java/util/PriorityQueue.java

 package java.util;

/**
 * An unbounded priority queue based on a priority heap.  This queue orders
 * elements according to an order specified at construction time, which is
 * specified in the same manner as {@link java.util.TreeSet} and
 * {@link java.util.TreeMap}: elements are ordered
 * either according to their <i>natural order</i> (see {@link Comparable}), or
 * according to a {@link java.util.Comparator}, depending on which
 * constructor is used.
 * <p>The <em>head</em> of this queue is the <em>least</em> element with
 * respect to the specified ordering.
 * If multiple elements are tied for least value, the
 * head is one of those elements. A priority queue does not permit
 * <tt>null</tt> elements.
 *
 * <p>The {@link #remove()} and {@link #poll()} methods remove and
 * return the head of the queue.
 *
 * <p>The {@link #element()} and {@link #peek()} methods return, but do
 * not delete, the head of the queue.
 *
 * <p>A priority queue has a <i>capacity</i>.  The capacity is the
 * size of the array used internally to store the elements on the
 * queue.
 * It is always at least as large as the queue size.  As
 * elements are added to a priority queue, its capacity grows
 * automatically.  The details of the growth policy are not specified.
 *
 * <p>Implementation note: this implementation provides O(log(n)) time
 * for the insertion methods (<tt>offer</tt>, <tt>poll</tt>,
 * <tt>remove()</tt> and <tt>add</tt>) methods; linear time for the
 * <tt>remove(Object)</tt> and <tt>contains(Object)</tt> methods; and
 * constant time for the retrieval methods (<tt>peek</tt>,
 * <tt>element</tt>, and <tt>size</tt>).
 *
 * <p>This class is a member of the
 * <a href="{@docRoot}/../guide/collections/index.html">
 * Java Collections Framework</a>.
 * @since 1.5
 * @author Josh Bloch
 */
public class PriorityQueue<E> extends AbstractQueue<E>
    implements Sorted, Queue<E>, java.io.Serializable {

    private static final int DEFAULT_INITIAL_CAPACITY = 11;

    /**
     * Priority queue represented as a balanced binary heap: the two children
     * of queue[n] are queue[2*n] and queue[2*n + 1].  The priority queue is
     * ordered by comparator, or by the elements' natural ordering, if
     * comparator is null:  For each node n in the heap and each descendant d
     * of n, n <= d.
     *
     * The element with the lowest value is in queue[1], assuming the queue is
     * nonempty.  (A one-based array is used in preference to the traditional
     * zero-based array to simplify parent and child calculations.)
     *
     * queue.length must be >= 2, even if size == 0.
     */
    private transient Object[] queue;

    /**
     * The number of elements in the priority queue.
     */
    private int size = 0;

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

    /**
     * The number of times this priority queue has been
     * <i>structurally modified</i>.  See AbstractList for gory details.
     */
    private transient int modCount = 0;

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

    /**
     * Creates a <tt>PriorityQueue</tt> with the specified initial capacity
     * that orders its elements according to their natural ordering
     * (using <tt>Comparable</tt>.)
     *
     * @param initialCapacity the initial capacity for this priority queue.
     */
    public PriorityQueue(int initialCapacity) {
        this(initialCapacity, null);
    }

    /**
     * Creates a <tt>PriorityQueue</tt> with the specified initial capacity
     * that orders its elements according to the specified comparator.
     *
     * @param initialCapacity the initial capacity for this priority queue.
     * @param comparator the comparator used to order this priority queue.
     * If <tt>null</tt> then the order depends on the elements' natural
     * ordering.
     * @throws IllegalArgumentException if <tt>initialCapacity</tt> is less
     * than 1
     */
    public PriorityQueue(int initialCapacity, Comparator<? super E> comparator) {
        if (initialCapacity < 1)
            throw new IllegalArgumentException();
        this.queue = new Object[initialCapacity + 1];
        this.comparator = comparator;
    }

