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).
  16  *
  17  * You should have received a copy of the GNU General Public License version
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  19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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  22  * or visit www.oracle.com if you need additional information or have any
  23  * questions.
  24  */
  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     @java.io.Serial
  91     private static final long serialVersionUID = -7720805057305804111L;
  92 
  93     private static final int DEFAULT_INITIAL_CAPACITY = 11;
  94 
  95     /**
  96      * Priority queue represented as a balanced binary heap: the two
  97      * children of queue[n] are queue[2*n+1] and queue[2*(n+1)].  The
  98      * priority queue is ordered by comparator, or by the elements'
  99      * natural ordering, if comparator is null: For each node n in the
 100      * heap and each descendant d of n, n <= d.  The element with the
 101      * lowest value is in queue[0], assuming the queue is nonempty.
 102      */
 103     transient Object[] queue; // non-private to simplify nested class access
 104 
 105     /**
 106      * The number of elements in the priority queue.
 107      */
 108     int size;
 109 
 110     /**
 111      * The comparator, or null if priority queue uses elements'
 112      * natural ordering.
 113      */
 114     private final Comparator<? super E> comparator;
 115 
 116     /**
 117      * The number of times this priority queue has been
 118      * <i>structurally modified</i>.  See AbstractList for gory details.
 119      */
 120     transient int modCount;     // non-private to simplify nested class access
 121 
 122     /**
 123      * Creates a {@code PriorityQueue} with the default initial
 124      * capacity (11) that orders its elements according to their
 125      * {@linkplain Comparable natural ordering}.
 126      */
 127     public PriorityQueue() {
 128         this(DEFAULT_INITIAL_CAPACITY, null);
 129     }
 130 
 131     /**
 132      * Creates a {@code PriorityQueue} with the specified initial
 133      * capacity that orders its elements according to their
 134      * {@linkplain Comparable natural ordering}.
 135      *
 136      * @param initialCapacity the initial capacity for this priority queue
 137      * @throws IllegalArgumentException if {@code initialCapacity} is less
 138      *         than 1
 139      */
 140     public PriorityQueue(int initialCapacity) {
 141         this(initialCapacity, null);
 142     }
 143 
 144     /**
 145      * Creates a {@code PriorityQueue} with the default initial capacity and
 146      * whose elements are ordered according to the specified comparator.
 147      *
 148      * @param  comparator the comparator that will be used to order this
 149      *         priority queue.  If {@code null}, the {@linkplain Comparable
 150      *         natural ordering} of the elements will be used.
 151      * @since 1.8
 152      */
 153     public PriorityQueue(Comparator<? super E> comparator) {
 154         this(DEFAULT_INITIAL_CAPACITY, comparator);
 155     }
 156 
 157     /**
 158      * Creates a {@code PriorityQueue} with the specified initial capacity
 159      * that orders its elements according to the specified comparator.
 160      *
 161      * @param  initialCapacity the initial capacity for this priority queue
 162      * @param  comparator the comparator that will be used to order this
 163      *         priority queue.  If {@code null}, the {@linkplain Comparable
 164      *         natural ordering} of the elements will be used.
 165      * @throws IllegalArgumentException if {@code initialCapacity} is
 166      *         less than 1
 167      */
 168     public PriorityQueue(int initialCapacity,
 169                          Comparator<? super E> comparator) {
 170         // Note: This restriction of at least one is not actually needed,
 171         // but continues for 1.5 compatibility
 172         if (initialCapacity < 1)
 173             throw new IllegalArgumentException();
 174         this.queue = new Object[initialCapacity];
 175         this.comparator = comparator;
 176     }
 177 
 178     /**
 179      * Creates a {@code PriorityQueue} containing the elements in the
 180      * specified collection.  If the specified collection is an instance of
 181      * a {@link SortedSet} or is another {@code PriorityQueue}, this
 182      * priority queue will be ordered according to the same ordering.
 183      * Otherwise, this priority queue will be ordered according to the
 184      * {@linkplain Comparable natural ordering} of its elements.
