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Comparing jsr166/src/main/java/util/PriorityQueue.java (file contents):
Revision 1.1 by tim, Wed May 14 21:30:45 2003 UTC vs.
Revision 1.80 by jsr166, Wed Jan 16 01:59:47 2013 UTC

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1	<	package java.util;
1	>	/*
2	>	* Copyright (c) 2003, 2006, 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
6	>	* under the terms of the GNU General Public License version 2 only, as
7	>	* published by the Free Software Foundation.  Sun designates this
8	>	* particular file as subject to the "Classpath" exception as provided
9	>	* by Sun 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
18	>	* 2 along with this work; if not, write to the Free Software Foundation,
19	>	* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20	>	*
21	>	* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22	>	* or visit www.oracle.com if you need additional information or have any
23	>	* questions.
24	>	*/
25
26	<	import java.util.*;
26	>	package java.util;
27
28		/**
29	<	* An unbounded (resizable) priority queue based on a priority
30	<	* heap.The take operation returns the least element with respect to
31	<	* the given ordering. (If more than one element is tied for least
32	<	* value, one of them is arbitrarily chosen to be returned -- no
33	<	* guarantees are made for ordering across ties.) Ordering follows the
34	<	* java.util.Collection conventions: Either the elements must be
35	<	* Comparable, or a Comparator must be supplied. Comparison failures
36	<	* throw ClassCastExceptions during insertions and extractions.
37	<	**/
38	<	public class PriorityQueue<E> extends AbstractCollection<E> implements Queue<E> {
39	<	public PriorityQueue(int initialCapacity) {}
40	<	public PriorityQueue(int initialCapacity, Comparator comparator) {}
29	>	* An unbounded priority {@linkplain Queue queue} based on a priority heap.
30	>	* The elements of the priority queue are ordered according to their
31	>	* {@linkplain Comparable natural ordering}, or by a {@link Comparator}
32	>	* provided at queue construction time, depending on which constructor is
33	>	* used.  A priority queue does not permit {@code null} elements.
34	>	* A priority queue relying on natural ordering also does not permit
35	>	* insertion of non-comparable objects (doing so may result in
36	>	* {@code ClassCastException}).
37	>	*
38	>	* <p>The <em>head</em> of this queue is the <em>least</em> element
39	>	* with respect to the specified ordering.  If multiple elements are
40	>	* tied for least value, the head is one of those elements -- ties are
41	>	* broken arbitrarily.  The queue retrieval operations {@code poll},
42	>	* {@code remove}, {@code peek}, and {@code element} access the
43	>	* element at the head of the queue.
44	>	*
45	>	* <p>A priority queue is unbounded, but has an internal
46	>	* <i>capacity</i> governing the size of an array used to store the
47	>	* elements on the queue.  It is always at least as large as the queue
48	>	* size.  As elements are added to a priority queue, its capacity
49	>	* grows automatically.  The details of the growth policy are not
50	>	* specified.
51	>	*
52	>	* <p>This class and its iterator implement all of the
53	>	* <em>optional</em> methods of the {@link Collection} and {@link
54	>	* Iterator} interfaces.  The Iterator provided in method {@link
55	>	* #iterator()} is <em>not</em> guaranteed to traverse the elements of
56	>	* the priority queue in any particular order. If you need ordered
57	>	* traversal, consider using {@code Arrays.sort(pq.toArray())}.
58	>	*
59	>	* <p><strong>Note that this implementation is not synchronized.</strong>
60	>	* Multiple threads should not access a {@code PriorityQueue}
61	>	* instance concurrently if any of the threads modifies the queue.
62	>	* Instead, use the thread-safe {@link
63	>	* java.util.concurrent.PriorityBlockingQueue} class.
64	>	*
65	>	* <p>Implementation note: this implementation provides
66	>	* O(log(n)) time for the enqueuing and dequeuing methods
67	>	* ({@code offer}, {@code poll}, {@code remove()} and {@code add});
68	>	* linear time for the {@code remove(Object)} and {@code contains(Object)}
69	>	* methods; and constant time for the retrieval methods
70	>	* ({@code peek}, {@code element}, and {@code size}).
71	>	*
72	>	* <p>This class is a member of the
73	>	* <a href="{@docRoot}/../technotes/guides/collections/index.html">
74	>	* Java Collections Framework</a>.
