java/util/PriorityQueue.java

 package java.util;

/*
 * Todo
 *
 *   1) Make it serializable.
 */

/**
 * An unbounded priority queue based on a priority heap.  This queue orders
 * elements according to the order specified at creation time.  This order is
 * specified as for {@link TreeSet} and {@link TreeMap}: Elements are ordered
 * either according to their <i>natural order</i> (see {@link Comparable}), or
 * according to a {@link Comparator}, depending on which constructor is used.
 * The {@link #peek}, {@link #poll}, and {@link #remove} methods return the
 * minimal element with respect to the specified ordering.  If multiple
 * these elements are tied for least value, no guarantees are made as to
 * which of elements is returned.
 *
 * <p>Each priority queue has a <i>capacity</i>.  The capacity is the size of
 * the array used 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 list,
 * 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 <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</tt> methods; and constant time for the <tt>peek</tt>,
 * <tt>element</tt>, and <tt>size</tt> methods.
 *
 * <p>This class is a member of the
 * <a href="{@docRoot}/../guide/collections/index.html">
 * Java Collections Framework</a>.
 */
public class PriorityQueue<E> extends AbstractQueue<E>
                              implements Queue<E>
{
    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
     * of n, d, 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 E[] 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<E> comparator;

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

    /**
     * Create a new priority queue with the default initial capacity (11)
     * that orders its elements according to their natural ordering.
     */
    public PriorityQueue() {
        this(DEFAULT_INITIAL_CAPACITY);
    }

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

    /**
     * Create a new priority queue with the specified initial capacity (11)
     * 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.
     */
    public PriorityQueue(int initialCapacity, Comparator<E> comparator) {
        if (initialCapacity < 1)
            initialCapacity = 1;
        queue = new E[initialCapacity + 1];
        this.comparator = comparator;
    }

    /**
     * Create a new priority queue containing the elements in the specified
     * collection.  The priority queue has an initial capacity of 110% of the
     * size of the specified collection. 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 the
     * <tt>Sorted</tt> interface, the priority queue is ordered according to
     * its elements' natural order.
     *
     * @param initialElements 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 the specified collection or an
     *         element of the specified collection is <tt>null</tt>.
     */
    public PriorityQueue(Collection<E> initialElements) {
        int sz = initialElements.size();
        int initialCapacity = (int)Math.min((sz * 110L) / 100,
                                            Integer.MAX_VALUE - 1);
        if (initialCapacity < 1)
            initialCapacity = 1;
        queue = new E[initialCapacity + 1];

        if (initialElements instanceof Sorted) {
            comparator = ((Sorted)initialElements).comparator();
            for (Iterator<E> i = initialElements.iterator(); i.hasNext(); )
                queue[++size] = i.next();
        } else {
            comparator = null;
            for (Iterator<E> i = initialElements.iterator(); i.hasNext(); )
                add(i.next());
        }
    }

    // Queue Methods

    /**
     * Remove and return the minimal element from this priority queue if
     * it contains one or more elements, otherwise <tt>null</tt>.  The term
     * <i>minimal</i> is defined according to this priority queue's order.
     *
     * @return the minimal element from this priority queue if it contains
     *         one or more elements, otherwise <tt>null</tt>.
     */
    public E poll() {
        if (size == 0)
            return null;
        return remove(1);
    }

    /**
     * Return, but do not remove, the minimal element from the priority queue,
     * or <tt>null</tt> if the queue is empty.  The term <i>minimal</i> is
     * defined according to this priority queue's order.  This method returns
     * the same object reference that would be returned by by the
     * <tt>poll</tt> method.  The two methods differ in that this method
     * does not remove the element from the priority queue.
     *
     * @return the minimal element from this priority queue if it contains
     *         one or more elements, otherwise <tt>null</tt>.
     */
    public E peek() {
        return queue[1];
    }

    // Collection Methods

    /**
     * Removes a single instance of the specified element from this priority
     * queue, if it is present.  Returns true if this collection contained the
     * specified element (or equivalently, if this collection changed as a
     * result of the call).
     *
     * @param o element to be removed from this collection, if present.
     * @return <tt>true</tt> if this collection changed as a result of the
     *         call
     * @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 null.
     */
    public boolean remove(Object element) {
        if (element == null)
            throw new NullPointerException();