 185      *
 186      * @param  c the collection whose elements are to be placed
 187      *         into this priority queue
 188      * @throws ClassCastException if elements of the specified collection
 189      *         cannot be compared to one another according to the priority
 190      *         queue's ordering
 191      * @throws NullPointerException if the specified collection or any
 192      *         of its elements are null
 193      */
 194     public PriorityQueue(Collection<? extends E> c) {
 195         if (c instanceof SortedSet<?>) {
 196             SortedSet<? extends E> ss = (SortedSet<? extends E>) c;
 197             this.comparator = (Comparator<? super E>) ss.comparator();
 198             initElementsFromCollection(ss);
 199         }
 200         else if (c instanceof PriorityQueue<?>) {
 201             PriorityQueue<? extends E> pq = (PriorityQueue<? extends E>) c;
 202             this.comparator = (Comparator<? super E>) pq.comparator();
 203             initFromPriorityQueue(pq);
 204         }
 205         else {
 206             this.comparator = null;
 207             initFromCollection(c);
 208         }
 209     }
 210 
 211     /**
 212      * Creates a {@code PriorityQueue} containing the elements in the
 213      * specified priority queue.  This priority queue will be
 214      * ordered according to the same ordering as the given priority
 215      * queue.
 216      *
 217      * @param  c the priority queue whose elements are to be placed
 218      *         into this priority queue
 219      * @throws ClassCastException if elements of {@code c} cannot be
 220      *         compared to one another according to {@code c}'s
 221      *         ordering
 222      * @throws NullPointerException if the specified priority queue or any
 223      *         of its elements are null
 224      */
 225     public PriorityQueue(PriorityQueue<? extends E> c) {
 226         this.comparator = (Comparator<? super E>) c.comparator();
 227         initFromPriorityQueue(c);
 228     }
 229 
 230     /**
 231      * Creates a {@code PriorityQueue} containing the elements in the
 232      * specified sorted set.   This priority queue will be ordered
 233      * according to the same ordering as the given sorted set.
 234      *
 235      * @param  c the sorted set whose elements are to be placed
 236      *         into this priority queue
 237      * @throws ClassCastException if elements of the specified sorted
 238      *         set cannot be compared to one another according to the
 239      *         sorted set's ordering
 240      * @throws NullPointerException if the specified sorted set or any
 241      *         of its elements are null
 242      */
 243     public PriorityQueue(SortedSet<? extends E> c) {
 244         this.comparator = (Comparator<? super E>) c.comparator();
 245         initElementsFromCollection(c);
 246     }
 247 
 248     /** Ensures that queue[0] exists, helping peek() and poll(). */
 249     private static Object[] ensureNonEmpty(Object[] es) {
 250         return (es.length > 0) ? es : new Object[1];
 251     }
 252 
 253     private void initFromPriorityQueue(PriorityQueue<? extends E> c) {
 254         if (c.getClass() == PriorityQueue.class) {
 255             this.queue = ensureNonEmpty(c.toArray());
 256             this.size = c.size();
 257         } else {
 258             initFromCollection(c);
 259         }
 260     }
 261 
 262     private void initElementsFromCollection(Collection<? extends E> c) {
 263         Object[] es = c.toArray();
 264         int len = es.length;
 265         // If c.toArray incorrectly doesn't return Object[], copy it.
 266         if (es.getClass() != Object[].class)
 267             es = Arrays.copyOf(es, len, Object[].class);
 268         if (len == 1 || this.comparator != null)
 269             for (Object e : es)
 270                 if (e == null)
 271                     throw new NullPointerException();
 272         this.queue = ensureNonEmpty(es);
 273         this.size = len;
 274     }
 275 
 276     /**
 277      * Initializes queue array with elements from the given Collection.
 278      *
 279      * @param c the collection
 280      */
 281     private void initFromCollection(Collection<? extends E> c) {
 282         initElementsFromCollection(c);
 283         heapify();
 284     }
 285 
 286     /**
 287      * Increases the capacity of the array.
