001    /*
002     * Copyright (C) 2010 Google Inc.
003     *
004     * Licensed under the Apache License, Version 2.0 (the "License");
005     * you may not use this file except in compliance with the License.
006     * You may obtain a copy of the License at
007     *
008     * http://www.apache.org/licenses/LICENSE-2.0
009     *
010     * Unless required by applicable law or agreed to in writing, software
011     * distributed under the License is distributed on an "AS IS" BASIS,
012     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
013     * See the License for the specific language governing permissions and
014     * limitations under the License.
015     */
016    
017    package com.google.common.collect;
018    
019    import static com.google.common.base.Preconditions.checkArgument;
020    import static com.google.common.base.Preconditions.checkNotNull;
021    import static com.google.common.base.Preconditions.checkPositionIndex;
022    import static com.google.common.base.Preconditions.checkState;
023    
024    import com.google.common.annotations.Beta;
025    import com.google.common.annotations.VisibleForTesting;
026    
027    import java.util.AbstractQueue;
028    import java.util.ArrayList;
029    import java.util.Collection;
030    import java.util.Collections;
031    import java.util.Comparator;
032    import java.util.ConcurrentModificationException;
033    import java.util.Iterator;
034    import java.util.LinkedList;
035    import java.util.List;
036    import java.util.NoSuchElementException;
037    import java.util.PriorityQueue;
038    import java.util.Queue;
039    
040    /**
041     * A double-ended priority queue, which provides constant-time access to both
042     * its least element and its greatest element, as determined by the queue's
043     * specified comparator. If no comparator is given at construction time, the
044     * natural order of elements is used.
045     *
046     * <p>As a {@link Queue} it functions exactly as a {@link PriorityQueue}: its
047     * head element -- the implicit target of the methods {@link #peek()}, {@link
048     * #poll()} and {@link #remove()} -- is defined as the <i>least</i> element in
049     * the queue according to the queue's comparator. But unlike a regular priority
050     * queue, the methods {@link #peekLast}, {@link #pollLast} and
051     * {@link #removeLast} are also provided, to act on the <i>greatest</i> element
052     * in the queue instead.
053     *
054     * <p>A min-max priority queue can be configured with a maximum size. If so,
055     * each time the size of the queue exceeds that value, the queue automatically
056     * removes its greatest element according to its comparator (which might be the
057     * element that was just added). This is different from conventional bounded
058     * queues, which either block or reject new elements when full.
059     *
060     * <p>This implementation is based on the
061     * <a href="http://portal.acm.org/citation.cfm?id=6621">min-max heap</a>
062     * developed by Atkinson, et al. Unlike many other double-ended priority queues,
063     * it stores elements in a single array, as compact as the traditional heap data
064     * structure used in {@link PriorityQueue}.
065     *
066     * <p>This class is not thread-safe, and does not accept null elements.
067     *
068     * <p><i>Performance notes:</i>
069     *
070     * <ul>
071     * <li>The retrieval operations {@link #peek}, {@link #peekFirst}, {@link
072     *     #peekLast}, {@link #element}, and {@link #size} are constant-time
073     * <li>The enqueing and dequeing operations ({@link #offer}, {@link #add}, and
074     *     all the forms of {@link #poll} and {@link #remove()}) run in {@code
075     *     O(log n) time}
076     * <li>The {@link #remove(Object)} and {@link #contains} operations require
077     *     linear ({@code O(n)}) time
078     * </ul>
079     *
080     * @author Sverre Sundsdal
081     * @author Torbjorn Gannholm
082     * @since 8
083     */
084    // TODO(kevinb): @GwtCompatible
085    @Beta
086    public final class MinMaxPriorityQueue<E> extends AbstractQueue<E> {
087    
088      /**
089       * Creates a new min-max priority queue with default settings: natural order,
090       * no maximum size, no initial contents, and an initial expected size of 11.
091       */
092      public static <E extends Comparable<E>> MinMaxPriorityQueue<E> create() {
093        return new Builder<Comparable>(Ordering.natural()).create();
094      }
095    
096      /**
097       * Creates a new min-max priority queue using natural order, no maximum size,
098       * and initially containing the given elements.
