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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 1.73 by jsr166, Tue Jun 21 19:29:21 2011 UTC

#	Line 1 | Line 1
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 enqueing and dequeing 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	>	public class PriorityQueue<E> extends AbstractQueue<E>
81	>	implements java.io.Serializable {
82
83	<	public PriorityQueue(int initialCapacity, Collection initialElements) {}
83	>	private static final long serialVersionUID = -7720805057305804111L;
84
85	<	public PriorityQueue(int initialCapacity, Comparator comparator, Collection initialElements) {}
85	>	private static final int DEFAULT_INITIAL_CAPACITY = 11;
86
87	<	public boolean add(E x) {
88	<	return false;
87	>	/**
88	>	* Priority queue represented as a balanced binary heap: the two
89	>	* children of queue[n] are queue[2*n+1] and queue[2*(n+1)].  The
90	>	* priority queue is ordered by comparator, or by the elements'
91	>	* natural ordering, if comparator is null: For each node n in the
92	>	* heap and each descendant d of n, n <= d.  The element with the
93	>	* lowest value is in queue[0], assuming the queue is nonempty.
94	>	*/
95	>	private transient Object[] queue;
96	>
97	>	/**
98	>	* The number of elements in the priority queue.
99	>	*/
100	>	private int size = 0;
101	>
102	>	/**
103	>	* The comparator, or null if priority queue uses elements'
104	>	* natural ordering.
105	>	*/
106	>	private final Comparator<? super E> comparator;
107	>
108	>	/**
109	>	* The number of times this priority queue has been
110	>	* <i>structurally modified</i>.  See AbstractList for gory details.
111	>	*/
112	>	private transient int modCount = 0;
113	>
114	>	/**
115	>	* Creates a {@code PriorityQueue} with the default initial
116	>	* capacity (11) that orders its elements according to their
117	>	* {@linkplain Comparable natural ordering}.
118	>	*/
119	>	public PriorityQueue() {
120	>	this(DEFAULT_INITIAL_CAPACITY, null);
121		}
122	<	public boolean offer(E x) {
123	<	return false;
122	>
123	>	/**
124	>	* Creates a {@code PriorityQueue} with the specified initial
125	>	* capacity that orders its elements according to their
126	>	* {@linkplain Comparable natural ordering}.
127	>	*
128	>	* @param initialCapacity the initial capacity for this priority queue
129	>	* @throws IllegalArgumentException if {@code initialCapacity} is less
130	>	*         than 1
131	>	*/
132	>	public PriorityQueue(int initialCapacity) {
133	>	this(initialCapacity, null);
134		}
135	<	public boolean remove(Object x) {
136	<	return false;
135	>
136	>	/**
137	>	* Creates a {@code PriorityQueue} with the specified initial capacity
138	>	* that orders its elements according to the specified comparator.
139	>	*
140	>	* @param  initialCapacity the initial capacity for this priority queue
141	>	* @param  comparator the comparator that will be used to order this
142	>	*         priority queue.  If {@code null}, the {@linkplain Comparable
143	>	*         natural ordering} of the elements will be used.
144	>	* @throws IllegalArgumentException if {@code initialCapacity} is
145	>	*         less than 1
146	>	*/
147	>	public PriorityQueue(int initialCapacity,
148	>	Comparator<? super E> comparator) {
149	>	// Note: This restriction of at least one is not actually needed,
150	>	// but continues for 1.5 compatibility
151	>	if (initialCapacity < 1)
152	>	throw new IllegalArgumentException();
153	>	this.queue = new Object[initialCapacity];
154	>	this.comparator = comparator;
155		}
156
157	<	public E remove() {
158	<	return null;
157	>	/**
158	>	* Creates a {@code PriorityQueue} containing the elements in the
159	>	* specified collection.  If the specified collection is an instance of
160	>	* a {@link SortedSet} or is another {@code PriorityQueue}, this
161	>	* priority queue will be ordered according to the same ordering.
162	>	* Otherwise, this priority queue will be ordered according to the
163	>	* {@linkplain Comparable natural ordering} of its elements.
