    001    /*
    002     * Copyright (C) 2010 The Guava Authors
    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    import com.google.common.math.IntMath;
    027
    028    import java.util.AbstractQueue;
    029    import java.util.ArrayDeque;
    030    import java.util.ArrayList;
    031    import java.util.Collection;
    032    import java.util.Collections;
    033    import java.util.Comparator;
    034    import java.util.ConcurrentModificationException;
    035    import java.util.Iterator;
    036    import java.util.List;
    037    import java.util.NoSuchElementException;
    038    import java.util.PriorityQueue;
    039    import java.util.Queue;
    040
    041    /**
    042     * A double-ended priority queue, which provides constant-time access to both
    043     * its least element and its greatest element, as determined by the queue's
    044     * specified comparator. If no comparator is given at construction time, the
    045     * natural order of elements is used.
    046     *
    047     * <p>As a {@link Queue} it functions exactly as a {@link PriorityQueue}: its
    048     * head element -- the implicit target of the methods {@link #peek()}, {@link
    049     * #poll()} and {@link #remove()} -- is defined as the <i>least</i> element in
    050     * the queue according to the queue's comparator. But unlike a regular priority
    051     * queue, the methods {@link #peekLast}, {@link #pollLast} and
    052     * {@link #removeLast} are also provided, to act on the <i>greatest</i> element
    053     * in the queue instead.
    054     *
    055     * <p>A min-max priority queue can be configured with a maximum size. If so,
    056     * each time the size of the queue exceeds that value, the queue automatically
    057     * removes its greatest element according to its comparator (which might be the
    058     * element that was just added). This is different from conventional bounded
    059     * queues, which either block or reject new elements when full.
    060     *
    061     * <p>This implementation is based on the
    062     * <a href="http://portal.acm.org/citation.cfm?id=6621">min-max heap</a>
    063     * developed by Atkinson, et al. Unlike many other double-ended priority queues,
    064     * it stores elements in a single array, as compact as the traditional heap data
    065     * structure used in {@link PriorityQueue}.
    066     *
    067     * <p>This class is not thread-safe, and does not accept null elements.
    068     *
    069     * <p><i>Performance notes:</i>
    070     *
    071     * <ul>
    072     * <li>The retrieval operations {@link #peek}, {@link #peekFirst}, {@link
    073     *     #peekLast}, {@link #element}, and {@link #size} are constant-time
    074     * <li>The enqueing and dequeing operations ({@link #offer}, {@link #add}, and
    075     *     all the forms of {@link #poll} and {@link #remove()}) run in {@code
    076     *     O(log n) time}
    077     * <li>The {@link #remove(Object)} and {@link #contains} operations require
    078     *     linear ({@code O(n)}) time
    079     * <li>If you only access one end of the queue, and don't use a maximum size,
    080     *     this class is functionally equivalent to {@link PriorityQueue}, but
    081     *     significantly slower.
    082     * </ul>
    083     *
    084     * @author Sverre Sundsdal
    085     * @author Torbjorn Gannholm
    086     * @since 8.0
    087     */
    088    // TODO(kevinb): GWT compatibility
    089    @Beta
    090    public final class MinMaxPriorityQueue<E> extends AbstractQueue<E> {
    091
    092      /**
    093       * Creates a new min-max priority queue with default settings: natural order,
    094       * no maximum size, no initial contents, and an initial expected size of 11.
    095       */
    096      public static <E extends Comparable<E>> MinMaxPriorityQueue<E> create() {
    097        return new Builder<Comparable>(Ordering.natural()).create();
    098      }
    099
    100      /**
    101       * Creates a new min-max priority queue using natural order, no maximum size,
    102       * and initially containing the given elements.
    103       */
    104      public static <E extends Comparable<E>> MinMaxPriorityQueue<E> create(
    105          Iterable<? extends E> initialContents) {
    106        return new Builder<E>(Ordering.<E>natural()).create(initialContents);
    107      }
    108
    109      /**
    110       * Creates and returns a new builder, configured to build {@code
    111       * MinMaxPriorityQueue} instances that use {@code comparator} to determine the
    112       * least and greatest elements.