099       */
100      public static <E extends Comparable<E>> MinMaxPriorityQueue<E> create(
101          Iterable<? extends E> initialContents) {
102        return new Builder<E>(Ordering.<E>natural()).create(initialContents);
103      }
104    
105      /**
106       * Creates and returns a new builder, configured to build {@code
107       * MinMaxPriorityQueue} instances that use {@code comparator} to determine the
108       * least and greatest elements.
109       */
110      public static <B> Builder<B> orderedBy(Comparator<B> comparator) {
111        return new Builder<B>(comparator);
112      }
113    
114      /**
115       * Creates and returns a new builder, configured to build {@code
116       * MinMaxPriorityQueue} instances sized appropriately to hold {@code
117       * expectedSize} elements.
118       */
119      public static Builder<Comparable> expectedSize(int expectedSize) {
120        return new Builder<Comparable>(Ordering.natural())
121            .expectedSize(expectedSize);
122      }
123    
124      /**
125       * Creates and returns a new builder, configured to build {@code
126       * MinMaxPriorityQueue} instances that are limited to {@code maximumSize}
127       * elements. Each time a queue grows beyond this bound, it immediately
128       * removes its greatest element (according to its comparator), which might be
129       * the element that was just added.
130       */
131      public static Builder<Comparable> maximumSize(int maximumSize) {
132        return new Builder<Comparable>(Ordering.natural())
133            .maximumSize(maximumSize);
134      }
135    
136      /**
137       * The builder class used in creation of min-max priority queues. Instead of
138       * constructing one directly, use {@link
139       * MinMaxPriorityQueue#orderedBy(Comparator)}, {@link
140       * MinMaxPriorityQueue#expectedSize(int)} or {@link
141       * MinMaxPriorityQueue#maximumSize(int)}.
142       *
143       * @param <B> the upper bound on the eventual type that can be produced by
144       *     this builder (for example, a {@code Builder<Number>} can produce a
145       *     {@code Queue<Number>} or {@code Queue<Integer>} but not a {@code
146       *     Queue<Object>}).
147       * @since 8
148       */
149      @Beta
150      public static final class Builder<B> {
151        /*
152         * TODO(kevinb): when the dust settles, see if we still need this or can
153         * just default to DEFAULT_CAPACITY.
154         */
155        private static final int UNSET_EXPECTED_SIZE = -1;
156    
157        private final Comparator<B> comparator;
158        private int expectedSize = UNSET_EXPECTED_SIZE;
159        private int maximumSize = Integer.MAX_VALUE;
160    
161        private Builder(Comparator<B> comparator) {
162          this.comparator = checkNotNull(comparator);
163        }
164    
165        /**
166         * Configures this builder to build min-max priority queues with an initial
167         * expected size of {@code expectedSize}.
168         */
169        public Builder<B> expectedSize(int expectedSize) {
170          checkArgument(expectedSize >= 0);
171          this.expectedSize = expectedSize;
172          return this;
173        }
174    
175        /**
176         * Configures this builder to build {@code MinMaxPriorityQueue} instances
177         * that are limited to {@code maximumSize} elements. Each time a queue grows
178         * beyond this bound, it immediately removes its greatest element (according
179         * to its comparator), which might be the element that was just added.
180         */
181        public Builder<B> maximumSize(int maximumSize) {
182          checkArgument(maximumSize > 0);
183          this.maximumSize = maximumSize;
184          return this;
185        }
186    
187        /**
188         * Builds a new min-max priority queue using the previously specified
189         * options, and having no initial contents.
190         */
191        public <T extends B> MinMaxPriorityQueue<T> create() {
192          return create(Collections.<T>emptySet());
193        }
194    
195        /**
196         * Builds a new min-max priority queue using the previously specified
197         * options, and having the given initial elements.
198         */
199        public <T extends B> MinMaxPriorityQueue<T> create(
200            Iterable<? extends T> initialContents) {
201          MinMaxPriorityQueue<T> queue = new MinMaxPriorityQueue<T>(
202              this, initialQueueSize(expectedSize, maximumSize, initialContents));
203          for (T element : initialContents) {
204            queue.offer(element);
205          }
206          return queue;
207        }
208    
209        @SuppressWarnings("unchecked") // safe "contravariant cast"
210        private <T extends B> Ordering<T> ordering() {
211          return Ordering.from((Comparator) comparator);
212        }
213      }
214    
215      private final Heap minHeap;
216      private final Heap maxHeap;
217      @VisibleForTesting final int maximumSize;
218      private Object[] queue;
219      private int size;
220      private int modCount;
221    
222      private MinMaxPriorityQueue(Builder<? super E> builder, int queueSize) {
223        Ordering<E> ordering = builder.ordering();
224        this.minHeap = new Heap(ordering);
225        this.maxHeap = new Heap(ordering.reverse());
226        minHeap.otherHeap = maxHeap;
227        maxHeap.otherHeap = minHeap;
228    
229        this.maximumSize = builder.maximumSize;
230        // TODO(kevinb): pad?