75	>	*
76	>	* @since 1.5
77	>	* @author Josh Bloch, Doug Lea
78	>	* @param <E> the type of elements held in this collection
79	>	*/
80	>	@SuppressWarnings("unchecked")
81	>	public class PriorityQueue<E> extends AbstractQueue<E>
82	>	implements java.io.Serializable {
83
84	<	public PriorityQueue(int initialCapacity, Collection initialElements) {}
84	>	private static final long serialVersionUID = -7720805057305804111L;
85
86	<	public PriorityQueue(int initialCapacity, Comparator comparator, Collection initialElements) {}
86	>	private static final int DEFAULT_INITIAL_CAPACITY = 11;
87
88	<	public boolean add(E x) {
89	<	return false;
88	>	/**
89	>	* Priority queue represented as a balanced binary heap: the two
90	>	* children of queue[n] are queue[2*n+1] and queue[2*(n+1)].  The
91	>	* priority queue is ordered by comparator, or by the elements'
92	>	* natural ordering, if comparator is null: For each node n in the
93	>	* heap and each descendant d of n, n <= d.  The element with the
94	>	* lowest value is in queue[0], assuming the queue is nonempty.
95	>	*/
96	>	private transient Object[] queue;
97	>
98	>	/**
99	>	* The number of elements in the priority queue.
100	>	*/
101	>	private int size = 0;
102	>
103	>	/**
104	>	* The comparator, or null if priority queue uses elements'
105	>	* natural ordering.
106	>	*/
107	>	private final Comparator<? super E> comparator;
108	>
109	>	/**
110	>	* The number of times this priority queue has been
111	>	* <i>structurally modified</i>.  See AbstractList for gory details.
112	>	*/
113	>	private transient int modCount = 0;
114	>
115	>	/**
116	>	* Creates a {@code PriorityQueue} with the default initial
117	>	* capacity (11) that orders its elements according to their
118	>	* {@linkplain Comparable natural ordering}.
119	>	*/
120	>	public PriorityQueue() {
121	>	this(DEFAULT_INITIAL_CAPACITY, null);
122		}
123	<	public boolean offer(E x) {
124	<	return false;
123	>
124	>	/**
125	>	* Creates a {@code PriorityQueue} with the specified initial
126	>	* capacity that orders its elements according to their
127	>	* {@linkplain Comparable natural ordering}.
128	>	*
129	>	* @param initialCapacity the initial capacity for this priority queue
130	>	* @throws IllegalArgumentException if {@code initialCapacity} is less
131	>	*         than 1
132	>	*/
133	>	public PriorityQueue(int initialCapacity) {
134	>	this(initialCapacity, null);
135		}
136	<	public boolean remove(Object x) {
137	<	return false;
136	>
137	>	/**
138	>	* Creates a {@code PriorityQueue} with the specified initial capacity
139	>	* that orders its elements according to the specified comparator.
140	>	*
141	>	* @param  initialCapacity the initial capacity for this priority queue
142	>	* @param  comparator the comparator that will be used to order this
143	>	*         priority queue.  If {@code null}, the {@linkplain Comparable
144	>	*         natural ordering} of the elements will be used.
145	>	* @throws IllegalArgumentException if {@code initialCapacity} is
146	>	*         less than 1
147	>	*/
148	>	public PriorityQueue(int initialCapacity,
149	>	Comparator<? super E> comparator) {
150	>	// Note: This restriction of at least one is not actually needed,
151	>	// but continues for 1.5 compatibility
152	>	if (initialCapacity < 1)
153	>	throw new IllegalArgumentException();
154	>	this.queue = new Object[initialCapacity];
155	>	this.comparator = comparator;
156		}
157
158	<	public E remove() {
159	<	return null;
158	>	/**
159	>	* Creates a {@code PriorityQueue} containing the elements in the
160	>	* specified collection.  If the specified collection is an instance of
161	>	* a {@link SortedSet} or is another {@code PriorityQueue}, this
162	>	* priority queue will be ordered according to the same ordering.
163	>	* Otherwise, this priority queue will be ordered according to the
164	>	* {@linkplain Comparable natural ordering} of its elements.