    /**
     * Creates a <tt>PriorityQueue</tt> containing the elements in the 
     * specified collection.  
     * The priority queue has an initial capacity of 110% of the
     * size of the specified collection or 1 if the collection is empty.
     * If the specified collection
     * implements the {@link Sorted} interface, the priority queue will be
     * sorted according to the same comparator, or according to its elements'
     * natural order if the collection is sorted according to its elements'
     * natural order.  If the specified collection does not implement
     * <tt>Sorted</tt>, the priority queue is ordered according to
     * its elements' natural order.
     *
     * @param c the collection whose elements are to be placed
     *        into this priority queue.
     * @throws ClassCastException if elements of the specified collection
     *         cannot be compared to one another according to the priority
     *         queue's ordering.
     * @throws NullPointerException if <tt>c</tt> or any element within it
     * is <tt>null</tt>
     */
    public PriorityQueue(Collection<? extends E> c) {
        int sz = c.size();
        int initialCapacity = (int)Math.min((sz * 110L) / 100,
                                            Integer.MAX_VALUE - 1);
        if (initialCapacity < 1)
            initialCapacity = 1;

        this.queue = new Object[initialCapacity + 1];

        if (c instanceof Sorted) {
            comparator = (Comparator<? super E>)((Sorted)c).comparator();
        } else {
            comparator = null;
        }

        for (Iterator<? extends E> i = c.iterator(); i.hasNext(); )
            add(i.next());
    }

    // Queue Methods

    /**
     * Add the specified element to this priority queue.
     *
     * @return <tt>true</tt>
     * @throws ClassCastException if the specified element cannot be compared
     * with elements currently in the priority queue according
     * to the priority queue's ordering.
     * @throws NullPointerException if the specified element is <tt>null</tt>.
     */
    public boolean offer(E o) {
        if (o == null)
            throw new NullPointerException();
        modCount++;
        ++size;

        // Grow backing store if necessary
        while (size >= queue.length) {
            Object[] newQueue = new Object[2 * queue.length];
            System.arraycopy(queue, 0, newQueue, 0, queue.length);
            queue = newQueue;
        }

        queue[size] = o;
        fixUp(size);
        return true;
    }

    public E poll() {
        if (size == 0)
            return null;
        return (E) remove(1);
    }

    public E peek() {
        return (E) queue[1];
    }

    // Collection Methods

    // these first two override just to get the throws docs

    /**
     * @throws NullPointerException if the specified element is <tt>null</tt>.
     * @throws ClassCastException if the specified element cannot be compared
     * with elements currently in the priority queue according
     * to the priority queue's ordering.
     */
    public boolean add(E o) {
        return super.add(o);
    }

    /**
     * @throws ClassCastException if any element cannot be compared
     * with elements currently in the priority queue according
     * to the priority queue's ordering.
     * @throws NullPointerException if <tt>c</tt> or any element in <tt>c</tt>
     * is <tt>null</tt>
     */
    public boolean addAll(Collection<? extends E> c) {
        return super.addAll(c);
    }

    public boolean remove(Object o) {
        if (o == null)
            return false;

        if (comparator == null) {
            for (int i = 1; i <= size; i++) {
                if (((Comparable<E>)queue[i]).compareTo((E)o) == 0) {
                    remove(i);
                    return true;
                }
            }
        } else {
            for (int i = 1; i <= size; i++) {
                if (comparator.compare((E)queue[i], (E)o) == 0) {
                    remove(i);
                    return true;
                }
            }
        }
        return false;
    }

    public Iterator<E> iterator() {
        return new Itr();
    }

    private class Itr implements Iterator<E> {
        /**
         * Index (into queue array) of element to be returned by
         * subsequent call to next.
         */
        private int cursor = 1;

        /**
         * Index of element returned by most recent call to next or
         * previous.  Reset to 0 if this element is deleted by a call
         * to remove.
         */
        private int lastRet = 0;