231        this.queue = new Object[queueSize];
232      }
233    
234      @Override public int size() {
235        return size;
236      }
237    
238      /**
239       * Adds the given element to this queue. If this queue has a maximum size,
240       * after adding {@code element} the queue will automatically evict its
241       * greatest element (according to its comparator), which may be {@code
242       * element} itself.
243       *
244       * @return {@code true} always
245       */
246      @Override public boolean add(E element) {
247        offer(element);
248        return true;
249      }
250    
251      @Override public boolean addAll(Collection<? extends E> newElements) {
252        boolean modified = false;
253        for (E element : newElements) {
254          offer(element);
255          modified = true;
256        }
257        return modified;
258      }
259    
260      /**
261       * Adds the given element to this queue. If this queue has a maximum size,
262       * after adding {@code element} the queue will automatically evict its
263       * greatest element (according to its comparator), which may be {@code
264       * element} itself.
265       */
266      @Override public boolean offer(E element) {
267        checkNotNull(element);
268        modCount++;
269        int insertIndex = size++;
270    
271        growIfNeeded();
272    
273        // Adds the element to the end of the heap and bubbles it up to the correct
274        // position.
275        heapForIndex(insertIndex).bubbleUp(insertIndex, element);
276        return size <= maximumSize || pollLast() != element;
277      }
278    
279      @Override public E poll() {
280        return isEmpty() ? null : removeAndGet(0);
281      }
282    
283      @SuppressWarnings("unchecked") // we must carefully only allow Es to get in
284      E elementData(int index) {
285        return (E) queue[index];
286      }
287    
288      @Override public E peek() {
289        return isEmpty() ? null : elementData(0);
290      }
291    
292      /**
293       * Returns the index of the max element.
294       */
295      private int getMaxElementIndex() {
296        switch (size) {
297          case 1:
298            return 0; // The lone element in the queue is the maximum.
299          case 2:
300            return 1; // The lone element in the maxHeap is the maximum.
301          default:
302            // The max element must sit on the first level of the maxHeap. It is
303            // actually the *lesser* of the two from the maxHeap's perspective.
304            return (maxHeap.compareElements(1, 2) <= 0) ? 1 : 2;
305        }
306      }
307    
308      /**
309       * Removes and returns the least element of this queue, or returns {@code
310       * null} if the queue is empty.
311       */
312      public E pollFirst() {
313        return poll();
314      }
315    
316      /**
317       * Removes and returns the least element of this queue.
318       *
319       * @throws NoSuchElementException if the queue is empty
320       */
321      public E removeFirst() {
322        return remove();
323      }
324    
325      /**
326       * Retrieves, but does not remove, the least element of this queue, or returns
327       * {@code null} if the queue is empty.
328       */
329      public E peekFirst() {
330        return peek();
331      }
332    
333      /**
334       * Removes and returns the greatest element of this queue, or returns {@code
335       * null} if the queue is empty.
336       */
337      public E pollLast() {
338        return isEmpty() ? null : removeAndGet(getMaxElementIndex());
339      }
340    
341      /**
342       * Removes and returns the greatest element of this queue.
343       *
344       * @throws NoSuchElementException if the queue is empty
345       */
346      public E removeLast() {
347        if (isEmpty()) {
348          throw new NoSuchElementException();
349        }
350        return removeAndGet(getMaxElementIndex());
351      }
352    
353      /**
354       * Retrieves, but does not remove, the greatest element of this queue, or
355       * returns {@code null} if the queue is empty.
356       */
357      public E peekLast() {
358        return isEmpty() ? null : elementData(getMaxElementIndex());
359      }
360    
361      /**
362       * Removes the element at position {@code index}.
363       *
364       * <p>Normally this method leaves the elements at up to {@code index - 1},
365       * inclusive, untouched.  Under these circumstances, it returns {@code null}.