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

    /**
     * Returns an iterator over the elements in this priority queue.  The
     * first element returned by this iterator is the same element that
     * would be returned by a call to <tt>peek</tt>.
     *
     * @return an <tt>Iterator</tt> over the elements in this priority queue.
     */
    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.
         */
        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.
         */
        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.
         */
        int expectedModCount = modCount;

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

        public E next() {
            checkForComodification();
            if (cursor > size)
                throw new NoSuchElementException();
            E result = 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;
    }

    /**
     * Add the specified element to this priority queue.
     *
     * @param element the element to add.
     * @return true
     * @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 null.
     */
    public boolean offer(E element) {
        if (element == null)
            throw new NullPointerException();
        modCount++;

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

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

    /**
     * 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 = 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)queue[j]).compareTo(queue[k]) <= 0)
                    break;
                E tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;
                k = j;
            }
        } else {
            while (k > 1) {
                int j = k >> 1;
                if (comparator.compare(queue[j], queue[k]) <= 0)
                    break;
                E 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)queue[j]).compareTo(queue[j+1]) > 0)
                    j++; // j indexes smallest kid
                if (((Comparable)queue[k]).compareTo(queue[j]) <= 0)
                    break;
                E tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;
                k = j;
            }
        } else {
            while ((j = k << 1) <= size) {
                if (j < size && comparator.compare(queue[j], queue[j+1]) > 0)
                    j++; // j indexes smallest kid
                if (comparator.compare(queue[k], queue[j]) <= 0)
                    break;
                E tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;
                k = j;
            }
        }
    }

