max(2, size + 1));
 765 
 766         // Write out all elements in the "proper order".
 767         final Object[] es = queue;
 768         for (int i = 0, n = size; i < n; i++)
 769             s.writeObject(es[i]);
 770     }
 771 
 772     /**
 773      * Reconstitutes the {@code PriorityQueue} instance from a stream
 774      * (that is, deserializes it).
 775      *
 776      * @param s the stream
 777      * @throws ClassNotFoundException if the class of a serialized object
 778      *         could not be found
 779      * @throws java.io.IOException if an I/O error occurs
 780      */
 781     private void readObject(java.io.ObjectInputStream s)
 782         throws java.io.IOException, ClassNotFoundException {
 783         // Read in size, and any hidden stuff
 784         s.defaultReadObject();
 785 
 786         // Read in (and discard) array length
 787         s.readInt();
 788 
 789         SharedSecrets.getJavaObjectInputStreamAccess().checkArray(s, Object[].class, size);
 790         final Object[] es = queue = new Object[Math.max(size, 1)];
 791 
 792         // Read in all elements.
 793         for (int i = 0, n = size; i < n; i++)
 794             es[i] = s.readObject();
 795 
 796         // Elements are guaranteed to be in "proper order", but the
 797         // spec has never explained what that might be.
 798         heapify();
 799     }
 800 
 801     /**
 802      * Creates a <em><a href="Spliterator.html#binding">late-binding</a></em>
 803      * and <em>fail-fast</em> {@link Spliterator} over the elements in this
 804      * queue. The spliterator does not traverse elements in any particular order
 805      * (the {@link Spliterator#ORDERED ORDERED} characteristic is not reported).
 806      *
 807      * <p>The {@code Spliterator} reports {@link Spliterator#SIZED},
 808      * {@link Spliterator#SUBSIZED}, and {@link Spliterator#NONNULL}.
 809      * Overriding implementations should document the reporting of additional
 810      * characteristic values.
 811      *
 812      * @return a {@code Spliterator} over the elements in this queue
 813      * @since 1.8
 814      */
 815     public final Spliterator<E> spliterator() {
 816         return new PriorityQueueSpliterator(0, -1, 0);
 817     }
 818 
 819     final class PriorityQueueSpliterator implements Spliterator<E> {
 820         private int index;            // current index, modified on advance/split
 821         private int fence;            // -1 until first use
 822         private int expectedModCount; // initialized when fence set
 823 
 824         /** Creates new spliterator covering the given range. */
 825         PriorityQueueSpliterator(int origin, int fence, int expectedModCount) {
 826             this.index = origin;
 827             this.fence = fence;
 828             this.expectedModCount = expectedModCount;
 829         }
 830 
 831         private int getFence() { // initialize fence to size on first use
 832             int hi;
 833             if ((hi = fence) < 0) {
 834                 expectedModCount = modCount;
 835                 hi = fence = size;
 836             }
 837             return hi;
 838         }
 839 
 840         public PriorityQueueSpliterator trySplit() {
 841             int hi = getFence(), lo = index, mid = (lo + hi) >>> 1;
 842             return (lo >= mid) ? null :
 843                 new PriorityQueueSpliterator(lo, index = mid, expectedModCount);
 844         }
 845 
 846         public void forEachRemaining(Consumer<? super E> action) {
 847             if (action == null)
 848                 throw new NullPointerException();
 849             if (fence < 0) { fence = size; expectedModCount = modCount; }
 850             final Object[] es = queue;
 851             int i, hi; E e;
 852             for (i = index, index = hi = fence; i < hi; i++) {
 853                 if ((e = (E) es[i]) == null)
 854                     break;      // must be CME
 855                 action.accept(e);
 856             }
 857             if (modCount != expectedModCount)
 858                 throw new ConcurrentModificationException();
 859         }
 860 
 861         public boolean tryAdvance(Consumer<? super E> action) {
 862             if (action == null)
 863                 throw new NullPointerException();
 864             if (fence < 0) { fence = size; expectedModCount = modCount; }
 865             int i;
 866             if ((i = index) < fence) {
 867                 index = i + 1;
 868                 E e;
 869                 if ((e = (E) queue[i]) == null
 870                     || modCount != expectedModCount)
 871                     throw new ConcurrentModificationException();
 872                 action.accept(e);
 873                 return true;
 874             }
 875             return false;
 876         }
 877 
 878         public long estimateSize() {
 879             return getFence() - index;
 880         }
 881 
 882         public int characteristics() {
 883             return Spliterator.SIZED | Spliterator.SUBSIZED | Spliterator.NONNULL;
 884         }
 885     }
 886 
 887     /**
 888      * @throws NullPointerException {@inheritDoc}
 889      */
 890     public boolean removeIf(Predicate<? super E> filter) {
 891         Objects.requireNonNull(filter);
 892         return bulkRemove(filter);
 893     }
 894 
 895     /**
 896      * @throws NullPointerException {@inheritDoc}
 897      */
 898     public boolean removeAll(Collection<?> c) {
 899         Objects.requireNonNull(c);
 900         return bulkRemove(e -> c.contains(e));
 901     }
 902 
 903     /**
 904      * @throws NullPointerException {@inheritDoc}
 905      */
 906     public boolean retainAll(Collection<?> c) {
 907         Objects.requireNonNull(c);
 908         return bulkRemove(e -> !c.contains(e));
 909     }
 910 
 911     // A tiny bit set implementation
 912 
 913     private static long[] nBits(int n) {
 914         return new long[((n - 1) >> 6) + 1];
 915     }
 916     private static void setBit(long[] bits, int i) {
 917         bits[i >> 6] |= 1L << i;
 918     }
 919     private static boolean isClear(long[] bits, int i) {
 920         return (bits[i >> 6] & (1L << i)) == 0;
 921     }
 922 
 923     /** Implementation of bulk remove methods. */
 924     private boolean bulkRemove(Predicate<? super E> filter) {
 925         final int expectedModCount = ++modCount;
 926         final Object[] es = queue;
 927         final int end = size;
 928         int i;
 929         // Optimize for initial run of survivors
 930         for (i = 0; i < end && !filter.test((E) es[i]); i++)
 931             ;
 932         if (i >= end) {
 933             if (modCount != expectedModCount)
 934                 throw new ConcurrentModificationException();
 935             return false;
 936         }
 937         // Tolerate predicates that reentrantly access the collection for
 938         // read (but writers still get CME), so traverse once to find
 939         // elements to delete, a second pass to physically expunge.
 940         final int beg = i;
 941         final long[] deathRow = nBits(end - beg);
 942         deathRow[0] = 1L;   // set bit 0
 943         for (i = beg + 1; i < end; i++)
 944             if (filter.test((E) es[i]))
 945                 setBit(deathRow, i - beg);
 946         if (modCount != expectedModCount)
 947             throw new ConcurrentModificationException();
 948         int w = beg;
 949         for (i = beg; i < end; i++)
 950             if (isClear(deathRow, i - beg))
 951                 es[w++] = es[i];
 952         for (i = size = w; i < end; i++)
 953             es[i] = null;
 954         heapify();
 955         return true;
 956     }
 957 
 958     /**
 959      * @throws NullPointerException {@inheritDoc}
 960      */
 961     public void forEach(Consumer<? super E> action) {
 962         Objects.requireNonNull(action);
 963         final int expectedModCount = modCount;
 964         final Object[] es = queue;
 965         for (int i = 0, n = size; i < n; i++)
 966             action.accept((E) es[i]);
 967         if (expectedModCount != modCount)
 968             throw new ConcurrentModificationException();
 969     }
 970 }