366       *
367       * <p>Occasionally, in order to maintain the heap invariant, it must swap a
368       * later element of the list with one before {@code index}. Under these
369       * circumstances it returns a pair of elements as a {@link MoveDesc}. The
370       * first one is the element that was previously at the end of the heap and is
371       * now at some position before {@code index}. The second element is the one
372       * that was swapped down to replace the element at {@code index}. This fact is
373       * used by iterator.remove so as to visit elements during a traversal once and
374       * only once.
375       */
376      @VisibleForTesting MoveDesc<E> removeAt(int index) {
377        checkPositionIndex(index, size);
378        modCount++;
379        size--;
380        if (size == index) {
381          queue[size] = null;
382          return null;
383        }
384        E toTrickle = elementData(size);
385        queue[size] = null;
386        Heap heap = heapForIndex(index);
387        // We consider elementData(index) a "hole", and we want to fill it
388        // with the last element of the heap, toTrickle.
389        // Since the last element of the heap is from the bottom level, we
390        // optimistically fill index position with elements from lower levels,
391        // moving the hole down. In most cases this reduces the number of
392        // comparisons with toTrickle, but in some cases we will need to bubble it
393        // all the way up again.
394        int vacated = heap.fillHoleAt(index);
395        // Try to see if toTrickle can be bubbled up min levels.
396        int bubbledTo = heap.bubbleUpAlternatingLevels(vacated, toTrickle);
397        if (bubbledTo == vacated) {
398          // Could not bubble toTrickle up min levels, try moving
399          // it from min level to max level (or max to min level) and bubble up
400          // there.
401          return heap.tryCrossOverAndBubbleUp(index, vacated, toTrickle);
402        } else {
403          return (bubbledTo < index)
404              ? new MoveDesc<E>(toTrickle, elementData(index))
405              : null;
406        }
407      }
408    
409      // Returned from removeAt() to iterator.remove()
410      static class MoveDesc<E> {
411        final E toTrickle;
412        final E replaced;
413    
414        MoveDesc(E toTrickle, E replaced) {
415          this.toTrickle = toTrickle;
416          this.replaced = replaced;
417        }
418      }
419    
420      /**
421       * Removes and returns the value at {@code index}.
422       */
423      private E removeAndGet(int index) {
424        E value = elementData(index);
425        removeAt(index);
426        return value;
427      }
428    
429      private Heap heapForIndex(int i) {
430        return isEvenLevel(i) ? minHeap : maxHeap;
431      }
432    
433      private static final int EVEN_POWERS_OF_TWO = 0x55555555;
434      private static final int ODD_POWERS_OF_TWO = 0xaaaaaaaa;
435    
436      @VisibleForTesting static boolean isEvenLevel(int index) {
437        int oneBased = index + 1;
438        checkState(oneBased > 0, "negative index");
439        return (oneBased & EVEN_POWERS_OF_TWO) > (oneBased & ODD_POWERS_OF_TWO);
440      }
441    
442      /**
443       * Returns {@code true} if the MinMax heap structure holds. This is only used
444       * in testing.
445       *
446       * TODO(kevinb): move to the test class?
447       */
448      @VisibleForTesting boolean isIntact() {
449        for (int i = 1; i < size; i++) {
450          if (!heapForIndex(i).verifyIndex(i)) {
451            return false;
452          }
453        }
454        return true;
455      }
456    
457      /**
458       * Each instance of MinMaxPriortyQueue encapsulates two instances of Heap:
459       * a min-heap and a max-heap. Conceptually, these might each have their own
460       * array for storage, but for efficiency's sake they are stored interleaved on
461       * alternate heap levels in the same array (MMPQ.queue).
462       */
463      private class Heap {
464        final Ordering<E> ordering;
465        Heap otherHeap;
466    
467        Heap(Ordering<E> ordering) {
468          this.ordering = ordering;
469        }
470    
471        int compareElements(int a, int b) {
472          return ordering.compare(elementData(a), elementData(b));
473        }
474    
475        /**
476         * Tries to move {@code toTrickle} from a min to a max level and
477         * bubble up there. If it moved before {@code removeIndex} this method
478         * returns a pair as described in {@link #removeAt}.
479         */
480        MoveDesc<E> tryCrossOverAndBubbleUp(
481            int removeIndex, int vacated, E toTrickle) {
482          int crossOver = crossOver(vacated, toTrickle);
483          if (crossOver == vacated) {
484            return null;
485          }
486          // Successfully crossed over from min to max.