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

        public boolean hasNext() {
            return cursor <= size;
        }

        public E next() {
            checkForComodification();
            if (cursor > size)
                throw new NoSuchElementException();
            E result = (E) queue[cursor];
            lastRet = cursor++;
            return result;
        }

        public void remove() {
            if (lastRet == 0)
                throw new IllegalStateException();
            checkForComodification();

            PriorityQueue.this.remove(lastRet);
            if (lastRet < cursor)
                cursor--;
            lastRet = 0;
            expectedModCount = modCount;
        }

        final void checkForComodification() {
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
        }
    }

    /**
     * Returns the number of elements in this priority queue.
     *
     * @return the number of elements in this priority queue.
     */
    public int size() {
        return size;
    }

    /**
     * Remove all elements from the priority queue.
     */
    public void clear() {
        modCount++;

        // Null out element references to prevent memory leak
        for (int i=1; i<=size; i++)
            queue[i] = null;

        size = 0;
    }

    /**
     * Removes and returns the ith element from queue.  Recall
     * that queue is one-based, so 1 <= i <= size.
     *
     * XXX: Could further special-case i==size, but is it worth it?
     * XXX: Could special-case i==0, but is it worth it?
     */
    private E remove(int i) {
        assert i <= size;
        modCount++;

        E result = (E) queue[i];
        queue[i] = queue[size];
        queue[size--] = null;  // Drop extra ref to prevent memory leak
        if (i <= size)
            fixDown(i);
        return result;
    }

    /**
     * Establishes the heap invariant (described above) assuming the heap
     * satisfies the invariant except possibly for the leaf-node indexed by k
     * (which may have a nextExecutionTime less than its parent's).
     *
     * This method functions by "promoting" queue[k] up the hierarchy
     * (by swapping it with its parent) repeatedly until queue[k]
     * is greater than or equal to its parent.
     */
    private void fixUp(int k) {
        if (comparator == null) {
            while (k > 1) {
                int j = k >> 1;
                if (((Comparable<E>)queue[j]).compareTo((E)queue[k]) <= 0)
                    break;
                Object tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;
                k = j;
            }
        } else {
            while (k > 1) {
                int j = k >> 1;
                if (comparator.compare((E)queue[j], (E)queue[k]) <= 0)
                    break;
                Object tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;
                k = j;
            }
        }
    }

    /**
     * Establishes the heap invariant (described above) in the subtree
     * rooted at k, which is assumed to satisfy the heap invariant except
     * possibly for node k itself (which may be greater than its children).
     *
     * This method functions by "demoting" queue[k] down the hierarchy
     * (by swapping it with its smaller child) repeatedly until queue[k]
     * is less than or equal to its children.
     */
    private void fixDown(int k) {
        int j;
        if (comparator == null) {
            while ((j = k << 1) <= size) {
                if (j<size && ((Comparable<E>)queue[j]).compareTo((E)queue[j+1]) > 0)
                    j++; // j indexes smallest kid
                if (((Comparable<E>)queue[k]).compareTo((E)queue[j]) <= 0)
                    break;
                Object tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;
                k = j;
            }
        } else {
            while ((j = k << 1) <= size) {
                if (j < size && comparator.compare((E)queue[j], (E)queue[j+1]) > 0)
                    j++; // j indexes smallest kid
                if (comparator.compare((E)queue[k], (E)queue[j]) <= 0)
                    break;
                Object tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;
                k = j;
            }
        }
    }

    public Comparator<? super E> comparator() {
        return comparator;
    }

    /**
     * Save the state of the instance to a stream (that
     * is, serialize it).
     *
     * @serialData The length of the array backing the instance is
     * emitted (int), followed by all of its elements (each an
     * <tt>Object</tt>) in the proper order.
     * @param s the stream
     */
    private synchronized void writeObject(java.io.ObjectOutputStream s)
        throws java.io.IOException{
        // Write out element count, and any hidden stuff
        s.defaultWriteObject();