165	>	*
166	>	* @param  c the collection whose elements are to be placed
167	>	*         into this priority queue
168	>	* @throws ClassCastException if elements of the specified collection
169	>	*         cannot be compared to one another according to the priority
170	>	*         queue's ordering
171	>	* @throws NullPointerException if the specified collection or any
172	>	*         of its elements are null
173	>	*/
174	>	@SuppressWarnings("unchecked")
175	>	public PriorityQueue(Collection<? extends E> c) {
176	>	if (c instanceof SortedSet<?>) {
177	>	SortedSet<? extends E> ss = (SortedSet<? extends E>) c;
178	>	this.comparator = (Comparator<? super E>) ss.comparator();
179	>	initElementsFromCollection(ss);
180	>	}
181	>	else if (c instanceof PriorityQueue<?>) {
182	>	PriorityQueue<? extends E> pq = (PriorityQueue<? extends E>) c;
183	>	this.comparator = (Comparator<? super E>) pq.comparator();
184	>	initFromPriorityQueue(pq);
185	>	}
186	>	else {
187	>	this.comparator = null;
188	>	initFromCollection(c);
189	>	}
190		}
191	<	public Iterator<E> iterator() {
192	<	return null;
191	>
192	>	/**
193	>	* Creates a {@code PriorityQueue} containing the elements in the
194	>	* specified priority queue.  This priority queue will be
195	>	* ordered according to the same ordering as the given priority
196	>	* queue.
197	>	*
198	>	* @param  c the priority queue whose elements are to be placed
199	>	*         into this priority queue
200	>	* @throws ClassCastException if elements of {@code c} cannot be
201	>	*         compared to one another according to {@code c}'s
202	>	*         ordering
203	>	* @throws NullPointerException if the specified priority queue or any
204	>	*         of its elements are null
205	>	*/
206	>	@SuppressWarnings("unchecked")
207	>	public PriorityQueue(PriorityQueue<? extends E> c) {
208	>	this.comparator = (Comparator<? super E>) c.comparator();
209	>	initFromPriorityQueue(c);
210		}
211
212	<	public E element() {
213	<	return null;
212	>	/**
213	>	* Creates a {@code PriorityQueue} containing the elements in the
214	>	* specified sorted set.   This priority queue will be ordered
215	>	* according to the same ordering as the given sorted set.
216	>	*
217	>	* @param  c the sorted set whose elements are to be placed
218	>	*         into this priority queue
219	>	* @throws ClassCastException if elements of the specified sorted
220	>	*         set cannot be compared to one another according to the
221	>	*         sorted set's ordering
222	>	* @throws NullPointerException if the specified sorted set or any
223	>	*         of its elements are null
224	>	*/
225	>	@SuppressWarnings("unchecked")
226	>	public PriorityQueue(SortedSet<? extends E> c) {
227	>	this.comparator = (Comparator<? super E>) c.comparator();
228	>	initElementsFromCollection(c);
229		}
230	<	public E poll() {
231	<	return null;
230	>
231	>	private void initFromPriorityQueue(PriorityQueue<? extends E> c) {
232	>	if (c.getClass() == PriorityQueue.class) {
233	>	this.queue = c.toArray();
234	>	this.size = c.size();
235	>	} else {
236	>	initFromCollection(c);
237	>	}
238	>	}
239	>
240	>	private void initElementsFromCollection(Collection<? extends E> c) {
241	>	Object[] a = c.toArray();
242	>	// If c.toArray incorrectly doesn't return Object[], copy it.
243	>	if (a.getClass() != Object[].class)
244	>	a = Arrays.copyOf(a, a.length, Object[].class);
245	>	int len = a.length;
246	>	if (len == 1 || this.comparator != null)
247	>	for (int i = 0; i < len; i++)
248	>	if (a[i] == null)
249	>	throw new NullPointerException();
250	>	this.queue = a;
251	>	this.size = a.length;
252	>	}
253	>
254	>	/**
255	>	* Initializes queue array with elements from the given Collection.
256	>	*
257	>	* @param c the collection
258	>	*/
259	>	private void initFromCollection(Collection<? extends E> c) {
260	>	initElementsFromCollection(c);
261	>	heapify();
262		}
263	+
264	+	/**
265	+	* The maximum size of array to allocate.
266	+	* Some VMs reserve some header words in an array.
267	+	* Attempts to allocate larger arrays may result in
268	+	* OutOfMemoryError: Requested array size exceeds VM limit
269	+	*/
270	+	private static final int MAX_ARRAY_SIZE = Integer.MAX_VALUE - 8;
271	+
272	+	/**
273	+	* Increases the capacity of the array.