164	>	*
165	>	* @param  c the collection whose elements are to be placed
166	>	*         into this priority queue
167	>	* @throws ClassCastException if elements of the specified collection
168	>	*         cannot be compared to one another according to the priority
169	>	*         queue's ordering
170	>	* @throws NullPointerException if the specified collection or any
171	>	*         of its elements are null
172	>	*/
173	>	@SuppressWarnings("unchecked")
174	>	public PriorityQueue(Collection<? extends E> c) {
175	>	if (c instanceof SortedSet<?>) {
176	>	SortedSet<? extends E> ss = (SortedSet<? extends E>) c;
177	>	this.comparator = (Comparator<? super E>) ss.comparator();
178	>	initElementsFromCollection(ss);
179	>	}
180	>	else if (c instanceof PriorityQueue<?>) {
181	>	PriorityQueue<? extends E> pq = (PriorityQueue<? extends E>) c;
182	>	this.comparator = (Comparator<? super E>) pq.comparator();
183	>	initFromPriorityQueue(pq);
184	>	}
185	>	else {
186	>	this.comparator = null;
187	>	initFromCollection(c);
188	>	}
189		}
190	<	public Iterator<E> iterator() {
191	<	return null;
190	>
191	>	/**
192	>	* Creates a {@code PriorityQueue} containing the elements in the
193	>	* specified priority queue.  This priority queue will be
194	>	* ordered according to the same ordering as the given priority
195	>	* queue.
196	>	*
197	>	* @param  c the priority queue whose elements are to be placed
198	>	*         into this priority queue
199	>	* @throws ClassCastException if elements of {@code c} cannot be
200	>	*         compared to one another according to {@code c}'s
201	>	*         ordering
202	>	* @throws NullPointerException if the specified priority queue or any
203	>	*         of its elements are null
204	>	*/
205	>	@SuppressWarnings("unchecked")
206	>	public PriorityQueue(PriorityQueue<? extends E> c) {
207	>	this.comparator = (Comparator<? super E>) c.comparator();
208	>	initFromPriorityQueue(c);
209		}
210
211	<	public E element() {
212	<	return null;
211	>	/**
212	>	* Creates a {@code PriorityQueue} containing the elements in the
213	>	* specified sorted set.   This priority queue will be ordered
214	>	* according to the same ordering as the given sorted set.
215	>	*
216	>	* @param  c the sorted set whose elements are to be placed
217	>	*         into this priority queue
218	>	* @throws ClassCastException if elements of the specified sorted
219	>	*         set cannot be compared to one another according to the
220	>	*         sorted set's ordering
221	>	* @throws NullPointerException if the specified sorted set or any
222	>	*         of its elements are null
223	>	*/
224	>	@SuppressWarnings("unchecked")
225	>	public PriorityQueue(SortedSet<? extends E> c) {
226	>	this.comparator = (Comparator<? super E>) c.comparator();
227	>	initElementsFromCollection(c);
228		}
229	<	public E poll() {
230	<	return null;
229	>
230	>	private void initFromPriorityQueue(PriorityQueue<? extends E> c) {
231	>	if (c.getClass() == PriorityQueue.class) {
232	>	this.queue = c.toArray();
233	>	this.size = c.size();
234	>	} else {
235	>	initFromCollection(c);
236	>	}
237	>	}
238	>
239	>	private void initElementsFromCollection(Collection<? extends E> c) {
240	>	Object[] a = c.toArray();
241	>	// If c.toArray incorrectly doesn't return Object[], copy it.
242	>	if (a.getClass() != Object[].class)
243	>	a = Arrays.copyOf(a, a.length, Object[].class);
244	>	int len = a.length;
245	>	if (len == 1 || this.comparator != null)
246	>	for (int i = 0; i < len; i++)
247	>	if (a[i] == null)
248	>	throw new NullPointerException();
249	>	this.queue = a;
250	>	this.size = a.length;
251	>	}
252	>
253	>	/**
254	>	* Initializes queue array with elements from the given Collection.