        // Write out array length
        s.writeInt(queue.length);

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

    /**
     * Reconstitute the <tt>ArrayList</tt> instance from a stream (that is,
     * deserialize it).
     * @param s the stream
     */
    private synchronized void readObject(java.io.ObjectInputStream s)
        throws java.io.IOException, ClassNotFoundException {
        // Read in size, and any hidden stuff
        s.defaultReadObject();

        // Read in array length and allocate array
        int arrayLength = s.readInt();
        queue = new Object[arrayLength];

        // Read in all elements in the proper order.
        for (int i=0; i<size; i++)
            queue[i] = s.readObject();
    }

}

Revision:	1.21
Committed:	Tue Aug 5 06:49:51 2003 UTC (20 years, 9 months ago) by dholmes
Branch:	MAIN
Changes since 1.20:	+6 -5 lines
Log Message:	MOre tense changes
#	Content
1	package java.util;
2
3	/**
4	* An unbounded priority queue based on a priority heap. This queue orders
5	* elements according to an order specified at construction time, which is
6	* specified in the same manner as {@link java.util.TreeSet} and
7	* {@link java.util.TreeMap}: elements are ordered
8	* either according to their <i>natural order</i> (see {@link Comparable}), or
9	* according to a {@link java.util.Comparator}, depending on which
10	* constructor is used.
11	* <p>The <em>head</em> of this queue is the <em>least</em> element with
12	* respect to the specified ordering.
13	* If multiple elements are tied for least value, the
14	* head is one of those elements. A priority queue does not permit
15	* <tt>null</tt> elements.
16	*
17	* <p>The {@link #remove()} and {@link #poll()} methods remove and
18	* return the head of the queue.
19	*
20	* <p>The {@link #element()} and {@link #peek()} methods return, but do
21	* not delete, the head of the queue.
22	*
23	* <p>A priority queue has a <i>capacity</i>. The capacity is the
24	* size of the array used internally to store the elements on the
25	* queue.
26	* It is always at least as large as the queue size. As
27	* elements are added to a priority queue, its capacity grows
28	* automatically. The details of the growth policy are not specified.
29	*
30	* <p>Implementation note: this implementation provides O(log(n)) time
31	* for the insertion methods (<tt>offer</tt>, <tt>poll</tt>,
32	* <tt>remove()</tt> and <tt>add</tt>) methods; linear time for the
33	* <tt>remove(Object)</tt> and <tt>contains(Object)</tt> methods; and
34	* constant time for the retrieval methods (<tt>peek</tt>,
35	* <tt>element</tt>, and <tt>size</tt>).
36	*
37	* <p>This class is a member of the
38	* <a href="{@docRoot}/../guide/collections/index.html">
39	* Java Collections Framework</a>.
40	* @since 1.5
41	* @author Josh Bloch
42	*/
43	public class PriorityQueue<E> extends AbstractQueue<E>
44	implements Sorted, Queue<E>, java.io.Serializable {
45
46	private static final int DEFAULT_INITIAL_CAPACITY = 11;
47
48	/**
49	* Priority queue represented as a balanced binary heap: the two children
50	* of queue[n] are queue[2n] and queue[2n + 1]. The priority queue is
51	* ordered by comparator, or by the elements' natural ordering, if
52	* comparator is null: For each node n in the heap and each descendant d
53	* of n, n <= d.
54	*
55	* The element with the lowest value is in queue[1], assuming the queue is
56	* nonempty. (A one-based array is used in preference to the traditional
57	* zero-based array to simplify parent and child calculations.)
58	*
59	* queue.length must be >= 2, even if size == 0.
60	*/
61	private transient Object[] queue;
62
63	/**
64	* The number of elements in the priority queue.
65	*/
66	private int size = 0;