274	+	*
275	+	* @param minCapacity the desired minimum capacity
276	+	*/
277	+	private void grow(int minCapacity) {
278	+	int oldCapacity = queue.length;
279	+	// Double size if small; else grow by 50%
280	+	int newCapacity = oldCapacity + ((oldCapacity < 64) ?
281	+	(oldCapacity + 2) :
282	+	(oldCapacity >> 1));
283	+	// overflow-conscious code
284	+	if (newCapacity - MAX_ARRAY_SIZE > 0)
285	+	newCapacity = hugeCapacity(minCapacity);
286	+	queue = Arrays.copyOf(queue, newCapacity);
287	+	}
288	+
289	+	private static int hugeCapacity(int minCapacity) {
290	+	if (minCapacity < 0) // overflow
291	+	throw new OutOfMemoryError();
292	+	return (minCapacity > MAX_ARRAY_SIZE) ?
293	+	Integer.MAX_VALUE :
294	+	MAX_ARRAY_SIZE;
295	+	}
296	+
297	+	/**
298	+	* Inserts the specified element into this priority queue.
299	+	*
300	+	* @return {@code true} (as specified by {@link Collection#add})
301	+	* @throws ClassCastException if the specified element cannot be
302	+	*         compared with elements currently in this priority queue
303	+	*         according to the priority queue's ordering
304	+	* @throws NullPointerException if the specified element is null
305	+	*/
306	+	public boolean add(E e) {
307	+	return offer(e);
308	+	}
309	+
310	+	/**
311	+	* Inserts the specified element into this priority queue.
312	+	*
313	+	* @return {@code true} (as specified by {@link Queue#offer})
314	+	* @throws ClassCastException if the specified element cannot be
315	+	*         compared with elements currently in this priority queue
316	+	*         according to the priority queue's ordering
317	+	* @throws NullPointerException if the specified element is null
318	+	*/
319	+	public boolean offer(E e) {
320	+	if (e == null)
321	+	throw new NullPointerException();
322	+	modCount++;
323	+	int i = size;
324	+	if (i >= queue.length)
325	+	grow(i + 1);
326	+	size = i + 1;
327	+	if (i == 0)
328	+	queue[0] = e;
329	+	else
330	+	siftUp(i, e);
331	+	return true;
332	+	}
333	+
334		public E peek() {
335	<	return null;
335	>	return (size == 0) ? null : (E) queue[0];
336		}
337
338	<	public boolean isEmpty() {
338	>	private int indexOf(Object o) {
339	>	if (o != null) {
340	>	for (int i = 0; i < size; i++)
341	>	if (o.equals(queue[i]))
342	>	return i;
343	>	}
344	>	return -1;
345	>	}
346	>
347	>	/**
348	>	* Removes a single instance of the specified element from this queue,
349	>	* if it is present.  More formally, removes an element {@code e} such
350	>	* that {@code o.equals(e)}, if this queue contains one or more such
351	>	* elements.  Returns {@code true} if and only if this queue contained
352	>	* the specified element (or equivalently, if this queue changed as a
353	>	* result of the call).
354	>	*
355	>	* @param o element to be removed from this queue, if present
356	>	* @return {@code true} if this queue changed as a result of the call
357	>	*/
358	>	public boolean remove(Object o) {
359	>	int i = indexOf(o);
360	>	if (i == -1)
361	>	return false;
362	>	else {
363	>	removeAt(i);
364	>	return true;
365	>	}
366	>	}
367	>
368	>	/**
369	>	* Version of remove using reference equality, not equals.
370	>	* Needed by iterator.remove.