    113       */
    114      public static <B> Builder<B> orderedBy(Comparator<B> comparator) {
    115        return new Builder<B>(comparator);
    116      }
    117
    118      /**
    119       * Creates and returns a new builder, configured to build {@code
    120       * MinMaxPriorityQueue} instances sized appropriately to hold {@code
    121       * expectedSize} elements.
    122       */
    123      public static Builder<Comparable> expectedSize(int expectedSize) {
    124        return new Builder<Comparable>(Ordering.natural())
    125            .expectedSize(expectedSize);
    126      }
    127
    128      /**
    129       * Creates and returns a new builder, configured to build {@code
    130       * MinMaxPriorityQueue} instances that are limited to {@code maximumSize}
    131       * elements. Each time a queue grows beyond this bound, it immediately
    132       * removes its greatest element (according to its comparator), which might be
    133       * the element that was just added.
    134       */
    135      public static Builder<Comparable> maximumSize(int maximumSize) {
    136        return new Builder<Comparable>(Ordering.natural())
    137            .maximumSize(maximumSize);
    138      }
    139
    140      /**
    141       * The builder class used in creation of min-max priority queues. Instead of
    142       * constructing one directly, use {@link
    143       * MinMaxPriorityQueue#orderedBy(Comparator)}, {@link
    144       * MinMaxPriorityQueue#expectedSize(int)} or {@link
    145       * MinMaxPriorityQueue#maximumSize(int)}.
    146       *
    147       * @param <B> the upper bound on the eventual type that can be produced by
    148       *     this builder (for example, a {@code Builder<Number>} can produce a
    149       *     {@code Queue<Number>} or {@code Queue<Integer>} but not a {@code
    150       *     Queue<Object>}).
    151       * @since 8.0
    152       */
    153      @Beta
    154      public static final class Builder<B> {
    155        /*
    156         * TODO(kevinb): when the dust settles, see if we still need this or can
    157         * just default to DEFAULT_CAPACITY.
    158         */
    159        private static final int UNSET_EXPECTED_SIZE = -1;
    160
    161        private final Comparator<B> comparator;
    162        private int expectedSize = UNSET_EXPECTED_SIZE;
    163        private int maximumSize = Integer.MAX_VALUE;
    164
    165        private Builder(Comparator<B> comparator) {
    166          this.comparator = checkNotNull(comparator);
    167        }
    168
    169        /**
    170         * Configures this builder to build min-max priority queues with an initial
    171         * expected size of {@code expectedSize}.
    172         */
    173        public Builder<B> expectedSize(int expectedSize) {
    174          checkArgument(expectedSize >= 0);
    175          this.expectedSize = expectedSize;
    176          return this;
    177        }
    178
    179        /**
    180         * Configures this builder to build {@code MinMaxPriorityQueue} instances
    181         * that are limited to {@code maximumSize} elements. Each time a queue grows
    182         * beyond this bound, it immediately removes its greatest element (according
    183         * to its comparator), which might be the element that was just added.
    184         */
    185        public Builder<B> maximumSize(int maximumSize) {
    186          checkArgument(maximumSize > 0);
    187          this.maximumSize = maximumSize;
    188          return this;
    189        }
    190
    191        /**
    192         * Builds a new min-max priority queue using the previously specified
    193         * options, and having no initial contents.
    194         */
    195        public <T extends B> MinMaxPriorityQueue<T> create() {
    196          return create(Collections.<T>emptySet());
    197        }
    198
    199        /**
    200         * Builds a new min-max priority queue using the previously specified
    201         * options, and having the given initial elements.
    202         */
    203        public <T extends B> MinMaxPriorityQueue<T> create(
    204            Iterable<? extends T> initialContents) {
    205          MinMaxPriorityQueue<T> queue = new MinMaxPriorityQueue<T>(
    206              this, initialQueueSize(expectedSize, maximumSize, initialContents));
    207          for (T element : initialContents) {
    208            queue.offer(element);
    209          }
    210          return queue;
    211        }
    212
    213        @SuppressWarnings("unchecked") // safe "contravariant cast"
    214        private <T extends B> Ordering<T> ordering() {
    215          return Ordering.from((Comparator<T>) comparator);
    216        }
    217      }
    218
    219      private final Heap minHeap;
    220      private final Heap maxHeap;
    221      @VisibleForTesting final int maximumSize;
    222      private Object[] queue;
    223      private int size;
    224      private int modCount;
    225
    226      private MinMaxPriorityQueue(Builder<? super E> builder, int queueSize) {
    227        Ordering<E> ordering = builder.ordering();
    228        this.minHeap = new Heap(ordering);
    229        this.maxHeap = new Heap(ordering.reverse());
    230        minHeap.otherHeap = maxHeap;
    231        maxHeap.otherHeap = minHeap;
    232
    233        this.maximumSize = builder.maximumSize;
    234        // TODO(kevinb): pad?