 288      *
 289      * @param minCapacity the desired minimum capacity
 290      */
 291     private void grow(int minCapacity) {
 292         int oldCapacity = queue.length;
 293         // Double size if small; else grow by 50%
 294         int newCapacity = ArraysSupport.newLength(oldCapacity,
 295                 minCapacity - oldCapacity, /* minimum growth */
 296                 oldCapacity < 64 ? oldCapacity + 2 : oldCapacity >> 1
 297                                            /* preferred growth */);
 298         queue = Arrays.copyOf(queue, newCapacity);
 299     }
 300 
 301     /**
 302      * Inserts the specified element into this priority queue.
 303      *
 304      * @return {@code true} (as specified by {@link Collection#add})
 305      * @throws ClassCastException if the specified element cannot be
 306      *         compared with elements currently in this priority queue
 307      *         according to the priority queue's ordering
 308      * @throws NullPointerException if the specified element is null
 309      */
 310     public boolean add(E e) {
 311         return offer(e);
 312     }
 313 
 314     /**
 315      * Inserts the specified element into this priority queue.
 316      *
 317      * @return {@code true} (as specified by {@link Queue#offer})
 318      * @throws ClassCastException if the specified element cannot be
 319      *         compared with elements currently in this priority queue
 320      *         according to the priority queue's ordering
 321      * @throws NullPointerException if the specified element is null
 322      */
 323     public boolean offer(E e) {
 324         if (e == null)
 325             throw new NullPointerException();
 326         modCount++;
 327         int i = size;
 328         if (i >= queue.length)
 329             grow(i + 1);
 330         siftUp(i, e);
 331         size = i + 1;
 332         return true;
 333     }
 334 
 335     public E peek() {
 336         return (E) queue[0];
 337     }
 338 
 339     private int indexOf(Object o) {
 340         if (o != null) {
 341             final Object[] es = queue;
 342             for (int i = 0, n = size; i < n; i++)
 343                 if (o.equals(es[i]))
 344                     return i;
 345         }
 346         return -1;
 347     }
 348 
 349     /**
 350      * Removes a single instance of the specified element from this queue,
 351      * if it is present.  More formally, removes an element {@code e} such
 352      * that {@code o.equals(e)}, if this queue contains one or more such
 353      * elements.  Returns {@code true} if and only if this queue contained
 354      * the specified element (or equivalently, if this queue changed as a
 355      * result of the call).
 356      *
 357      * @param o element to be removed from this queue, if present
 358      * @return {@code true} if this queue changed as a result of the call
 359      */
 360     public boolean remove(Object o) {
 361         int i = indexOf(o);
 362         if (i == -1)
 363             return false;
 364         else {
 365             removeAt(i);
 366             return true;
 367         }
 368     }
 369 
 370     /**
 371      * Identity-based version for use in Itr.remove.
 372      *
 373      * @param o element to be removed from this queue, if present
 374      */
 375     void removeEq(Object o) {
 376         final Object[] es = queue;
 377         for (int i = 0, n = size; i < n; i++) {
 378             if (o == es[i]) {
 379                 removeAt(i);
 380                 break;
 381             }
 382         }
 383     }
 384 
 385     /**
 386      * Returns {@code true} if this queue contains the specified element.
 387      * More formally, returns {@code true} if and only if this queue contains
 388      * at least one element {@code e} such that {@code o.equals(e)}.
 389      *
 390      * @param o object to be checked for containment in this queue
 391      * @return {@code true} if this queue contains the specified element
 392      */
 393     public boolean contains(Object o) {
 394         return indexOf(o) >= 0;
 395     }
 396 
 397     /**
 398      * Returns an array containing all of the elements in this queue.
 399      * The elements are in no particular order.
 400      *
 401      * <p>The returned array will be "safe" in that no references to it are
 402      * maintained by this queue.  (In other words, this method must allocate
 403      * a new array).  The caller is thus free to modify the returned array.
 404      *
 405      * <p>This method acts as bridge between array-based and collection-based
 406      * APIs.
 407      *
 408      * @return an array containing all of the elements in this queue
 409      */
 410     public Object[] toArray() {
 411         return Arrays.copyOf(queue, size);
 412     }
 413 
 414     /**
 415      * Returns an array containing all of the elements in this queue; the
 416      * runtime type of the returned array is that of the specified array.