371	>	*
372	>	* @param o element to be removed from this queue, if present
373	>	* @return {@code true} if removed
374	>	*/
375	>	boolean removeEq(Object o) {
376	>	for (int i = 0; i < size; i++) {
377	>	if (o == queue[i]) {
378	>	removeAt(i);
379	>	return true;
380	>	}
381	>	}
382		return false;
383		}
384	<	public int size() {
385	<	return 0;
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) != -1;
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 null;
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	>	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 = 0;
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 = null;
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 = null;
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	>	public boolean hasNext() {
511	>	return cursor < size ||
512	>	(forgetMeNot != null && !forgetMeNot.isEmpty());
513	>	}
514	>
515	>	public E next() {
516	>	if (expectedModCount != modCount)
517	>	throw new ConcurrentModificationException();
518	>	if (cursor < size)
519	>	return (E) queue[lastRet = cursor++];
520	>	if (forgetMeNot != null) {
521	>	lastRet = -1;
522	>	lastRetElt = forgetMeNot.poll();
523	>	if (lastRetElt != null)
524	>	return lastRetElt;
525	>	}
526	>	throw new NoSuchElementException();
527	>	}
528	>
529	>	public void remove() {
530	>	if (expectedModCount != modCount)
531	>	throw new ConcurrentModificationException();
532	>	if (lastRet != -1) {
533	>	E moved = PriorityQueue.this.removeAt(lastRet);
534	>	lastRet = -1;
535	>	if (moved == null)
536	>	cursor--;
537	>	else {
538	>	if (forgetMeNot == null)
539	>	forgetMeNot = new ArrayDeque<E>();
540	>	forgetMeNot.add(moved);
541	>	}
542	>	} else if (lastRetElt != null) {
543	>	PriorityQueue.this.removeEq(lastRetElt);
544	>	lastRetElt = null;
545	>	} else {
546	>	throw new IllegalStateException();
547	>	}
548	>	expectedModCount = modCount;
549	>	}
550		}
551
552	<	public <T> T[] toArray(T[] array) {
552	>	public int size() {
553	>	return size;
554	>	}
555	>
556	>	/**
557	>	* Removes all of the elements from this priority queue.
558	>	* The queue will be empty after this call returns.
559	>	*/
560	>	public void clear() {
561	>	modCount++;
562	>	for (int i = 0; i < size; i++)
563	>	queue[i] = null;
564	>	size = 0;
565	>	}
566	>
567	>	public E poll() {
568	>	if (size == 0)
569	>	return null;
570	>	int s = --size;
571	>	modCount++;
572	>	E result = (E) queue[0];
573	>	E x = (E) queue[s];
574	>	queue[s] = null;
575	>	if (s != 0)
576	>	siftDown(0, x);
577	>	return result;
578	>	}
579	>
580	>	/**
581	>	* Removes the ith element from queue.
582	>	*
583	>	* Normally this method leaves the elements at up to i-1,
584	>	* inclusive, untouched.  Under these circumstances, it returns
585	>	* null.  Occasionally, in order to maintain the heap invariant,
586	>	* it must swap a later element of the list with one earlier than
587	>	* i.  Under these circumstances, this method returns the element
588	>	* that was previously at the end of the list and is now at some
589	>	* position before i. This fact is used by iterator.remove so as to
590	>	* avoid missing traversing elements.
591	>	*/
592	>	private E removeAt(int i) {
593	>	// assert i >= 0 && i < size;
594	>	modCount++;
595	>	int s = --size;
596	>	if (s == i) // removed last element
597	>	queue[i] = null;
598	>	else {
599	>	E moved = (E) queue[s];
600	>	queue[s] = null;
601	>	siftDown(i, moved);
602	>	if (queue[i] == moved) {
603	>	siftUp(i, moved);
604	>	if (queue[i] != moved)
605	>	return moved;
606	>	}
607	>	}
608		return null;
609		}
610
611	+	/**
612	+	* Inserts item x at position k, maintaining heap invariant by
613	+	* promoting x up the tree until it is greater than or equal to
614	+	* its parent, or is the root.
615	+	*
616	+	* To simplify and speed up coercions and comparisons. the
617	+	* Comparable and Comparator versions are separated into different
618	+	* methods that are otherwise identical. (Similarly for siftDown.)
619	+	*
620	+	* @param k the position to fill
621	+	* @param x the item to insert
622	+	*/
623	+	private void siftUp(int k, E x) {
624	+	if (comparator != null)
625	+	siftUpUsingComparator(k, x);
626	+	else
627	+	siftUpComparable(k, x);
628	+	}
629	+
630	+	private void siftUpComparable(int k, E x) {
631	+	Comparable<? super E> key = (Comparable<? super E>) x;
632	+	while (k > 0) {
633	+	int parent = (k - 1) >>> 1;
634	+	Object e = queue[parent];
635	+	if (key.compareTo((E) e) >= 0)
636	+	break;
637	+	queue[k] = e;
638	+	k = parent;
639	+	}
640	+	queue[k] = key;
641	+	}
642	+
643	+	private void siftUpUsingComparator(int k, E x) {
644	+	while (k > 0) {
645	+	int parent = (k - 1) >>> 1;
646	+	Object e = queue[parent];
647	+	if (comparator.compare(x, (E) e) >= 0)
648	+	break;
649	+	queue[k] = e;
650	+	k = parent;
651	+	}
652	+	queue[k] = x;
653	+	}
654	+
655	+	/**
656	+	* Inserts item x at position k, maintaining heap invariant by
657	+	* demoting x down the tree repeatedly until it is less than or
658	+	* equal to its children or is a leaf.