67
68	/**
69	* The comparator, or null if priority queue uses elements'
70	* natural ordering.
71	*/
72	private final Comparator<? super E> comparator;
73
74	/**
75	* The number of times this priority queue has been
76	* <i>structurally modified</i>. See AbstractList for gory details.
77	*/
78	private transient int modCount = 0;
79
80	/**
81	* Creates a <tt>PriorityQueue</tt> with the default initial capacity
82	* (11) that orders its elements according to their natural
83	* ordering (using <tt>Comparable</tt>.)
84	*/
85	public PriorityQueue() {
86	this(DEFAULT_INITIAL_CAPACITY, null);
87	}
88
89	/**
90	* Creates a <tt>PriorityQueue</tt> with the specified initial capacity
91	* that orders its elements according to their natural ordering
92	* (using <tt>Comparable</tt>.)
93	*
94	* @param initialCapacity the initial capacity for this priority queue.
95	*/
96	public PriorityQueue(int initialCapacity) {
97	this(initialCapacity, null);
98	}
99
100	/**
101	* Creates a <tt>PriorityQueue</tt> with the specified initial capacity
102	* that orders its elements according to the specified comparator.
103	*
104	* @param initialCapacity the initial capacity for this priority queue.
105	* @param comparator the comparator used to order this priority queue.
106	* If <tt>null</tt> then the order depends on the elements' natural
107	* ordering.
108	* @throws IllegalArgumentException if <tt>initialCapacity</tt> is less
109	* than 1
110	*/
111	public PriorityQueue(int initialCapacity, Comparator<? super E> comparator) {
112	if (initialCapacity < 1)
113	throw new IllegalArgumentException();
114	this.queue = new Object[initialCapacity + 1];
115	this.comparator = comparator;
116	}
117
118	/**
119	* Creates a <tt>PriorityQueue</tt> containing the elements in the
120	* specified collection.
121	* The priority queue has an initial capacity of 110% of the
122	* size of the specified collection or 1 if the collection is empty.
123	* If the specified collection
124	* implements the {@link Sorted} interface, the priority queue will be
125	* sorted according to the same comparator, or according to its elements'
126	* natural order if the collection is sorted according to its elements'
127	* natural order. If the specified collection does not implement
128	* <tt>Sorted</tt>, the priority queue is ordered according to
129	* its elements' natural order.
130	*
131	* @param c the collection whose elements are to be placed
132	* into this priority queue.
133	* @throws ClassCastException if elements of the specified collection
134	* cannot be compared to one another according to the priority
135	* queue's ordering.
136	* @throws NullPointerException if <tt>c</tt> or any element within it
137	* is <tt>null</tt>
138	*/
139	public PriorityQueue(Collection<? extends E> c) {
140	int sz = c.size();
141	int initialCapacity = (int)Math.min((sz * 110L) / 100,
142	Integer.MAX_VALUE - 1);
143	if (initialCapacity < 1)
144	initialCapacity = 1;
145
146	this.queue = new Object[initialCapacity + 1];
147
148	if (c instanceof Sorted) {
149	comparator = (Comparator<? super E>)((Sorted)c).comparator();
150	} else {
151	comparator = null;
152	}
153
154	for (Iterator<? extends E> i = c.iterator(); i.hasNext(); )
155	add(i.next());
156	}
157
158	// Queue Methods
159
160	/**
161	* Add the specified element to this priority queue.
162	*
163	* @return <tt>true</tt>
164	* @throws ClassCastException if the specified element cannot be compared
165	* with elements currently in the priority queue according
166	* to the priority queue's ordering.
167	* @throws NullPointerException if the specified element is <tt>null</tt>.
168	*/
169	public boolean offer(E o) {
170	if (o == null)