    /**
     * Returns the comparator associated with this priority queue, or
     * <tt>null</tt> if it uses its elements' natural ordering.
     *
     * @return the comparator associated with this priority queue, or
     *         <tt>null</tt> if it uses its elements' natural ordering.
     */
    Comparator<E> comparator() {
        return comparator;
    }
}
Revision:	1.4
Committed:	Mon May 19 02:45:07 2003 UTC (20 years, 11 months ago) by tim
Branch:	MAIN
Changes since 1.3:	+0 -4 lines
Log Message:	Use temp version of Sorted to allow a portion of PQ impl to be uncommented.
#	User	Rev	Content
1	tim	1.2	package java.util;
2	tim	1.1
3	tim	1.2	/*
4			* Todo
5			*
6			* 1) Make it serializable.
7			*/
8	tim	1.1
9			/**
10	tim	1.2	* An unbounded priority queue based on a priority heap. This queue orders
11			* elements according to the order specified at creation time. This order is
12			* specified as for {@link TreeSet} and {@link TreeMap}: Elements are ordered
13			* either according to their <i>natural order</i> (see {@link Comparable}), or
14			* according to a {@link Comparator}, depending on which constructor is used.
15			* The {@link #peek}, {@link #poll}, and {@link #remove} methods return the
16			* minimal element with respect to the specified ordering. If multiple
17			* these elements are tied for least value, no guarantees are made as to
18			* which of elements is returned.
19			*
20			* <p>Each priority queue has a <i>capacity</i>. The capacity is the size of
21			* the array used to store the elements on the queue. It is always at least
22			* as large as the queue size. As elements are added to a priority list,
23			* its capacity grows automatically. The details of the growth policy are not
24			* specified.
25			*
26			*<p>Implementation note: this implementation provides O(log(n)) time for
27			* the <tt>offer</tt>, <tt>poll</tt>, <tt>remove()</tt> and <tt>add</tt>
28			* methods; linear time for the <tt>remove(Object)</tt> and
29			* <tt>contains</tt> methods; and constant time for the <tt>peek</tt>,
30			* <tt>element</tt>, and <tt>size</tt> methods.
31			*
32			* <p>This class is a member of the
33			* <a href="{@docRoot}/../guide/collections/index.html">
34			* Java Collections Framework</a>.
35			*/
36			public class PriorityQueue<E> extends AbstractQueue<E>
37			implements Queue<E>
38			{
39			private static final int DEFAULT_INITIAL_CAPACITY = 11;
40	tim	1.1
41	tim	1.2	/**
42			* Priority queue represented as a balanced binary heap: the two children
43			* of queue[n] are queue[2n] and queue[2n + 1]. The priority queue is
44			* ordered by comparator, or by the elements' natural ordering, if
45			* comparator is null: For each node n in the heap, and each descendant
46			* of n, d, n <= d.
47			*
48			* The element with the lowest value is in queue[1] (assuming the queue is
49			* nonempty). A one-based array is used in preference to the traditional
50			* zero-based array to simplify parent and child calculations.
51			*
52			* queue.length must be >= 2, even if size == 0.
53			*/
54			private E[] queue;
55	tim	1.1
56	tim	1.2	/**
57			* The number of elements in the priority queue.
58			*/
59			private int size = 0;
60	tim	1.1
61	tim	1.2	/**
62			* The comparator, or null if priority queue uses elements'
63			* natural ordering.
64			*/
65			private final Comparator<E> comparator;
66
67			/**
68			* The number of times this priority queue has been
69			* <i>structurally modified</i>. See AbstractList for gory details.
70			*/
71			private int modCount = 0;
72
73			/**
74			* Create a new priority queue with the default initial capacity (11)
75			* that orders its elements according to their natural ordering.
76			*/
77			public PriorityQueue() {
78			this(DEFAULT_INITIAL_CAPACITY);
79	tim	1.1	}
80	tim	1.2
81			/**
82			* Create a new priority queue with the specified initial capacity
83			* that orders its elements according to their natural ordering.
84			*
85			* @param initialCapacity the initial capacity for this priority queue.
86			*/
87			public PriorityQueue(int initialCapacity) {
88			this(initialCapacity, null);
89	tim	1.1	}
90	tim	1.2
91			/**
92			* Create a new priority queue with the specified initial capacity (11)
93			* that orders its elements according to the specified comparator.
94			*
95			* @param initialCapacity the initial capacity for this priority queue.
96			* @param comparator the comparator used to order this priority queue.
97			*/
98			public PriorityQueue(int initialCapacity, Comparator<E> comparator) {
99			if (initialCapacity < 1)
100			initialCapacity = 1;
101			queue = new E[initialCapacity + 1];
102			this.comparator = comparator;
103	tim	1.1	}
104
105	tim	1.2	/**
106			* Create a new priority queue containing the elements in the specified
107			* collection. The priority queue has an initial capacity of 110% of the
108			* size of the specified collection. If the specified collection
109			* implements the {@link Sorted} interface, the priority queue will be