    235        this.queue = new Object[queueSize];
    236      }
    237
    238      @Override public int size() {
    239        return size;
    240      }
    241
    242      /**
    243       * Adds the given element to this queue. If this queue has a maximum size,
    244       * after adding {@code element} the queue will automatically evict its
    245       * greatest element (according to its comparator), which may be {@code
    246       * element} itself.
    247       *
    248       * @return {@code true} always
    249       */
    250      @Override public boolean add(E element) {
    251        offer(element);
    252        return true;
    253      }
    254
    255      @Override public boolean addAll(Collection<? extends E> newElements) {
    256        boolean modified = false;
    257        for (E element : newElements) {
    258          offer(element);
    259          modified = true;
    260        }
    261        return modified;
    262      }
    263
    264      /**
    265       * Adds the given element to this queue. If this queue has a maximum size,
    266       * after adding {@code element} the queue will automatically evict its
    267       * greatest element (according to its comparator), which may be {@code
    268       * element} itself.
    269       */
    270      @Override public boolean offer(E element) {
    271        checkNotNull(element);
    272        modCount++;
    273        int insertIndex = size++;
    274
    275        growIfNeeded();
    276
    277        // Adds the element to the end of the heap and bubbles it up to the correct
    278        // position.
    279        heapForIndex(insertIndex).bubbleUp(insertIndex, element);
    280        return size <= maximumSize || pollLast() != element;
    281      }
    282
    283      @Override public E poll() {
    284        return isEmpty() ? null : removeAndGet(0);
    285      }
    286
    287      @SuppressWarnings("unchecked") // we must carefully only allow Es to get in
    288      E elementData(int index) {
    289        return (E) queue[index];
    290      }
    291
    292      @Override public E peek() {
    293        return isEmpty() ? null : elementData(0);
    294      }
    295
    296      /**
    297       * Returns the index of the max element.
    298       */
    299      private int getMaxElementIndex() {
    300        switch (size) {
    301          case 1:
    302            return 0; // The lone element in the queue is the maximum.
    303          case 2:
    304            return 1; // The lone element in the maxHeap is the maximum.
    305          default:
    306            // The max element must sit on the first level of the maxHeap. It is
    307            // actually the *lesser* of the two from the maxHeap's perspective.
    308            return (maxHeap.compareElements(1, 2) <= 0) ? 1 : 2;
    309        }
    310      }
    311
    312      /**
    313       * Removes and returns the least element of this queue, or returns {@code
    314       * null} if the queue is empty.
    315       */
    316      public E pollFirst() {
    317        return poll();
    318      }
    319
    320      /**
    321       * Removes and returns the least element of this queue.
    322       *
    323       * @throws NoSuchElementException if the queue is empty
    324       */
    325      public E removeFirst() {
    326        return remove();
    327      }
    328
    329      /**
    330       * Retrieves, but does not remove, the least element of this queue, or returns
    331       * {@code null} if the queue is empty.
    332       */
    333      public E peekFirst() {
    334        return peek();
    335      }
    336
    337      /**
    338       * Removes and returns the greatest element of this queue, or returns {@code
    339       * null} if the queue is empty.
    340       */
    341      public E pollLast() {
    342        return isEmpty() ? null : removeAndGet(getMaxElementIndex());
    343      }
    344
    345      /**
    346       * Removes and returns the greatest element of this queue.
    347       *
    348       * @throws NoSuchElementException if the queue is empty
    349       */
    350      public E removeLast() {
    351        if (isEmpty()) {
    352          throw new NoSuchElementException();
    353        }
    354        return removeAndGet(getMaxElementIndex());
    355      }
    356
    357      /**
    358       * Retrieves, but does not remove, the greatest element of this queue, or
    359       * returns {@code null} if the queue is empty.