 417      * The returned array elements are in no particular order.
 418      * If the queue fits in the specified array, it is returned therein.
 419      * Otherwise, a new array is allocated with the runtime type of the
 420      * specified array and the size of this queue.
 421      *
 422      * <p>If the queue fits in the specified array with room to spare
 423      * (i.e., the array has more elements than the queue), the element in
 424      * the array immediately following the end of the collection is set to
 425      * {@code null}.
 426      *
 427      * <p>Like the {@link #toArray()} method, this method acts as bridge between
 428      * array-based and collection-based APIs.  Further, this method allows
 429      * precise control over the runtime type of the output array, and may,
 430      * under certain circumstances, be used to save allocation costs.
 431      *
 432      * <p>Suppose {@code x} is a queue known to contain only strings.
 433      * The following code can be used to dump the queue into a newly
 434      * allocated array of {@code String}:
 435      *
 436      * <pre> {@code String[] y = x.toArray(new String[0]);}</pre>
 437      *
 438      * Note that {@code toArray(new Object[0])} is identical in function to
 439      * {@code toArray()}.
 440      *
 441      * @param a the array into which the elements of the queue are to
 442      *          be stored, if it is big enough; otherwise, a new array of the
 443      *          same runtime type is allocated for this purpose.
 444      * @return an array containing all of the elements in this queue
 445      * @throws ArrayStoreException if the runtime type of the specified array
 446      *         is not a supertype of the runtime type of every element in
 447      *         this queue
 448      * @throws NullPointerException if the specified array is null
 449      */
 450     public <T> T[] toArray(T[] a) {
 451         final int size = this.size;
 452         if (a.length < size)
 453             // Make a new array of a's runtime type, but my contents:
 454             return (T[]) Arrays.copyOf(queue, size, a.getClass());
 455         System.arraycopy(queue, 0, a, 0, size);
 456         if (a.length > size)
 457             a[size] = null;
 458         return a;
 459     }
 460 
 461     /**
 462      * Returns an iterator over the elements in this queue. The iterator
 463      * does not return the elements in any particular order.
 464      *
 465      * @return an iterator over the elements in this queue
 466      */
 467     public Iterator<E> iterator() {
 468         return new Itr();
 469     }
 470 
 471     private final class Itr implements Iterator<E> {
 472         /**
 473          * Index (into queue array) of element to be returned by
 474          * subsequent call to next.
 475          */
 476         private int cursor;
 477 
 478         /**
 479          * Index of element returned by most recent call to next,
 480          * unless that element came from the forgetMeNot list.
 481          * Set to -1 if element is deleted by a call to remove.
 482          */
 483         private int lastRet = -1;
 484 
 485         /**
 486          * A queue of elements that were moved from the unvisited portion of
 487          * the heap into the visited portion as a result of "unlucky" element
 488          * removals during the iteration.  (Unlucky element removals are those
 489          * that require a siftup instead of a siftdown.)  We must visit all of
 490          * the elements in this list to complete the iteration.  We do this
 491          * after we've completed the "normal" iteration.
 492          *
 493          * We expect that most iterations, even those involving removals,
 494          * will not need to store elements in this field.
 495          */
 496         private ArrayDeque<E> forgetMeNot;
 497 
 498         /**
 499          * Element returned by the most recent call to next iff that
 500          * element was drawn from the forgetMeNot list.
 501          */
 502         private E lastRetElt;
 503 
 504         /**
 505          * The modCount value that the iterator believes that the backing
 506          * Queue should have.  If this expectation is violated, the iterator
 507          * has detected concurrent modification.