487          // Bubble up max levels.
488          E parent;
489          // If toTrickle is moved up to a parent of removeIndex, the parent is
490          // placed in removeIndex position. We must return that to the iterator so
491          // that it knows to skip it.
492          if (crossOver < removeIndex) {
493            // We crossed over to the parent level in crossOver, so the parent
494            // has already been moved.
495            parent = elementData(removeIndex);
496          } else {
497            parent = elementData(getParentIndex(removeIndex));
498          }
499          // bubble it up the opposite heap
500          if (otherHeap.bubbleUpAlternatingLevels(crossOver, toTrickle)
501              < removeIndex) {
502            return new MoveDesc<E>(toTrickle, parent);
503          } else {
504            return null;
505          }
506        }
507    
508        /**
509         * Bubbles a value from {@code index} up the appropriate heap if required.
510         */
511        void bubbleUp(int index, E x) {
512          int crossOver = crossOverUp(index, x);
513    
514          Heap heap;
515          if (crossOver == index) {
516            heap = this;
517          } else {
518            index = crossOver;
519            heap = otherHeap;
520          }
521          heap.bubbleUpAlternatingLevels(index, x);
522        }
523    
524        /**
525         * Bubbles a value from {@code index} up the levels of this heap, and
526         * returns the index the element ended up at.
527         */
528        int bubbleUpAlternatingLevels(int index, E x) {
529          while (index > 2) {
530            int grandParentIndex = getGrandparentIndex(index);
531            E e = elementData(grandParentIndex);
532            if (ordering.compare(e, x) <= 0) {
533              break;
534            }
535            queue[index] = e;
536            index = grandParentIndex;
537          }
538          queue[index] = x;
539          return index;
540        }
541    
542        /**
543         * Returns the index of minimum value between {@code index} and
544         * {@code index + len}, or {@code -1} if {@code index} is greater than
545         * {@code size}.
546         */
547        int findMin(int index, int len) {
548          if (index >= size) {
549            return -1;
550          }
551          checkState(index > 0);
552          int limit = Math.min(index, size - len) + len;
553          int minIndex = index;
554          for (int i = index + 1; i < limit; i++) {
555            if (compareElements(i, minIndex) < 0) {
556              minIndex = i;
557            }
558          }
559          return minIndex;
560        }
561    
562        /**
563         * Returns the minimum child or {@code -1} if no child exists.
564         */
565        int findMinChild(int index) {
566          return findMin(getLeftChildIndex(index), 2);
567        }
568    
569        /**
570         * Returns the minimum grand child or -1 if no grand child exists.
571         */
572        int findMinGrandChild(int index) {
573          int leftChildIndex = getLeftChildIndex(index);
574          if (leftChildIndex < 0) {
575            return -1;
576          }
577          return findMin(getLeftChildIndex(leftChildIndex), 4);
578        }
579    
580        /**
581         * Moves an element one level up from a min level to a max level
582         * (or vice versa).
583         * Returns the new position of the element.
584         */
585        int crossOverUp(int index, E x) {
586          if (index == 0) {
587            queue[0] = x;
588            return 0;
589          }
590          int parentIndex = getParentIndex(index);
591          E parentElement = elementData(parentIndex);
592          if (ordering.compare(parentElement, x) < 0) {
593            queue[index] = parentElement;
594            queue[parentIndex] = x;
595            return parentIndex;
596          }
597          queue[index] = x;
598          return index;
599        }
600    
601        /**
602         * Crosses an element over to the opposite heap by moving it one level down
603         * (or up if there are no elements below it).
604         *
605         * Returns the new position of the element.
606         */
607        int crossOver(int index, E x) {
608          int minChildIndex = findMinChild(index);
609          // TODO(kevinb): split the && into two if's and move crossOverUp so it's
610          // only called when there's no child.
611          if ((minChildIndex > 0)
612              && (ordering.compare(elementData(minChildIndex), x) < 0)) {
613            queue[index] = elementData(minChildIndex);
614            queue[minChildIndex] = x;
615            return minChildIndex;
616          }
617          return crossOverUp(index, x);
618        }
619    
620        /**
621         * Fills the hole at {@code index} by moving in the least of its
622         * grandchildren to this position, then recursively filling the new hole
623         * created.