659	+	*
660	+	* @param k the position to fill
661	+	* @param x the item to insert
662	+	*/
663	+	private void siftDown(int k, E x) {
664	+	if (comparator != null)
665	+	siftDownUsingComparator(k, x);
666	+	else
667	+	siftDownComparable(k, x);
668	+	}
669	+
670	+	private void siftDownComparable(int k, E x) {
671	+	Comparable<? super E> key = (Comparable<? super E>)x;
672	+	int half = size >>> 1;        // loop while a non-leaf
673	+	while (k < half) {
674	+	int child = (k << 1) + 1; // assume left child is least
675	+	Object c = queue[child];
676	+	int right = child + 1;
677	+	if (right < size &&
678	+	((Comparable<? super E>) c).compareTo((E) queue[right]) > 0)
679	+	c = queue[child = right];
680	+	if (key.compareTo((E) c) <= 0)
681	+	break;
682	+	queue[k] = c;
683	+	k = child;
684	+	}
685	+	queue[k] = key;
686	+	}
687	+
688	+	private void siftDownUsingComparator(int k, E x) {
689	+	int half = size >>> 1;
690	+	while (k < half) {
691	+	int child = (k << 1) + 1;
692	+	Object c = queue[child];
693	+	int right = child + 1;
694	+	if (right < size &&
695	+	comparator.compare((E) c, (E) queue[right]) > 0)
696	+	c = queue[child = right];
697	+	if (comparator.compare(x, (E) c) <= 0)
698	+	break;
699	+	queue[k] = c;
700	+	k = child;
701	+	}
702	+	queue[k] = x;
703	+	}
704	+
705	+	/**
706	+	* Establishes the heap invariant (described above) in the entire tree,
707	+	* assuming nothing about the order of the elements prior to the call.
708	+	*/
709	+	private void heapify() {
710	+	for (int i = (size >>> 1) - 1; i >= 0; i--)
711	+	siftDown(i, (E) queue[i]);
712	+	}
713	+
714	+	/**
715	+	* Returns the comparator used to order the elements in this
716	+	* queue, or {@code null} if this queue is sorted according to
717	+	* the {@linkplain Comparable natural ordering} of its elements.
718	+	*
719	+	* @return the comparator used to order this queue, or
720	+	*         {@code null} if this queue is sorted according to the
721	+	*         natural ordering of its elements
722	+	*/
723	+	public Comparator<? super E> comparator() {
724	+	return comparator;
725	+	}
726	+
727	+	/**
728	+	* Saves this queue to a stream (that is, serializes it).
729	+	*
730	+	* @serialData The length of the array backing the instance is
731	+	*             emitted (int), followed by all of its elements
732	+	*             (each an {@code Object}) in the proper order.
733	+	*/
734	+	private void writeObject(java.io.ObjectOutputStream s)
735	+	throws java.io.IOException {
736	+	// Write out element count, and any hidden stuff
737	+	s.defaultWriteObject();
738	+
739	+	// Write out array length, for compatibility with 1.5 version
740	+	s.writeInt(Math.max(2, size + 1));
741	+
742	+	// Write out all elements in the "proper order".
743	+	for (int i = 0; i < size; i++)
744	+	s.writeObject(queue[i]);
745	+	}
746	+
747	+	/**
748	+	* Reconstitutes this queue from a stream (that is, deserializes it).
749	+	*/
750	+	private void readObject(java.io.ObjectInputStream s)
751	+	throws java.io.IOException, ClassNotFoundException {
752	+	// Read in size, and any hidden stuff
753	+	s.defaultReadObject();
754	+
755	+	// Read in (and discard) array length
756	+	s.readInt();
757	+
758	+	queue = new Object[size];
759	+
760	+	// Read in all elements.
761	+	for (int i = 0; i < size; i++)
762	+	queue[i] = s.readObject();
763	+
764	+	// Elements are guaranteed to be in "proper order", but the
765	+	// spec has never explained what that might be.
766	+	heapify();
767	+	}
768		}

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