 508          */
 509         private int expectedModCount = modCount;
 510 
 511         Itr() {}                        // prevent access constructor creation
 512 
 513         public boolean hasNext() {
 514             return cursor < size ||
 515                 (forgetMeNot != null && !forgetMeNot.isEmpty());
 516         }
 517 
 518         public E next() {
 519             if (expectedModCount != modCount)
 520                 throw new ConcurrentModificationException();
 521             if (cursor < size)
 522                 return (E) queue[lastRet = cursor++];
 523             if (forgetMeNot != null) {
 524                 lastRet = -1;
 525                 lastRetElt = forgetMeNot.poll();
 526                 if (lastRetElt != null)
 527                     return lastRetElt;
 528             }
 529             throw new NoSuchElementException();
 530         }
 531 
 532         public void remove() {
 533             if (expectedModCount != modCount)
 534                 throw new ConcurrentModificationException();
 535             if (lastRet != -1) {
 536                 E moved = PriorityQueue.this.removeAt(lastRet);
 537                 lastRet = -1;
 538                 if (moved == null)
 539                     cursor--;
 540                 else {
 541                     if (forgetMeNot == null)
 542                         forgetMeNot = new ArrayDeque<>();
 543                     forgetMeNot.add(moved);
 544                 }
 545             } else if (lastRetElt != null) {
 546                 PriorityQueue.this.removeEq(lastRetElt);
 547                 lastRetElt = null;
 548             } else {
 549                 throw new IllegalStateException();
 550             }
 551             expectedModCount = modCount;
 552         }
 553     }
 554 
 555     public int size() {
 556         return size;
 557     }
 558 
 559     /**
 560      * Removes all of the elements from this priority queue.
 561      * The queue will be empty after this call returns.
 562      */
 563     public void clear() {
 564         modCount++;
 565         final Object[] es = queue;
 566         for (int i = 0, n = size; i < n; i++)
 567             es[i] = null;
 568         size = 0;
 569     }
 570 
 571     public E poll() {
 572         final Object[] es;
 573         final E result;
 574 
 575         if ((result = (E) ((es = queue)[0])) != null) {
 576             modCount++;
 577             final int n;
 578             final E x = (E) es[(n = --size)];
 579             es[n] = null;
 580             if (n > 0) {
 581                 final Comparator<? super E> cmp;
 582                 if ((cmp = comparator) == null)
 583                     siftDownComparable(0, x, es, n);
 584                 else
 585                     siftDownUsingComparator(0, x, es, n, cmp);
 586             }
 587         }
 588         return result;
 589     }
 590 
 591     /**
 592      * Removes the ith element from queue.
 593      *
 594      * Normally this method leaves the elements at up to i-1,
 595      * inclusive, untouched.  Under these circumstances, it returns
 596      * null.  Occasionally, in order to maintain the heap invariant,
 597      * it must swap a later element of the list with one earlier than
 598      * i.  Under these circumstances, this method returns the element
 599      * that was previously at the end of the list and is now at some
 600      * position before i. This fact is used by iterator.remove so as to
 601      * avoid missing traversing elements.
 602      */
 603     E removeAt(int i) {
 604         // assert i >= 0 && i < size;
 605         final Object[] es = queue;
 606         modCount++;
 607         int s = --size;
 608         if (s == i) // removed last element
 609             es[i] = null;
 610         else {
 611             E moved = (E) es[s];
 612             es[s] = null;
 613             siftDown(i, moved);
 614             if (es[i] == moved) {
 615                 siftUp(i, moved);
 616                 if (es[i] != moved)
 617                     return moved;
 618             }
 619         }
 620         return null;
 621     }
 622 
 623     /**
 624      * Inserts item x at position k, maintaining heap invariant by
 625      * promoting x up the tree until it is greater than or equal to
 626      * its parent, or is the root.
 627      *
 628      * To simplify and speed up coercions and comparisons, the
 629      * Comparable and Comparator versions are separated into different
 630      * methods that are otherwise identical. (Similarly for siftDown.)