    360       */
    361      public E peekLast() {
    362        return isEmpty() ? null : elementData(getMaxElementIndex());
    363      }
    364
    365      /**
    366       * Removes the element at position {@code index}.
    367       *
    368       * <p>Normally this method leaves the elements at up to {@code index - 1},
    369       * inclusive, untouched.  Under these circumstances, it returns {@code null}.
    370       *
    371       * <p>Occasionally, in order to maintain the heap invariant, it must swap a
    372       * later element of the list with one before {@code index}. Under these
    373       * circumstances it returns a pair of elements as a {@link MoveDesc}. The
    374       * first one is the element that was previously at the end of the heap and is
    375       * now at some position before {@code index}. The second element is the one
    376       * that was swapped down to replace the element at {@code index}. This fact is
    377       * used by iterator.remove so as to visit elements during a traversal once and
    378       * only once.
    379       */
    380      @VisibleForTesting MoveDesc<E> removeAt(int index) {
    381        checkPositionIndex(index, size);
    382        modCount++;
    383        size--;
    384        if (size == index) {
    385          queue[size] = null;
    386          return null;
    387        }
    388        E actualLastElement = elementData(size);
    389        int lastElementAt = heapForIndex(size)
    390            .getCorrectLastElement(actualLastElement);
    391        E toTrickle = elementData(size);
    392        queue[size] = null;
    393        MoveDesc<E> changes = fillHole(index, toTrickle);
    394        if (lastElementAt < index) {
    395          // Last element is moved to before index, swapped with trickled element.
    396          if (changes == null) {
    397            // The trickled element is still after index.
    398            return new MoveDesc<E>(actualLastElement, toTrickle);
    399          } else {
    400            // The trickled element is back before index, but the replaced element
    401            // has now been moved after index.
    402            return new MoveDesc<E>(actualLastElement, changes.replaced);
    403          }
    404        }
    405        // Trickled element was after index to begin with, no adjustment needed.
    406        return changes;
    407      }
    408
    409      private MoveDesc<E> fillHole(int index, E toTrickle) {
    410        Heap heap = heapForIndex(index);
    411        // We consider elementData(index) a "hole", and we want to fill it
    412        // with the last element of the heap, toTrickle.
    413        // Since the last element of the heap is from the bottom level, we
    414        // optimistically fill index position with elements from lower levels,
    415        // moving the hole down. In most cases this reduces the number of
    416        // comparisons with toTrickle, but in some cases we will need to bubble it
    417        // all the way up again.
    418        int vacated = heap.fillHoleAt(index);
    419        // Try to see if toTrickle can be bubbled up min levels.
    420        int bubbledTo = heap.bubbleUpAlternatingLevels(vacated, toTrickle);
    421        if (bubbledTo == vacated) {
    422          // Could not bubble toTrickle up min levels, try moving
    423          // it from min level to max level (or max to min level) and bubble up
    424          // there.
    425          return heap.tryCrossOverAndBubbleUp(index, vacated, toTrickle);
    426        } else {
    427          return (bubbledTo < index)
    428              ? new MoveDesc<E>(toTrickle, elementData(index))
    429              : null;
    430        }
    431      }
    432
    433      // Returned from removeAt() to iterator.remove()
    434      static class MoveDesc<E> {
    435        final E toTrickle;
    436        final E replaced;
    437
    438        MoveDesc(E toTrickle, E replaced) {
    439          this.toTrickle = toTrickle;
    440          this.replaced = replaced;
    441        }
    442      }
    443
    444      /**
    445       * Removes and returns the value at {@code index}.
    446       */
    447      private E removeAndGet(int index) {
    448        E value = elementData(index);
    449        removeAt(index);
    450        return value;
    451      }
    452
    453      private Heap heapForIndex(int i) {
    454        return isEvenLevel(i) ? minHeap : maxHeap;
    455      }
    456
    457      private static final int EVEN_POWERS_OF_TWO = 0x55555555;
    458      private static final int ODD_POWERS_OF_TWO = 0xaaaaaaaa;
    459
    460      @VisibleForTesting static boolean isEvenLevel(int index) {
    461        int oneBased = index + 1;
    462        checkState(oneBased > 0, "negative index");
    463        return (oneBased & EVEN_POWERS_OF_TWO) > (oneBased & ODD_POWERS_OF_TWO);
    464      }
    465
    466      /**
    467       * Returns {@code true} if the MinMax heap structure holds. This is only used
    468       * in testing.