255	>	*
256	>	* @param c the collection
257	>	*/
258	>	private void initFromCollection(Collection<? extends E> c) {
259	>	initElementsFromCollection(c);
260	>	heapify();
261		}
262	+
263	+	/**
264	+	* The maximum size of array to allocate.
265	+	* Some VMs reserve some header words in an array.
266	+	* Attempts to allocate larger arrays may result in
267	+	* OutOfMemoryError: Requested array size exceeds VM limit
268	+	*/
269	+	private static final int MAX_ARRAY_SIZE = Integer.MAX_VALUE - 8;
270	+
271	+	/**
272	+	* Increases the capacity of the array.
273	+	*
274	+	* @param minCapacity the desired minimum capacity
275	+	*/
276	+	private void grow(int minCapacity) {
277	+	int oldCapacity = queue.length;
278	+	// Double size if small; else grow by 50%
279	+	int newCapacity = oldCapacity + ((oldCapacity < 64) ?
280	+	(oldCapacity + 2) :
281	+	(oldCapacity >> 1));
282	+	// overflow-conscious code
283	+	if (newCapacity - MAX_ARRAY_SIZE > 0)
284	+	newCapacity = hugeCapacity(minCapacity);
285	+	queue = Arrays.copyOf(queue, newCapacity);
286	+	}
287	+
288	+	private static int hugeCapacity(int minCapacity) {
289	+	if (minCapacity < 0) // overflow
290	+	throw new OutOfMemoryError();
291	+	return (minCapacity > MAX_ARRAY_SIZE) ?
292	+	Integer.MAX_VALUE :
293	+	MAX_ARRAY_SIZE;
294	+	}
295	+
296	+	/**
297	+	* Inserts the specified element into this priority queue.
298	+	*
299	+	* @return {@code true} (as specified by {@link Collection#add})
300	+	* @throws ClassCastException if the specified element cannot be
301	+	*         compared with elements currently in this priority queue
302	+	*         according to the priority queue's ordering
303	+	* @throws NullPointerException if the specified element is null
304	+	*/
305	+	public boolean add(E e) {
306	+	return offer(e);
307	+	}
308	+
309	+	/**
310	+	* Inserts the specified element into this priority queue.
311	+	*
312	+	* @return {@code true} (as specified by {@link Queue#offer})
313	+	* @throws ClassCastException if the specified element cannot be
314	+	*         compared with elements currently in this priority queue
315	+	*         according to the priority queue's ordering
316	+	* @throws NullPointerException if the specified element is null
317	+	*/
318	+	public boolean offer(E e) {
319	+	if (e == null)
320	+	throw new NullPointerException();
321	+	modCount++;
322	+	int i = size;
323	+	if (i >= queue.length)
324	+	grow(i + 1);
325	+	size = i + 1;
326	+	if (i == 0)
327	+	queue[0] = e;
328	+	else
329	+	siftUp(i, e);
330	+	return true;
331	+	}
332	+
333		public E peek() {
334	<	return null;
334	>	return (size == 0) ? null : (E) queue[0];
335		}
336
337	<	public boolean isEmpty() {
337	>	private int indexOf(Object o) {
338	>	if (o != null) {
339	>	for (int i = 0; i < size; i++)
340	>	if (o.equals(queue[i]))
341	>	return i;
342	>	}
343	>	return -1;
344	>	}
345	>
346	>	/**
347	>	* Removes a single instance of the specified element from this queue,
348	>	* if it is present.  More formally, removes an element {@code e} such
349	>	* that {@code o.equals(e)}, if this queue contains one or more such
350	>	* elements.  Returns {@code true} if and only if this queue contained
351	>	* the specified element (or equivalently, if this queue changed as a
352	>	* result of the call).
353	>	*
354	>	* @param o element to be removed from this queue, if present
355	>	* @return {@code true} if this queue changed as a result of the call
356	>	*/
357	>	public boolean remove(Object o) {
358	>	int i = indexOf(o);
359	>	if (i == -1)
360	>	return false;
361	>	else {
362	>	removeAt(i);
363	>	return true;
364	>	}
365	>	}
366	>
367	>	/**
368	>	* Version of remove using reference equality, not equals.