 631      *
 632      * @param k the position to fill
 633      * @param x the item to insert
 634      */
 635     private void siftUp(int k, E x) {
 636         if (comparator != null)
 637             siftUpUsingComparator(k, x, queue, comparator);
 638         else
 639             siftUpComparable(k, x, queue);
 640     }
 641 
 642     private static <T> void siftUpComparable(int k, T x, Object[] es) {
 643         Comparable<? super T> key = (Comparable<? super T>) x;
 644         while (k > 0) {
 645             int parent = (k - 1) >>> 1;
 646             Object e = es[parent];
 647             if (key.compareTo((T) e) >= 0)
 648                 break;
 649             es[k] = e;
 650             k = parent;
 651         }
 652         es[k] = key;
 653     }
 654 
 655     private static <T> void siftUpUsingComparator(
 656         int k, T x, Object[] es, Comparator<? super T> cmp) {
 657         while (k > 0) {
 658             int parent = (k - 1) >>> 1;
 659             Object e = es[parent];
 660             if (cmp.compare(x, (T) e) >= 0)
 661                 break;
 662             es[k] = e;
 663             k = parent;
 664         }
 665         es[k] = x;
 666     }
 667 
 668     /**
 669      * Inserts item x at position k, maintaining heap invariant by
 670      * demoting x down the tree repeatedly until it is less than or
 671      * equal to its children or is a leaf.
 672      *
 673      * @param k the position to fill
 674      * @param x the item to insert
 675      */
 676     private void siftDown(int k, E x) {
 677         if (comparator != null)
 678             siftDownUsingComparator(k, x, queue, size, comparator);
 679         else
 680             siftDownComparable(k, x, queue, size);
 681     }
 682 
 683     private static <T> void siftDownComparable(int k, T x, Object[] es, int n) {
 684         // assert n > 0;
 685         Comparable<? super T> key = (Comparable<? super T>)x;
 686         int half = n >>> 1;           // loop while a non-leaf
 687         while (k < half) {
 688             int child = (k << 1) + 1; // assume left child is least
 689             Object c = es[child];
 690             int right = child + 1;
 691             if (right < n &&
 692                 ((Comparable<? super T>) c).compareTo((T) es[right]) > 0)
 693                 c = es[child = right];
 694             if (key.compareTo((T) c) <= 0)
 695                 break;
 696             es[k] = c;
 697             k = child;
 698         }
 699         es[k] = key;
 700     }
 701 
 702     private static <T> void siftDownUsingComparator(
 703         int k, T x, Object[] es, int n, Comparator<? super T> cmp) {
 704         // assert n > 0;
 705         int half = n >>> 1;
 706         while (k < half) {
 707             int child = (k << 1) + 1;
 708             Object c = es[child];
 709             int right = child + 1;
 710             if (right < n && cmp.compare((T) c, (T) es[right]) > 0)
 711                 c = es[child = right];
 712             if (cmp.compare(x, (T) c) <= 0)
 713                 break;
 714             es[k] = c;
 715             k = child;
 716         }
 717         es[k] = x;
 718     }
 719 
 720     /**
 721      * Establishes the heap invariant (described above) in the entire tree,
 722      * assuming nothing about the order of the elements prior to the call.
 723      * This classic algorithm due to Floyd (1964) is known to be O(size).
 724      */
 725     private void heapify() {
 726         final Object[] es = queue;
 727         int n = size, i = (n >>> 1) - 1;
 728         final Comparator<? super E> cmp;
 729         if ((cmp = comparator) == null)
 730             for (; i >= 0; i--)
 731                 siftDownComparable(i, (E) es[i], es, n);
 732         else
 733             for (; i >= 0; i--)
 734                 siftDownUsingComparator(i, (E) es[i], es, n, cmp);
 735     }
 736 
 737     /**
 738      * Returns the comparator used to order the elements in this
 739      * queue, or {@code null} if this queue is sorted according to
 740      * the {@linkplain Comparable natural ordering} of its elements.
 741      *
 742      * @return the comparator used to order this queue, or
 743      *         {@code null} if this queue is sorted according to the
 744      *         natural ordering of its elements
 745      */
 746     public Comparator<? super E> comparator() {
 747         return comparator;
 748     }
 749 
 750     /**
 751      * Saves this queue to a stream (that is, serializes it).
 752      *
 753      * @param s the stream
 754      * @throws java.io.IOException if an I/O error occurs
 755      * @serialData The length of the array backing the instance is
 756      *             emitted (int), followed by all of its elements
 757      *             (each an {@code Object}) in the proper order.