    469       *
    470       * TODO(kevinb): move to the test class?
    471       */
    472      @VisibleForTesting boolean isIntact() {
    473        for (int i = 1; i < size; i++) {
    474          if (!heapForIndex(i).verifyIndex(i)) {
    475            return false;
    476          }
    477        }
    478        return true;
    479      }
    480
    481      /**
    482       * Each instance of MinMaxPriortyQueue encapsulates two instances of Heap:
    483       * a min-heap and a max-heap. Conceptually, these might each have their own
    484       * array for storage, but for efficiency's sake they are stored interleaved on
    485       * alternate heap levels in the same array (MMPQ.queue).
    486       */
    487      private class Heap {
    488        final Ordering<E> ordering;
    489        Heap otherHeap;
    490
    491        Heap(Ordering<E> ordering) {
    492          this.ordering = ordering;
    493        }
    494
    495        int compareElements(int a, int b) {
    496          return ordering.compare(elementData(a), elementData(b));
    497        }
    498
    499        /**
    500         * Tries to move {@code toTrickle} from a min to a max level and
    501         * bubble up there. If it moved before {@code removeIndex} this method
    502         * returns a pair as described in {@link #removeAt}.
    503         */
    504        MoveDesc<E> tryCrossOverAndBubbleUp(
    505            int removeIndex, int vacated, E toTrickle) {
    506          int crossOver = crossOver(vacated, toTrickle);
    507          if (crossOver == vacated) {
    508            return null;
    509          }
    510          // Successfully crossed over from min to max.
    511          // Bubble up max levels.
    512          E parent;
    513          // If toTrickle is moved up to a parent of removeIndex, the parent is
    514          // placed in removeIndex position. We must return that to the iterator so
    515          // that it knows to skip it.
    516          if (crossOver < removeIndex) {
    517            // We crossed over to the parent level in crossOver, so the parent
    518            // has already been moved.
    519            parent = elementData(removeIndex);
    520          } else {
    521            parent = elementData(getParentIndex(removeIndex));
    522          }
    523          // bubble it up the opposite heap
    524          if (otherHeap.bubbleUpAlternatingLevels(crossOver, toTrickle)
    525              < removeIndex) {
    526            return new MoveDesc<E>(toTrickle, parent);
    527          } else {
    528            return null;
    529          }
    530        }
    531
    532        /**
    533         * Bubbles a value from {@code index} up the appropriate heap if required.
    534         */
    535        void bubbleUp(int index, E x) {
    536          int crossOver = crossOverUp(index, x);
    537
    538          Heap heap;
    539          if (crossOver == index) {
    540            heap = this;
    541          } else {
    542            index = crossOver;
    543            heap = otherHeap;
    544          }
    545          heap.bubbleUpAlternatingLevels(index, x);
    546        }
    547
    548        /**
    549         * Bubbles a value from {@code index} up the levels of this heap, and
    550         * returns the index the element ended up at.
    551         */
    552        int bubbleUpAlternatingLevels(int index, E x) {
    553          while (index > 2) {
    554            int grandParentIndex = getGrandparentIndex(index);
    555            E e = elementData(grandParentIndex);
    556            if (ordering.compare(e, x) <= 0) {
    557              break;
    558            }
    559            queue[index] = e;
    560            index = grandParentIndex;
    561          }
    562          queue[index] = x;
    563          return index;
    564        }
    565
    566        /**
    567         * Returns the index of minimum value between {@code index} and
    568         * {@code index + len}, or {@code -1} if {@code index} is greater than
    569         * {@code size}.
    570         */
    571        int findMin(int index, int len) {
    572          if (index >= size) {
    573            return -1;
    574          }
    575          checkState(index > 0);
    576          int limit = Math.min(index, size - len) + len;
    577          int minIndex = index;
    578          for (int i = index + 1; i < limit; i++) {
    579            if (compareElements(i, minIndex) < 0) {
    580              minIndex = i;
    581            }
    582          }
    583          return minIndex;
    584        }
    585
    586        /**
    587         * Returns the minimum child or {@code -1} if no child exists.