369	>	* Needed by iterator.remove.
370	>	*
371	>	* @param o element to be removed from this queue, if present
372	>	* @return {@code true} if removed
373	>	*/
374	>	boolean removeEq(Object o) {
375	>	for (int i = 0; i < size; i++) {
376	>	if (o == queue[i]) {
377	>	removeAt(i);
378	>	return true;
379	>	}
380	>	}
381		return false;
382		}
383	<	public int size() {
384	<	return 0;
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) != -1;
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 null;
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 <tt>x</tt> 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 <tt>String</tt>:
434	>	*
435	>	*  <pre> {@code String[] y = x.toArray(new String[0]);}</pre>
436	>	*
437	>	* Note that <tt>toArray(new Object[0])</tt> is identical in function to
438	>	* <tt>toArray()</tt>.
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	>	if (a.length < size)
451	>	// Make a new array of a's runtime type, but my contents:
452	>	return (T[]) Arrays.copyOf(queue, size, a.getClass());
453	>	System.arraycopy(queue, 0, a, 0, size);
454	>	if (a.length > size)
455	>	a[size] = null;
456	>	return a;
457	>	}
458	>
459	>	/**
460	>	* Returns an iterator over the elements in this queue. The iterator
461	>	* does not return the elements in any particular order.
462	>	*
463	>	* @return an iterator over the elements in this queue
464	>	*/
465	>	public Iterator<E> iterator() {
466	>	return new Itr();
467	>	}
468	>
469	>	private final class Itr implements Iterator<E> {
470	>	/**
471	>	* Index (into queue array) of element to be returned by
472	>	* subsequent call to next.
473	>	*/
474	>	private int cursor = 0;
475	>
476	>	/**
477	>	* Index of element returned by most recent call to next,
478	>	* unless that element came from the forgetMeNot list.
479	>	* Set to -1 if element is deleted by a call to remove.
480	>	*/
481	>	private int lastRet = -1;
482	>
483	>	/**
484	>	* A queue of elements that were moved from the unvisited portion of
485	>	* the heap into the visited portion as a result of "unlucky" element
486	>	* removals during the iteration.  (Unlucky element removals are those
487	>	* that require a siftup instead of a siftdown.)  We must visit all of
488	>	* the elements in this list to complete the iteration.  We do this
489	>	* after we've completed the "normal" iteration.
490	>	*
491	>	* We expect that most iterations, even those involving removals,
492	>	* will not need to store elements in this field.
493	>	*/
494	>	private ArrayDeque<E> forgetMeNot = null;
495	>
496	>	/**
497	>	* Element returned by the most recent call to next iff that
498	>	* element was drawn from the forgetMeNot list.
499	>	*/
500	>	private E lastRetElt = null;
501	>
502	>	/**
503	>	* The modCount value that the iterator believes that the backing
504	>	* Queue should have.  If this expectation is violated, the iterator
505	>	* has detected concurrent modification.
506	>	*/
507	>	private int expectedModCount = modCount;
508	>
509	>	public boolean hasNext() {
510	>	return cursor < size ||
511	>	(forgetMeNot != null && !forgetMeNot.isEmpty());
512	>	}
513	>
514	>	public E next() {
515	>	if (expectedModCount != modCount)
516	>	throw new ConcurrentModificationException();
517	>	if (cursor < size)
518	>	return (E) queue[lastRet = cursor++];
519	>	if (forgetMeNot != null) {
520	>	lastRet = -1;
521	>	lastRetElt = forgetMeNot.poll();
522	>	if (lastRetElt != null)
523	>	return lastRetElt;
524	>	}
525	>	throw new NoSuchElementException();
526	>	}
527	>
528	>	public void remove() {
529	>	if (expectedModCount != modCount)
530	>	throw new ConcurrentModificationException();
531	>	if (lastRet != -1) {
532	>	E moved = PriorityQueue.this.removeAt(lastRet);
533	>	lastRet = -1;
534	>	if (moved == null)
535	>	cursor--;
536	>	else {
537	>	if (forgetMeNot == null)
538	>	forgetMeNot = new ArrayDeque<E>();
539	>	forgetMeNot.add(moved);
540	>	}
541	>	} else if (lastRetElt != null) {
542	>	PriorityQueue.this.removeEq(lastRetElt);
543	>	lastRetElt = null;
544	>	} else {
545	>	throw new IllegalStateException();
546	>	}
547	>	expectedModCount = modCount;
548	>	}
549		}
550
551	<	public <T> T[] toArray(T[] array) {
551	>	public int size() {
552	>	return size;
553	>	}
554	>
555	>	/**
556	>	* Removes all of the elements from this priority queue.