624         *
625         * @return the position of the new hole (where the lowest grandchild moved
626         *     from, that had no grandchild to replace it)
627         */
628        int fillHoleAt(int index) {
629          int minGrandchildIndex;
630          while ((minGrandchildIndex = findMinGrandChild(index)) > 0) {
631            queue[index] = elementData(minGrandchildIndex);
632            index = minGrandchildIndex;
633          }
634          return index;
635        }
636    
637        private boolean verifyIndex(int i) {
638          if ((getLeftChildIndex(i) < size)
639              && (compareElements(i, getLeftChildIndex(i)) > 0)) {
640            return false;
641          }
642          if ((getRightChildIndex(i) < size)
643              && (compareElements(i, getRightChildIndex(i)) > 0)) {
644            return false;
645          }
646          if ((i > 0) && (compareElements(i, getParentIndex(i)) > 0)) {
647            return false;
648          }
649          if ((i > 2) && (compareElements(getGrandparentIndex(i), i) > 0)) {
650            return false;
651          }
652          return true;
653        }
654    
655        // These would be static if inner classes could have static members.
656    
657        private int getLeftChildIndex(int i) {
658          return i * 2 + 1;
659        }
660    
661        private int getRightChildIndex(int i) {
662          return i * 2 + 2;
663        }
664    
665        private int getParentIndex(int i) {
666          return (i - 1) / 2;
667        }
668    
669        private int getGrandparentIndex(int i) {
670          return getParentIndex(getParentIndex(i)); // (i - 3) / 4
671        }
672      }
673    
674      /**
675       * Iterates the elements of the queue in no particular order.
676       *
677       * If the underlying queue is modified during iteration an exception will be
678       * thrown.
679       */
680      private class QueueIterator implements Iterator<E> {
681        private int cursor = -1;
682        private int expectedModCount = modCount;
683        // TODO(user): Switch to ArrayDeque once Guava supports it.
684        private Queue<E> forgetMeNot;
685        private List<E> skipMe;
686        private E lastFromForgetMeNot;
687        private boolean canRemove;
688    
689        @Override public boolean hasNext() {
690          checkModCount();
691          return (nextNotInSkipMe(cursor + 1) < size())
692              || ((forgetMeNot != null) && !forgetMeNot.isEmpty());
693        }
694    
695        @Override public E next() {
696          checkModCount();
697          int tempCursor = nextNotInSkipMe(cursor + 1);
698          if (tempCursor < size()) {
699            cursor = tempCursor;
700            canRemove = true;
701            return elementData(cursor);
702          } else if (forgetMeNot != null) {
703            cursor = size();
704            lastFromForgetMeNot = forgetMeNot.poll();
705            if (lastFromForgetMeNot != null) {
706              canRemove = true;
707              return lastFromForgetMeNot;
708            }
709          }
710          throw new NoSuchElementException(
711              "iterator moved past last element in queue.");
712        }
713    
714        @Override public void remove() {
715          checkState(canRemove,
716              "no calls to remove() since the last call to next()");
717          checkModCount();
718          canRemove = false;
719          expectedModCount++;
720          if (cursor < size()) {
721            MoveDesc<E> moved = removeAt(cursor);
722            if (moved != null) {
723              if (forgetMeNot == null) {
724                forgetMeNot = new LinkedList<E>();
725                skipMe = new ArrayList<E>(3);
726              }
727              forgetMeNot.add(moved.toTrickle);
728              skipMe.add(moved.replaced);
729            }
730            cursor--;
731          } else { // we must have set lastFromForgetMeNot in next()
732            checkState(removeExact(lastFromForgetMeNot));
733            lastFromForgetMeNot = null;
734          }
735        }
736    
737        // Finds only this exact instance, not others that are equals()
738        private boolean containsExact(Iterable<E> elements, E target) {
739          for (E element : elements) {
740            if (element == target) {
741              return true;
742            }
743          }
744          return false;
745        }
746    
747        // Removes only this exact instance, not others that are equals()
748        boolean removeExact(Object target) {
749          for (int i = 0; i < size; i++) {
750            if (queue[i] == target) {
751              removeAt(i);
752              return true;
753            }
754          }
755          return false;
756        }
757    
758        void checkModCount() {
759          if (modCount != expectedModCount) {
760            throw new ConcurrentModificationException();
761          }
762        }
763    
764        /**
765         * Returns the index of the first element after {@code c} that is not in
766         * {@code skipMe} and returns {@code size()} if there is no such element.