 758      */
 759     @java.io.Serial
 760     private void writeObject(java.io.ObjectOutputStream s)
 761         throws java.io.IOException {
 762         // Write out element count, and any hidden stuff
 763         s.defaultWriteObject();
 764 
 765         // Write out array length, for compatibility with 1.5 version
 766         s.writeInt(Math.max(2, size + 1));
 767 
 768         // Write out all elements in the "proper order".
 769         final Object[] es = queue;
 770         for (int i = 0, n = size; i < n; i++)
 771             s.writeObject(es[i]);
 772     }
 773 
 774     /**
 775      * Reconstitutes the {@code PriorityQueue} instance from a stream
 776      * (that is, deserializes it).
 777      *
 778      * @param s the stream
 779      * @throws ClassNotFoundException if the class of a serialized object
 780      *         could not be found
 781      * @throws java.io.IOException if an I/O error occurs
 782      */
 783     @java.io.Serial
 784     private void readObject(java.io.ObjectInputStream s)
 785         throws java.io.IOException, ClassNotFoundException {
 786         // Read in size, and any hidden stuff
 787         s.defaultReadObject();
 788 
 789         // Read in (and discard) array length
 790         s.readInt();
 791 
 792         SharedSecrets.getJavaObjectInputStreamAccess().checkArray(s, Object[].class, size);
 793         final Object[] es = queue = new Object[Math.max(size, 1)];
 794 
 795         // Read in all elements.
 796         for (int i = 0, n = size; i < n; i++)
 797             es[i] = s.readObject();
 798 
 799         // Elements are guaranteed to be in "proper order", but the
 800         // spec has never explained what that might be.
 801         heapify();
 802     }
 803 
 804     /**
 805      * Creates a <em><a href="Spliterator.html#binding">late-binding</a></em>
 806      * and <em>fail-fast</em> {@link Spliterator} over the elements in this
 807      * queue. The spliterator does not traverse elements in any particular order
 808      * (the {@link Spliterator#ORDERED ORDERED} characteristic is not reported).
 809      *
 810      * <p>The {@code Spliterator} reports {@link Spliterator#SIZED},
 811      * {@link Spliterator#SUBSIZED}, and {@link Spliterator#NONNULL}.
 812      * Overriding implementations should document the reporting of additional
 813      * characteristic values.
 814      *
 815      * @return a {@code Spliterator} over the elements in this queue
 816      * @since 1.8
 817      */
 818     public final Spliterator<E> spliterator() {
 819         return new PriorityQueueSpliterator(0, -1, 0);
 820     }
 821 
 822     final class PriorityQueueSpliterator implements Spliterator<E> {
 823         private int index;            // current index, modified on advance/split
 824         private int fence;            // -1 until first use
 825         private int expectedModCount; // initialized when fence set
 826 
 827         /** Creates new spliterator covering the given range. */
 828         PriorityQueueSpliterator(int origin, int fence, int expectedModCount) {
 829             this.index = origin;
 830             this.fence = fence;
 831             this.expectedModCount = expectedModCount;
 832         }
 833 
 834         private int getFence() { // initialize fence to size on first use
 835             int hi;
 836             if ((hi = fence) < 0) {
 837                 expectedModCount = modCount;
 838                 hi = fence = size;
 839             }
 840             return hi;
 841         }
 842 
 843         public PriorityQueueSpliterator trySplit() {
 844             int hi = getFence(), lo = index, mid = (lo + hi) >>> 1;
 845             return (lo >= mid) ? null :
 846                 new PriorityQueueSpliterator(lo, index = mid, expectedModCount);
 847         }
 848 
 849         public void forEachRemaining(Consumer<? super E> action) {
 850             if (action == null)
 851                 throw new NullPointerException();
 852             if (fence < 0) { fence = size; expectedModCount = modCount; }
 853             final Object[] es = queue;
 854             int i, hi; E e;
 855             for (i = index, index = hi = fence; i < hi; i++) {
 856                 if ((e = (E) es[i]) == null)
 857                     break;      // must be CME