557	>	* The queue will be empty after this call returns.
558	>	*/
559	>	public void clear() {
560	>	modCount++;
561	>	for (int i = 0; i < size; i++)
562	>	queue[i] = null;
563	>	size = 0;
564	>	}
565	>
566	>	public E poll() {
567	>	if (size == 0)
568	>	return null;
569	>	int s = --size;
570	>	modCount++;
571	>	E result = (E) queue[0];
572	>	E x = (E) queue[s];
573	>	queue[s] = null;
574	>	if (s != 0)
575	>	siftDown(0, x);
576	>	return result;
577	>	}
578	>
579	>	/**
580	>	* Removes the ith element from queue.
581	>	*
582	>	* Normally this method leaves the elements at up to i-1,
583	>	* inclusive, untouched.  Under these circumstances, it returns
584	>	* null.  Occasionally, in order to maintain the heap invariant,
585	>	* it must swap a later element of the list with one earlier than
586	>	* i.  Under these circumstances, this method returns the element
587	>	* that was previously at the end of the list and is now at some
588	>	* position before i. This fact is used by iterator.remove so as to
589	>	* avoid missing traversing elements.
590	>	*/
591	>	private E removeAt(int i) {
592	>	assert i >= 0 && i < size;
593	>	modCount++;
594	>	int s = --size;
595	>	if (s == i) // removed last element
596	>	queue[i] = null;
597	>	else {
598	>	E moved = (E) queue[s];
599	>	queue[s] = null;
600	>	siftDown(i, moved);
601	>	if (queue[i] == moved) {
602	>	siftUp(i, moved);
603	>	if (queue[i] != moved)
604	>	return moved;
605	>	}
606	>	}
607		return null;
608		}
609
610	+	/**
611	+	* Inserts item x at position k, maintaining heap invariant by
612	+	* promoting x up the tree until it is greater than or equal to
613	+	* its parent, or is the root.
614	+	*
615	+	* To simplify and speed up coercions and comparisons. the
616	+	* Comparable and Comparator versions are separated into different
617	+	* methods that are otherwise identical. (Similarly for siftDown.)
618	+	*
619	+	* @param k the position to fill
620	+	* @param x the item to insert
621	+	*/
622	+	private void siftUp(int k, E x) {
623	+	if (comparator != null)
624	+	siftUpUsingComparator(k, x);
625	+	else
626	+	siftUpComparable(k, x);
627	+	}
628	+
629	+	private void siftUpComparable(int k, E x) {
630	+	Comparable<? super E> key = (Comparable<? super E>) x;
631	+	while (k > 0) {
632	+	int parent = (k - 1) >>> 1;
633	+	Object e = queue[parent];
634	+	if (key.compareTo((E) e) >= 0)
635	+	break;
636	+	queue[k] = e;
637	+	k = parent;
638	+	}
639	+	queue[k] = key;
640	+	}
641	+
642	+	private void siftUpUsingComparator(int k, E x) {
643	+	while (k > 0) {
644	+	int parent = (k - 1) >>> 1;
645	+	Object e = queue[parent];
646	+	if (comparator.compare(x, (E) e) >= 0)
647	+	break;
648	+	queue[k] = e;
649	+	k = parent;
650	+	}
651	+	queue[k] = x;
652	+	}
653	+
654	+	/**
655	+	* Inserts item x at position k, maintaining heap invariant by
656	+	* demoting x down the tree repeatedly until it is less than or
657	+	* equal to its children or is a leaf.