767         */
768        private int nextNotInSkipMe(int c) {
769          if (skipMe != null) {
770            while (c < size() && containsExact(skipMe, elementData(c))) {
771              c++;
772            }
773          }
774          return c;
775        }
776      }
777    
778      /**
779       * Returns an iterator over the elements contained in this collection,
780       * <i>in no particular order</i>.
781       *
782       * <p>The iterator is <i>fail-fast</i>: If the MinMaxPriorityQueue is modified
783       * at any time after the iterator is created, in any way except through the
784       * iterator's own remove method, the iterator will generally throw a
785       * {@link ConcurrentModificationException}. Thus, in the face of concurrent
786       * modification, the iterator fails quickly and cleanly, rather than risking
787       * arbitrary, non-deterministic behavior at an undetermined time in the
788       * future.
789       *
790       * <p>Note that the fail-fast behavior of an iterator cannot be guaranteed
791       * as it is, generally speaking, impossible to make any hard guarantees in the
792       * presence of unsynchronized concurrent modification.  Fail-fast iterators
793       * throw {@code ConcurrentModificationException} on a best-effort basis.
794       * Therefore, it would be wrong to write a program that depended on this
795       * exception for its correctness: <i>the fail-fast behavior of iterators
796       * should be used only to detect bugs.</i>
797       *
798       * @return an iterator over the elements contained in this collection
799       */
800      @Override public Iterator<E> iterator() {
801        return new QueueIterator();
802      }
803    
804      @Override public void clear() {
805        for (int i = 0; i < size; i++) {
806          queue[i] = null;
807        }
808        size = 0;
809      }
810    
811      @Override public Object[] toArray() {
812        Object[] copyTo = new Object[size];
813        System.arraycopy(queue, 0, copyTo, 0, size);
814        return copyTo;
815      }
816    
817      /**
818       * Returns the comparator used to order the elements in this queue. Obeys the
819       * general contract of {@link PriorityQueue#comparator}, but returns {@link
820       * Ordering#natural} instead of {@code null} to indicate natural ordering.
821       */
822      public Comparator<? super E> comparator() {
823        return minHeap.ordering;
824      }
825    
826      @VisibleForTesting int capacity() {
827        return queue.length;
828      }
829    
830      // Size/capacity-related methods
831    
832      private static final int DEFAULT_CAPACITY = 11;
833    
834      @VisibleForTesting static int initialQueueSize(int configuredExpectedSize,
835          int maximumSize, Iterable<?> initialContents) {
836        // Start with what they said, if they said it, otherwise DEFAULT_CAPACITY
837        int result = (configuredExpectedSize == Builder.UNSET_EXPECTED_SIZE)
838            ? DEFAULT_CAPACITY
839            : configuredExpectedSize;
840    
841        // Enlarge to contain initial contents
842        if (initialContents instanceof Collection) {
843          int initialSize = ((Collection<?>) initialContents).size();
844          result = Math.max(result, initialSize);
845        }
846    
847        // Now cap it at maxSize + 1
848        return capAtMaximumSize(result, maximumSize);
849      }
850    
851      private void growIfNeeded() {
852        if (size > queue.length) {
853          int newCapacity = calculateNewCapacity();
854          Object[] newQueue = new Object[newCapacity];
855          System.arraycopy(queue, 0, newQueue, 0, queue.length);
856          queue = newQueue;
857        }
858      }
859    
860      /** Returns ~2x the old capacity if small; ~1.5x otherwise. */
861      private int calculateNewCapacity() {
862        int oldCapacity = queue.length;
863        int newCapacity = (oldCapacity < 64)
864            ? (oldCapacity + 1) * 2
865            : (oldCapacity / 2) * 3;
866        if (newCapacity < 0) {
867          newCapacity = Integer.MAX_VALUE; // overflow - hotspot will throw OOME
868        }
869        return capAtMaximumSize(newCapacity, maximumSize);
870      }
871    
872      /** There's no reason for the queueSize to ever be more than maxSize + 1 */
873      private static int capAtMaximumSize(int queueSize, int maximumSize) {
874        return Math.min(queueSize - 1, maximumSize) + 1; // don't overflow
875      }
876    }