    588         */
    589        int findMinChild(int index) {
    590          return findMin(getLeftChildIndex(index), 2);
    591        }
    592
    593        /**
    594         * Returns the minimum grand child or -1 if no grand child exists.
    595         */
    596        int findMinGrandChild(int index) {
    597          int leftChildIndex = getLeftChildIndex(index);
    598          if (leftChildIndex < 0) {
    599            return -1;
    600          }
    601          return findMin(getLeftChildIndex(leftChildIndex), 4);
    602        }
    603
    604        /**
    605         * Moves an element one level up from a min level to a max level
    606         * (or vice versa).
    607         * Returns the new position of the element.
    608         */
    609        int crossOverUp(int index, E x) {
    610          if (index == 0) {
    611            queue[0] = x;
    612            return 0;
    613          }
    614          int parentIndex = getParentIndex(index);
    615          E parentElement = elementData(parentIndex);
    616          if (parentIndex != 0) {
    617            // This is a guard for the case of the childless uncle.
    618            // Since the end of the array is actually the middle of the heap,
    619            // a smaller childless uncle can become a child of x when we
    620            // bubble up alternate levels, violating the invariant.
    621            int grandparentIndex = getParentIndex(parentIndex);
    622            int uncleIndex = getRightChildIndex(grandparentIndex);
    623            if (uncleIndex != parentIndex
    624                && getLeftChildIndex(uncleIndex) >= size) {
    625              E uncleElement = elementData(uncleIndex);
    626              if (ordering.compare(uncleElement, parentElement) < 0) {
    627                parentIndex = uncleIndex;
    628                parentElement = uncleElement;
    629              }
    630            }
    631          }
    632          if (ordering.compare(parentElement, x) < 0) {
    633            queue[index] = parentElement;
    634            queue[parentIndex] = x;
    635            return parentIndex;
    636          }
    637          queue[index] = x;
    638          return index;
    639        }
    640
    641        /**
    642         * Returns the conceptually correct last element of the heap.
    643         *
    644         * <p>Since the last element of the array is actually in the
    645         * middle of the sorted structure, a childless uncle node could be
    646         * smaller, which would corrupt the invariant if this element
    647         * becomes the new parent of the uncle. In that case, we first
    648         * switch the last element with its uncle, before returning.
    649         */
    650        int getCorrectLastElement(E actualLastElement) {
    651          int parentIndex = getParentIndex(size);
    652          if (parentIndex != 0) {
    653            int grandparentIndex = getParentIndex(parentIndex);
    654            int uncleIndex = getRightChildIndex(grandparentIndex);
    655            if (uncleIndex != parentIndex
    656                && getLeftChildIndex(uncleIndex) >= size) {
    657              E uncleElement = elementData(uncleIndex);
    658              if (ordering.compare(uncleElement, actualLastElement) < 0) {
    659                queue[uncleIndex] = actualLastElement;
    660                queue[size] = uncleElement;
    661                return uncleIndex;
    662              }
    663            }
    664          }
    665          return size;
    666        }
    667
    668        /**
    669         * Crosses an element over to the opposite heap by moving it one level down
    670         * (or up if there are no elements below it).
    671         *
    672         * Returns the new position of the element.
    673         */
    674        int crossOver(int index, E x) {
    675          int minChildIndex = findMinChild(index);
    676          // TODO(kevinb): split the && into two if's and move crossOverUp so it's
    677          // only called when there's no child.
    678          if ((minChildIndex > 0)
    679              && (ordering.compare(elementData(minChildIndex), x) < 0)) {
    680            queue[index] = elementData(minChildIndex);
    681            queue[minChildIndex] = x;
    682            return minChildIndex;
    683          }
    684          return crossOverUp(index, x);
    685        }
    686
    687        /**
    688         * Fills the hole at {@code index} by moving in the least of its
    689         * grandchildren to this position, then recursively filling the new hole
    690         * created.