658	+	*
659	+	* @param k the position to fill
660	+	* @param x the item to insert
661	+	*/
662	+	private void siftDown(int k, E x) {
663	+	if (comparator != null)
664	+	siftDownUsingComparator(k, x);
665	+	else
666	+	siftDownComparable(k, x);
667	+	}
668	+
669	+	private void siftDownComparable(int k, E x) {
670	+	Comparable<? super E> key = (Comparable<? super E>)x;
671	+	int half = size >>> 1;        // loop while a non-leaf
672	+	while (k < half) {
673	+	int child = (k << 1) + 1; // assume left child is least
674	+	Object c = queue[child];
675	+	int right = child + 1;
676	+	if (right < size &&
677	+	((Comparable<? super E>) c).compareTo((E) queue[right]) > 0)
678	+	c = queue[child = right];
679	+	if (key.compareTo((E) c) <= 0)
680	+	break;
681	+	queue[k] = c;
682	+	k = child;
683	+	}
684	+	queue[k] = key;
685	+	}
686	+
687	+	private void siftDownUsingComparator(int k, E x) {
688	+	int half = size >>> 1;
689	+	while (k < half) {
690	+	int child = (k << 1) + 1;
691	+	Object c = queue[child];
692	+	int right = child + 1;
693	+	if (right < size &&
694	+	comparator.compare((E) c, (E) queue[right]) > 0)
695	+	c = queue[child = right];
696	+	if (comparator.compare(x, (E) c) <= 0)
697	+	break;
698	+	queue[k] = c;
699	+	k = child;
700	+	}
701	+	queue[k] = x;
702	+	}
703	+
704	+	/**
705	+	* Establishes the heap invariant (described above) in the entire tree,
706	+	* assuming nothing about the order of the elements prior to the call.
707	+	*/
708	+	private void heapify() {
709	+	for (int i = (size >>> 1) - 1; i >= 0; i--)
710	+	siftDown(i, (E) queue[i]);
711	+	}
712	+
713	+	/**
714	+	* Returns the comparator used to order the elements in this
715	+	* queue, or {@code null} if this queue is sorted according to
716	+	* the {@linkplain Comparable natural ordering} of its elements.
717	+	*
718	+	* @return the comparator used to order this queue, or
719	+	*         {@code null} if this queue is sorted according to the
720	+	*         natural ordering of its elements
721	+	*/
722	+	public Comparator<? super E> comparator() {
723	+	return comparator;
724	+	}
725	+
726	+	/**
727	+	* Saves the state of the instance to a stream (that
728	+	* 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	+	* @param s the stream
734	+	*/
735	+	private void writeObject(java.io.ObjectOutputStream s)
736	+	throws java.io.IOException{
737	+	// Write out element count, and any hidden stuff
738	+	s.defaultWriteObject();
739	+
740	+	// Write out array length, for compatibility with 1.5 version
741	+	s.writeInt(Math.max(2, size + 1));
742	+
743	+	// Write out all elements in the "proper order".
744	+	for (int i = 0; i < size; i++)
745	+	s.writeObject(queue[i]);
746	+	}
747	+
748	+	/**
749	+	* Reconstitutes the {@code PriorityQueue} instance from a stream
750	+	* (that is, deserializes it).
751	+	*
752	+	* @param s the stream
753	+	*/
754	+	private void readObject(java.io.ObjectInputStream s)
755	+	throws java.io.IOException, ClassNotFoundException {
756	+	// Read in size, and any hidden stuff
757	+	s.defaultReadObject();
758	+
759	+	// Read in (and discard) array length
760	+	s.readInt();
761	+
762	+	queue = new Object[size];
763	+
764	+	// Read in all elements.
765	+	for (int i = 0; i < size; i++)
766	+	queue[i] = s.readObject();
767	+
768	+	// Elements are guaranteed to be in "proper order", but the
769	+	// spec has never explained what that might be.
770	+	heapify();
771	+	}
772		}

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