110			* sorted according to the same comparator, or according to its elements'
111			* natural order if the collection is sorted according to its elements'
112			* natural order. If the specified collection does not implement the
113			* <tt>Sorted</tt> interface, the priority queue is ordered according to
114			* its elements' natural order.
115			*
116			* @param initialElements the collection whose elements are to be placed
117			* into this priority queue.
118			* @throws ClassCastException if elements of the specified collection
119			* cannot be compared to one another according to the priority
120			* queue's ordering.
121			* @throws NullPointerException if the specified collection or an
122			* element of the specified collection is <tt>null</tt>.
123			*/
124			public PriorityQueue(Collection<E> initialElements) {
125			int sz = initialElements.size();
126			int initialCapacity = (int)Math.min((sz * 110L) / 100,
127			Integer.MAX_VALUE - 1);
128			if (initialCapacity < 1)
129			initialCapacity = 1;
130			queue = new E[initialCapacity + 1];
131
132			if (initialElements instanceof Sorted) {
133			comparator = ((Sorted)initialElements).comparator();
134			for (Iterator<E> i = initialElements.iterator(); i.hasNext(); )
135			queue[++size] = i.next();
136			} else {
137			comparator = null;
138			for (Iterator<E> i = initialElements.iterator(); i.hasNext(); )
139			add(i.next());
140			}
141	tim	1.1	}
142
143	tim	1.2	// Queue Methods
144
145			/**
146			* Remove and return the minimal element from this priority queue if
147			* it contains one or more elements, otherwise <tt>null</tt>. The term
148			* <i>minimal</i> is defined according to this priority queue's order.
149			*
150			* @return the minimal element from this priority queue if it contains
151			* one or more elements, otherwise <tt>null</tt>.
152			*/
153	tim	1.1	public E poll() {
154	tim	1.2	if (size == 0)
155			return null;
156			return remove(1);
157	tim	1.1	}
158	tim	1.2
159			/**
160			* Return, but do not remove, the minimal element from the priority queue,
161			* or <tt>null</tt> if the queue is empty. The term <i>minimal</i> is
162			* defined according to this priority queue's order. This method returns
163			* the same object reference that would be returned by by the
164			* <tt>poll</tt> method. The two methods differ in that this method
165			* does not remove the element from the priority queue.
166			*
167			* @return the minimal element from this priority queue if it contains
168			* one or more elements, otherwise <tt>null</tt>.
169			*/
170	tim	1.1	public E peek() {
171	tim	1.2	return queue[1];
172	tim	1.1	}
173
174	tim	1.2	// Collection Methods
175
176			/**
177			* Removes a single instance of the specified element from this priority
178			* queue, if it is present. Returns true if this collection contained the
179			* specified element (or equivalently, if this collection changed as a
180			* result of the call).
181			*
182			* @param o element to be removed from this collection, if present.
183			* @return <tt>true</tt> if this collection changed as a result of the
184			* call
185			* @throws ClassCastException if the specified element cannot be compared
186			* with elements currently in the priority queue according
187			* to the priority queue's ordering.
188			* @throws NullPointerException if the specified element is null.
189			*/
190			public boolean remove(Object element) {
191			if (element == null)
192			throw new NullPointerException();
193
194			if (comparator == null) {
195			for (int i = 1; i <= size; i++) {
196			if (((Comparable)queue[i]).compareTo(element) == 0) {
197			remove(i);
198			return true;
199			}
200			}
201			} else {
202			for (int i = 1; i <= size; i++) {
203			if (comparator.compare(queue[i], (E) element) == 0) {
204			remove(i);
205			return true;
206			}
207			}
208			}
209	tim	1.1	return false;
210			}
211	tim	1.2
212			/**
213			* Returns an iterator over the elements in this priority queue. The
214			* first element returned by this iterator is the same element that
215			* would be returned by a call to <tt>peek</tt>.
216			*
217			* @return an <tt>Iterator</tt> over the elements in this priority queue.
218			*/
219			public Iterator<E> iterator() {
220			return new Itr();
221			}
222
223			private class Itr implements Iterator<E> {
224			/**
225			* Index (into queue array) of element to be returned by
226			* subsequent call to next.
227			*/
228			int cursor = 1;
229
230			/**
231			* Index of element returned by most recent call to next or
232			* previous. Reset to 0 if this element is deleted by a call
233			* to remove.
234			*/
235			int lastRet = 0;
236
237			/**
238			* The modCount value that the iterator believes that the backing
239			* List should have. If this expectation is violated, the iterator
240			* has detected concurrent modification.
241			*/
242			int expectedModCount = modCount;
243
244			public boolean hasNext() {
245			return cursor <= size;
246			}
247