    691         *
    692         * @return the position of the new hole (where the lowest grandchild moved
    693         *     from, that had no grandchild to replace it)
    694         */
    695        int fillHoleAt(int index) {
    696          int minGrandchildIndex;
    697          while ((minGrandchildIndex = findMinGrandChild(index)) > 0) {
    698            queue[index] = elementData(minGrandchildIndex);
    699            index = minGrandchildIndex;
    700          }
    701          return index;
    702        }
    703
    704        private boolean verifyIndex(int i) {
    705          if ((getLeftChildIndex(i) < size)
    706              && (compareElements(i, getLeftChildIndex(i)) > 0)) {
    707            return false;
    708          }
    709          if ((getRightChildIndex(i) < size)
    710              && (compareElements(i, getRightChildIndex(i)) > 0)) {
    711            return false;
    712          }
    713          if ((i > 0) && (compareElements(i, getParentIndex(i)) > 0)) {
    714            return false;
    715          }
    716          if ((i > 2) && (compareElements(getGrandparentIndex(i), i) > 0)) {
    717            return false;
    718          }
    719          return true;
    720        }
    721
    722        // These would be static if inner classes could have static members.
    723
    724        private int getLeftChildIndex(int i) {
    725          return i * 2 + 1;
    726        }
    727
    728        private int getRightChildIndex(int i) {
    729          return i * 2 + 2;
    730        }
    731
    732        private int getParentIndex(int i) {
    733          return (i - 1) / 2;
    734        }
    735
    736        private int getGrandparentIndex(int i) {
    737          return getParentIndex(getParentIndex(i)); // (i - 3) / 4
    738        }
    739      }
    740
    741      /**
    742       * Iterates the elements of the queue in no particular order.
    743       *
    744       * If the underlying queue is modified during iteration an exception will be
    745       * thrown.
    746       */
    747      private class QueueIterator implements Iterator<E> {
    748        private int cursor = -1;
    749        private int expectedModCount = modCount;
    750        private Queue<E> forgetMeNot;
    751        private List<E> skipMe;
    752        private E lastFromForgetMeNot;
    753        private boolean canRemove;
    754
    755        @Override public boolean hasNext() {
    756          checkModCount();
    757          return (nextNotInSkipMe(cursor + 1) < size())
    758              || ((forgetMeNot != null) && !forgetMeNot.isEmpty());
    759        }
    760
    761        @Override public E next() {
    762          checkModCount();
    763          int tempCursor = nextNotInSkipMe(cursor + 1);
    764          if (tempCursor < size()) {
    765            cursor = tempCursor;
    766            canRemove = true;
    767            return elementData(cursor);
    768          } else if (forgetMeNot != null) {
    769            cursor = size();
    770            lastFromForgetMeNot = forgetMeNot.poll();
    771            if (lastFromForgetMeNot != null) {
    772              canRemove = true;
    773              return lastFromForgetMeNot;
    774            }
    775          }
    776          throw new NoSuchElementException(
    777              "iterator moved past last element in queue.");
    778        }
    779
    780        @Override public void remove() {
    781          checkState(canRemove,
    782              "no calls to remove() since the last call to next()");
    783          checkModCount();
    784          canRemove = false;
    785          expectedModCount++;
    786          if (cursor < size()) {
    787            MoveDesc<E> moved = removeAt(cursor);
    788            if (moved != null) {
    789              if (forgetMeNot == null) {
    790                forgetMeNot = new ArrayDeque<E>();
    791                skipMe = new ArrayList<E>(3);
    792              }
    793              forgetMeNot.add(moved.toTrickle);
    794              skipMe.add(moved.replaced);
    795            }
    796            cursor--;
    797          } else { // we must have set lastFromForgetMeNot in next()
    798            checkState(removeExact(lastFromForgetMeNot));
    799            lastFromForgetMeNot = null;
    800          }
    801        }
    802
    803        // Finds only this exact instance, not others that are equals()
    804        private boolean containsExact(Iterable<E> elements, E target) {
    805          for (E element : elements) {
    806            if (element == target) {
    807              return true;
    808            }
    809          }
    810          return false;
    811        }
    812
    813        // Removes only this exact instance, not others that are equals()
    814        boolean removeExact(Object target) {
    815          for (int i = 0; i < size; i++) {
    816            if (queue[i] == target) {
    817              removeAt(i);
    818              return true;
    819            }
    820          }
    821          return false;
    822        }
    823
    824        void checkModCount() {
    825          if (modCount != expectedModCount) {
    826            throw new ConcurrentModificationException();
    827          }
    828        }
    829
    830        /**
    831         * Returns the index of the first element after {@code c} that is not in
    832         * {@code skipMe} and returns {@code size()} if there is no such element.