171	throw new NullPointerException();
172	modCount++;
173	++size;
174
175	// Grow backing store if necessary
176	while (size >= queue.length) {
177	Object[] newQueue = new Object[2 * queue.length];
178	System.arraycopy(queue, 0, newQueue, 0, queue.length);
179	queue = newQueue;
180	}
181
182	queue[size] = o;
183	fixUp(size);
184	return true;
185	}
186
187	public E poll() {
188	if (size == 0)
189	return null;
190	return (E) remove(1);
191	}
192
193	public E peek() {
194	return (E) queue[1];
195	}
196
197	// Collection Methods
198
199	// these first two override just to get the throws docs
200
201	/**
202	* @throws NullPointerException if the specified element is <tt>null</tt>.
203	* @throws ClassCastException if the specified element cannot be compared
204	* with elements currently in the priority queue according
205	* to the priority queue's ordering.
206	*/
207	public boolean add(E o) {
208	return super.add(o);
209	}
210
211	/**
212	* @throws ClassCastException if any element cannot be compared
213	* with elements currently in the priority queue according
214	* to the priority queue's ordering.
215	* @throws NullPointerException if <tt>c</tt> or any element in <tt>c</tt>
216	* is <tt>null</tt>
217	*/
218	public boolean addAll(Collection<? extends E> c) {
219	return super.addAll(c);
220	}
221
222	public boolean remove(Object o) {
223	if (o == null)
224	return false;
225
226	if (comparator == null) {
227	for (int i = 1; i <= size; i++) {
228	if (((Comparable<E>)queue[i]).compareTo((E)o) == 0) {
229	remove(i);
230	return true;
231	}
232	}
233	} else {
234	for (int i = 1; i <= size; i++) {
235	if (comparator.compare((E)queue[i], (E)o) == 0) {
236	remove(i);
237	return true;
238	}
239	}
240	}
241	return false;
242	}
243
244	public Iterator<E> iterator() {
245	return new Itr();
246	}
247
248	private class Itr implements Iterator<E> {
249	/**
250	* Index (into queue array) of element to be returned by
251	* subsequent call to next.
252	*/
253	private int cursor = 1;
254
255	/**
256	* Index of element returned by most recent call to next or
257	* previous. Reset to 0 if this element is deleted by a call
258	* to remove.
259	*/
260	private int lastRet = 0;
261
262	/**
263	* The modCount value that the iterator believes that the backing
264	* List should have. If this expectation is violated, the iterator
265	* has detected concurrent modification.
266	*/
267	private int expectedModCount = modCount;
268
269	public boolean hasNext() {
270	return cursor <= size;
271	}
272
273	public E next() {
274	checkForComodification();
275	if (cursor > size)
276	throw new NoSuchElementException();
277	E result = (E) queue[cursor];
278	lastRet = cursor++;
279	return result;
280	}
281
282	public void remove() {
283	if (lastRet == 0)
284	throw new IllegalStateException();
285	checkForComodification();
286
287	PriorityQueue.this.remove(lastRet);
288	if (lastRet < cursor)
289	cursor--;
290	lastRet = 0;
291	expectedModCount = modCount;
292	}
293
294	final void checkForComodification() {
295	if (modCount != expectedModCount)
296	throw new ConcurrentModificationException();
297	}
298	}
299
300	/**
301	* Returns the number of elements in this priority queue.
302	*
303	* @return the number of elements in this priority queue.
304	*/
305	public int size() {
306	return size;
307	}
308
309	/**
310	* Remove all elements from the priority queue.
311	*/
312	public void clear() {
313	modCount++;
314
315	// Null out element references to prevent memory leak
316	for (int i=1; i<=size; i++)
317	queue[i] = null;
318
319	size = 0;
320	}
321
322	/**
323	* Removes and returns the ith element from queue. Recall
324	* that queue is one-based, so 1 <= i <= size.
325	*
326	* XXX: Could further special-case i==size, but is it worth it?