248			public E next() {
249			checkForComodification();
250			if (cursor > size)
251			throw new NoSuchElementException();
252			E result = queue[cursor];
253			lastRet = cursor++;
254			return result;
255			}
256
257			public void remove() {
258			if (lastRet == 0)
259			throw new IllegalStateException();
260			checkForComodification();
261
262			PriorityQueue.this.remove(lastRet);
263			if (lastRet < cursor)
264			cursor--;
265			lastRet = 0;
266			expectedModCount = modCount;
267			}
268
269			final void checkForComodification() {
270			if (modCount != expectedModCount)
271			throw new ConcurrentModificationException();
272			}
273			}
274
275			/**
276			* Returns the number of elements in this priority queue.
277			*
278			* @return the number of elements in this priority queue.
279			*/
280	tim	1.1	public int size() {
281	tim	1.2	return size;
282	tim	1.1	}
283	tim	1.2
284			/**
285			* Add the specified element to this priority queue.
286			*
287			* @param element the element to add.
288			* @return true
289			* @throws ClassCastException if the specified element cannot be compared
290			* with elements currently in the priority queue according
291			* to the priority queue's ordering.
292			* @throws NullPointerException if the specified element is null.
293			*/
294			public boolean offer(E element) {
295			if (element == null)
296			throw new NullPointerException();
297			modCount++;
298
299			// Grow backing store if necessary
300			if (++size == queue.length) {
301			E[] newQueue = new E[2 * queue.length];
302			System.arraycopy(queue, 0, newQueue, 0, size);
303			queue = newQueue;
304			}
305
306			queue[size] = element;
307			fixUp(size);
308			return true;
309	tim	1.1	}
310
311	tim	1.2	/**
312			* Remove all elements from the priority queue.
313			*/
314			public void clear() {
315			modCount++;
316
317			// Null out element references to prevent memory leak
318			for (int i=1; i<=size; i++)
319			queue[i] = null;
320
321			size = 0;
322			}
323
324			/**
325			* Removes and returns the ith element from queue. Recall
326			* that queue is one-based, so 1 <= i <= size.
327			*
328			* XXX: Could further special-case i==size, but is it worth it?
329			* XXX: Could special-case i==0, but is it worth it?
330			*/
331			private E remove(int i) {
332			assert i <= size;
333			modCount++;
334
335			E result = queue[i];
336			queue[i] = queue[size];
337			queue[size--] = null; // Drop extra ref to prevent memory leak
338			if (i <= size)
339			fixDown(i);
340			return result;
341	tim	1.1	}
342
343	tim	1.2	/**
344			* Establishes the heap invariant (described above) assuming the heap
345			* satisfies the invariant except possibly for the leaf-node indexed by k
346			* (which may have a nextExecutionTime less than its parent's).
347			*
348			* This method functions by "promoting" queue[k] up the hierarchy
349			* (by swapping it with its parent) repeatedly until queue[k]
350			* is greater than or equal to its parent.
351			*/
352			private void fixUp(int k) {
353			if (comparator == null) {
354			while (k > 1) {
355			int j = k >> 1;
356			if (((Comparable)queue[j]).compareTo(queue[k]) <= 0)
357			break;
358			E tmp = queue[j]; queue[j] = queue[k]; queue[k] = tmp;
359			k = j;
360			}
361			} else {
362			while (k > 1) {
363			int j = k >> 1;
364			if (comparator.compare(queue[j], queue[k]) <= 0)
365			break;
366			E tmp = queue[j]; queue[j] = queue[k]; queue[k] = tmp;
367			k = j;
368			}
369			}
370			}
371
372			/**
373			* Establishes the heap invariant (described above) in the subtree
374			* rooted at k, which is assumed to satisfy the heap invariant except
375			* possibly for node k itself (which may be greater than its children).
376			*
377			* This method functions by "demoting" queue[k] down the hierarchy
378			* (by swapping it with its smaller child) repeatedly until queue[k]
379			* is less than or equal to its children.
380			*/
381			private void fixDown(int k) {
382			int j;
383			if (comparator == null) {
384			while ((j = k << 1) <= size) {
385			if (j<size && ((Comparable)queue[j]).compareTo(queue[j+1]) > 0)
386			j++; // j indexes smallest kid
387			if (((Comparable)queue[k]).compareTo(queue[j]) <= 0)
388			break;
389			E tmp = queue[j]; queue[j] = queue[k]; queue[k] = tmp;
390			k = j;
391			}
392			} else {
393			while ((j = k << 1) <= size) {
394			if (j < size && comparator.compare(queue[j], queue[j+1]) > 0)
395			j++; // j indexes smallest kid
396			if (comparator.compare(queue[k], queue[j]) <= 0)
397			break;
398			E tmp = queue[j]; queue[j] = queue[k]; queue[k] = tmp;
399			k = j;
400			}
401			}
402			}
403
404			/**
405			* Returns the comparator associated with this priority queue, or
406			* <tt>null</tt> if it uses its elements' natural ordering.
407			*
408			* @return the comparator associated with this priority queue, or
409			* <tt>null</tt> if it uses its elements' natural ordering.
410			*/
411	tim	1.3	Comparator<E> comparator() {
412	tim	1.2	return comparator;
413			}
414	tim	1.1	}