    833         */
    834        private int nextNotInSkipMe(int c) {
    835          if (skipMe != null) {
    836            while (c < size() && containsExact(skipMe, elementData(c))) {
    837              c++;
    838            }
    839          }
    840          return c;
    841        }
    842      }
    843
    844      /**
    845       * Returns an iterator over the elements contained in this collection,
    846       * <i>in no particular order</i>.
    847       *
    848       * <p>The iterator is <i>fail-fast</i>: If the MinMaxPriorityQueue is modified
    849       * at any time after the iterator is created, in any way except through the
    850       * iterator's own remove method, the iterator will generally throw a
    851       * {@link ConcurrentModificationException}. Thus, in the face of concurrent
    852       * modification, the iterator fails quickly and cleanly, rather than risking
    853       * arbitrary, non-deterministic behavior at an undetermined time in the
    854       * future.
    855       *
    856       * <p>Note that the fail-fast behavior of an iterator cannot be guaranteed
    857       * as it is, generally speaking, impossible to make any hard guarantees in the
    858       * presence of unsynchronized concurrent modification.  Fail-fast iterators
    859       * throw {@code ConcurrentModificationException} on a best-effort basis.
    860       * Therefore, it would be wrong to write a program that depended on this
    861       * exception for its correctness: <i>the fail-fast behavior of iterators
    862       * should be used only to detect bugs.</i>
    863       *
    864       * @return an iterator over the elements contained in this collection
    865       */
    866      @Override public Iterator<E> iterator() {
    867        return new QueueIterator();
    868      }
    869
    870      @Override public void clear() {
    871        for (int i = 0; i < size; i++) {
    872          queue[i] = null;
    873        }
    874        size = 0;
    875      }
    876
    877      @Override public Object[] toArray() {
    878        Object[] copyTo = new Object[size];
    879        System.arraycopy(queue, 0, copyTo, 0, size);
    880        return copyTo;
    881      }
    882
    883      /**
    884       * Returns the comparator used to order the elements in this queue. Obeys the
    885       * general contract of {@link PriorityQueue#comparator}, but returns {@link
    886       * Ordering#natural} instead of {@code null} to indicate natural ordering.
    887       */
    888      public Comparator<? super E> comparator() {
    889        return minHeap.ordering;
    890      }
    891
    892      @VisibleForTesting int capacity() {
    893        return queue.length;
    894      }
    895
    896      // Size/capacity-related methods
    897
    898      private static final int DEFAULT_CAPACITY = 11;
    899
    900      @VisibleForTesting static int initialQueueSize(int configuredExpectedSize,
    901          int maximumSize, Iterable<?> initialContents) {
    902        // Start with what they said, if they said it, otherwise DEFAULT_CAPACITY
    903        int result = (configuredExpectedSize == Builder.UNSET_EXPECTED_SIZE)
    904            ? DEFAULT_CAPACITY
    905            : configuredExpectedSize;
    906
    907        // Enlarge to contain initial contents
    908        if (initialContents instanceof Collection) {
    909          int initialSize = ((Collection<?>) initialContents).size();
    910          result = Math.max(result, initialSize);
    911        }
    912
    913        // Now cap it at maxSize + 1
    914        return capAtMaximumSize(result, maximumSize);
    915      }
    916
    917      private void growIfNeeded() {
    918        if (size > queue.length) {
    919          int newCapacity = calculateNewCapacity();
    920          Object[] newQueue = new Object[newCapacity];
    921          System.arraycopy(queue, 0, newQueue, 0, queue.length);
    922          queue = newQueue;
    923        }
    924      }
    925
    926      /** Returns ~2x the old capacity if small; ~1.5x otherwise. */
    927      private int calculateNewCapacity() {
    928        int oldCapacity = queue.length;
    929        int newCapacity = (oldCapacity < 64)
    930            ? (oldCapacity + 1) * 2
    931            : IntMath.checkedMultiply(oldCapacity / 2, 3);
    932        return capAtMaximumSize(newCapacity, maximumSize);
    933      }
    934
    935      /** There's no reason for the queueSize to ever be more than maxSize + 1 */
    936      private static int capAtMaximumSize(int queueSize, int maximumSize) {
    937        return Math.min(queueSize - 1, maximumSize) + 1; // don't overflow
    938      }
    939    }