327	* XXX: Could special-case i==0, but is it worth it?
328	*/
329	private E remove(int i) {
330	assert i <= size;
331	modCount++;
332
333	E result = (E) queue[i];
334	queue[i] = queue[size];
335	queue[size--] = null; // Drop extra ref to prevent memory leak
336	if (i <= size)
337	fixDown(i);
338	return result;
339	}
340
341	/**
342	* Establishes the heap invariant (described above) assuming the heap
343	* satisfies the invariant except possibly for the leaf-node indexed by k
344	* (which may have a nextExecutionTime less than its parent's).
345	*
346	* This method functions by "promoting" queue[k] up the hierarchy
347	* (by swapping it with its parent) repeatedly until queue[k]
348	* is greater than or equal to its parent.
349	*/
350	private void fixUp(int k) {
351	if (comparator == null) {
352	while (k > 1) {
353	int j = k >> 1;
354	if (((Comparable<E>)queue[j]).compareTo((E)queue[k]) <= 0)
355	break;
356	Object tmp = queue[j]; queue[j] = queue[k]; queue[k] = tmp;
357	k = j;
358	}
359	} else {
360	while (k > 1) {
361	int j = k >> 1;
362	if (comparator.compare((E)queue[j], (E)queue[k]) <= 0)
363	break;
364	Object tmp = queue[j]; queue[j] = queue[k]; queue[k] = tmp;
365	k = j;
366	}
367	}
368	}
369
370	/**
371	* Establishes the heap invariant (described above) in the subtree
372	* rooted at k, which is assumed to satisfy the heap invariant except
373	* possibly for node k itself (which may be greater than its children).
374	*
375	* This method functions by "demoting" queue[k] down the hierarchy
376	* (by swapping it with its smaller child) repeatedly until queue[k]
377	* is less than or equal to its children.
378	*/
379	private void fixDown(int k) {
380	int j;
381	if (comparator == null) {
382	while ((j = k << 1) <= size) {
383	if (j<size && ((Comparable<E>)queue[j]).compareTo((E)queue[j+1]) > 0)
384	j++; // j indexes smallest kid
385	if (((Comparable<E>)queue[k]).compareTo((E)queue[j]) <= 0)
386	break;
387	Object tmp = queue[j]; queue[j] = queue[k]; queue[k] = tmp;
388	k = j;
389	}
390	} else {
391	while ((j = k << 1) <= size) {
392	if (j < size && comparator.compare((E)queue[j], (E)queue[j+1]) > 0)
393	j++; // j indexes smallest kid
394	if (comparator.compare((E)queue[k], (E)queue[j]) <= 0)
395	break;
396	Object tmp = queue[j]; queue[j] = queue[k]; queue[k] = tmp;
397	k = j;
398	}
399	}
400	}
401
402	public Comparator<? super E> comparator() {
403	return comparator;
404	}
405
406	/**
407	* Save the state of the instance to a stream (that
408	* is, serialize it).
409	*
410	* @serialData The length of the array backing the instance is
411	* emitted (int), followed by all of its elements (each an
412	* <tt>Object</tt>) in the proper order.
413	* @param s the stream
414	*/
415	private synchronized void writeObject(java.io.ObjectOutputStream s)
416	throws java.io.IOException{
417	// Write out element count, and any hidden stuff
418	s.defaultWriteObject();
419
420	// Write out array length
421	s.writeInt(queue.length);
422
423	// Write out all elements in the proper order.
424	for (int i=0; i<size; i++)
425	s.writeObject(queue[i]);
426	}
427
428	/**
429	* Reconstitute the <tt>ArrayList</tt> instance from a stream (that is,
430	* deserialize it).
431	* @param s the stream
432	*/
433	private synchronized void readObject(java.io.ObjectInputStream s)
434	throws java.io.IOException, ClassNotFoundException {
435	// Read in size, and any hidden stuff
436	s.defaultReadObject();
437
438	// Read in array length and allocate array
439	int arrayLength = s.readInt();
440	queue = new Object[arrayLength];
441
442	// Read in all elements in the proper order.
443	for (int i=0; i<size; i++)
444	queue[i] = s.readObject();
445	}
446
447	}
448