 858                 action.accept(e);
 859             }
 860             if (modCount != expectedModCount)
 861                 throw new ConcurrentModificationException();
 862         }
 863 
 864         public boolean tryAdvance(Consumer<? super E> action) {
 865             if (action == null)
 866                 throw new NullPointerException();
 867             if (fence < 0) { fence = size; expectedModCount = modCount; }
 868             int i;
 869             if ((i = index) < fence) {
 870                 index = i + 1;
 871                 E e;
 872                 if ((e = (E) queue[i]) == null
 873                     || modCount != expectedModCount)
 874                     throw new ConcurrentModificationException();
 875                 action.accept(e);
 876                 return true;
 877             }
 878             return false;
 879         }
 880 
 881         public long estimateSize() {
 882             return getFence() - index;
 883         }
 884 
 885         public int characteristics() {
 886             return Spliterator.SIZED | Spliterator.SUBSIZED | Spliterator.NONNULL;
 887         }
 888     }
 889 
 890     /**
 891      * @throws NullPointerException {@inheritDoc}
 892      */
 893     public boolean removeIf(Predicate<? super E> filter) {
 894         Objects.requireNonNull(filter);
 895         return bulkRemove(filter);
 896     }
 897 
 898     /**
 899      * @throws NullPointerException {@inheritDoc}
 900      */
 901     public boolean removeAll(Collection<?> c) {
 902         Objects.requireNonNull(c);
 903         return bulkRemove(e -> c.contains(e));
 904     }
 905 
 906     /**
 907      * @throws NullPointerException {@inheritDoc}
 908      */
 909     public boolean retainAll(Collection<?> c) {
 910         Objects.requireNonNull(c);
 911         return bulkRemove(e -> !c.contains(e));
 912     }
 913 
 914     // A tiny bit set implementation
 915 
 916     private static long[] nBits(int n) {
 917         return new long[((n - 1) >> 6) + 1];
 918     }
 919     private static void setBit(long[] bits, int i) {
 920         bits[i >> 6] |= 1L << i;
 921     }
 922     private static boolean isClear(long[] bits, int i) {
 923         return (bits[i >> 6] & (1L << i)) == 0;
 924     }
 925 
 926     /** Implementation of bulk remove methods. */
 927     private boolean bulkRemove(Predicate<? super E> filter) {
 928         final int expectedModCount = ++modCount;
 929         final Object[] es = queue;
 930         final int end = size;
 931         int i;
 932         // Optimize for initial run of survivors
 933         for (i = 0; i < end && !filter.test((E) es[i]); i++)
 934             ;
 935         if (i >= end) {
 936             if (modCount != expectedModCount)
 937                 throw new ConcurrentModificationException();
 938             return false;
 939         }
 940         // Tolerate predicates that reentrantly access the collection for
 941         // read (but writers still get CME), so traverse once to find
 942         // elements to delete, a second pass to physically expunge.
 943         final int beg = i;
 944         final long[] deathRow = nBits(end - beg);
 945         deathRow[0] = 1L;   // set bit 0
 946         for (i = beg + 1; i < end; i++)
 947             if (filter.test((E) es[i]))
 948                 setBit(deathRow, i - beg);
 949         if (modCount != expectedModCount)
 950             throw new ConcurrentModificationException();
 951         int w = beg;
 952         for (i = beg; i < end; i++)
 953             if (isClear(deathRow, i - beg))
 954                 es[w++] = es[i];
 955         for (i = size = w; i < end; i++)
 956             es[i] = null;
 957         heapify();
 958         return true;
 959     }
 960 
 961     /**
 962      * @throws NullPointerException {@inheritDoc}
 963      */
 964     public void forEach(Consumer<? super E> action) {
 965         Objects.requireNonNull(action);
 966         final int expectedModCount = modCount;
 967         final Object[] es = queue;
 968         for (int i = 0, n = size; i < n; i++)
 969             action.accept((E) es[i]);
 970         if (expectedModCount != modCount)
 971             throw new ConcurrentModificationException();
 972     }
 973 }