guava/src/com/google/common/collect/MinMaxPriorityQueue.java

/*
 * Copyright (C) 2010 The Guava Authors
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package com.google.common.collect;

import static com.google.common.base.Preconditions.checkArgument;
import static com.google.common.base.Preconditions.checkNotNull;
import static com.google.common.base.Preconditions.checkPositionIndex;
import static com.google.common.base.Preconditions.checkState;
import static com.google.common.collect.CollectPreconditions.checkRemove;

import com.google.common.annotations.Beta;
import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.VisibleForTesting;
import com.google.common.math.IntMath;
import com.google.errorprone.annotations.CanIgnoreReturnValue;
import com.google.j2objc.annotations.Weak;
import com.google.j2objc.annotations.WeakOuter;
import java.util.AbstractQueue;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.ConcurrentModificationException;
import java.util.Iterator;
import java.util.List;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;
import java.util.Queue;
import org.checkerframework.checker.nullness.qual.MonotonicNonNull;
import org.checkerframework.checker.nullness.qual.Nullable;

/**
 * A double-ended priority queue, which provides constant-time access to both its least element and
 * its greatest element, as determined by the queue's specified comparator. If no comparator is
 * given at creation time, the natural order of elements is used. If no maximum size is given at
 * creation time, the queue is unbounded.
 *
 * <p>Usage example:
 *
 * <pre>{@code
 * MinMaxPriorityQueue<User> users = MinMaxPriorityQueue.orderedBy(userComparator)
 *     .maximumSize(1000)
 *     .create();
 * }</pre>
 *
 * <p>As a {@link Queue} it functions exactly as a {@link PriorityQueue}: its head element -- the
 * implicit target of the methods {@link #peek()}, {@link #poll()} and {@link #remove()} -- is
 * defined as the <i>least</i> element in the queue according to the queue's comparator. But unlike
 * a regular priority queue, the methods {@link #peekLast}, {@link #pollLast} and {@link
 * #removeLast} are also provided, to act on the <i>greatest</i> element in the queue instead.
 *
 * <p>A min-max priority queue can be configured with a maximum size. If so, each time the size of
 * the queue exceeds that value, the queue automatically removes its greatest element according to
 * its comparator (which might be the element that was just added). This is different from
 * conventional bounded queues, which either block or reject new elements when full.
 *
 * <p>This implementation is based on the <a
 * href="http://portal.acm.org/citation.cfm?id=6621">min-max heap</a> developed by Atkinson, et al.
 * Unlike many other double-ended priority queues, it stores elements in a single array, as compact
 * as the traditional heap data structure used in {@link PriorityQueue}.
 *
 * <p>This class is not thread-safe, and does not accept null elements.
 *
 * <p><i>Performance notes:</i>
 *
 * <ul>
 *   <li>If you only access one end of the queue, and do use a maximum size, this class will perform
 *       significantly worse than a {@code PriorityQueue} with manual eviction above the maximum
 *       size. In many cases {@link Ordering#leastOf} may work for your use case with significantly
 *       improved (and asymptotically superior) performance.
 *   <li>The retrieval operations {@link #peek}, {@link #peekFirst}, {@link #peekLast}, {@link
 *       #element}, and {@link #size} are constant-time.
 *   <li>The enqueuing and dequeuing operations ({@link #offer}, {@link #add}, and all the forms of
 *       {@link #poll} and {@link #remove()}) run in {@code O(log n) time}.
 *   <li>The {@link #remove(Object)} and {@link #contains} operations require linear ({@code O(n)})
 *       time.
 *   <li>If you only access one end of the queue, and don't use a maximum size, this class is
 *       functionally equivalent to {@link PriorityQueue}, but significantly slower.
 * </ul>
 *
 * @author Sverre Sundsdal
 * @author Torbjorn Gannholm
 * @since 8.0
 */
@Beta
@GwtCompatible
public final class MinMaxPriorityQueue<E> extends AbstractQueue<E> {

  /**
   * Creates a new min-max priority queue with default settings: natural order, no maximum size, no
   * initial contents, and an initial expected size of 11.
   */
  public static <E extends Comparable<E>> MinMaxPriorityQueue<E> create() {
    return new Builder<Comparable>(Ordering.natural()).create();
  }

  /**
   * Creates a new min-max priority queue using natural order, no maximum size, and initially
   * containing the given elements.
   */
  public static <E extends Comparable<E>> MinMaxPriorityQueue<E> create(
      Iterable<? extends E> initialContents) {
    return new Builder<E>(Ordering.<E>natural()).create(initialContents);
  }

  /**
   * Creates and returns a new builder, configured to build {@code MinMaxPriorityQueue} instances
   * that use {@code comparator} to determine the least and greatest elements.
   */
  public static <B> Builder<B> orderedBy(Comparator<B> comparator) {
    return new Builder<B>(comparator);
  }

  /**
   * Creates and returns a new builder, configured to build {@code MinMaxPriorityQueue} instances
   * sized appropriately to hold {@code expectedSize} elements.
   */
  public static Builder<Comparable> expectedSize(int expectedSize) {
    return new Builder<Comparable>(Ordering.natural()).expectedSize(expectedSize);
  }

  /**
   * Creates and returns a new builder, configured to build {@code MinMaxPriorityQueue} instances
   * that are limited to {@code maximumSize} elements. Each time a queue grows beyond this bound, it
   * immediately removes its greatest element (according to its comparator), which might be the
   * element that was just added.
   */
  public static Builder<Comparable> maximumSize(int maximumSize) {
    return new Builder<Comparable>(Ordering.natural()).maximumSize(maximumSize);
  }

  /**
   * The builder class used in creation of min-max priority queues. Instead of constructing one
   * directly, use {@link MinMaxPriorityQueue#orderedBy(Comparator)}, {@link
   * MinMaxPriorityQueue#expectedSize(int)} or {@link MinMaxPriorityQueue#maximumSize(int)}.
   *
   * @param <B> the upper bound on the eventual type that can be produced by this builder (for
   *     example, a {@code Builder<Number>} can produce a {@code Queue<Number>} or {@code
   *     Queue<Integer>} but not a {@code Queue<Object>}).
   * @since 8.0
   */
  @Beta
  public static final class Builder<B> {
    /*
     * TODO(kevinb): when the dust settles, see if we still need this or can
     * just default to DEFAULT_CAPACITY.
     */
    private static final int UNSET_EXPECTED_SIZE = -1;

    private final Comparator<B> comparator;
    private int expectedSize = UNSET_EXPECTED_SIZE;
    private int maximumSize = Integer.MAX_VALUE;

    private Builder(Comparator<B> comparator) {
      this.comparator = checkNotNull(comparator);
    }

    /**
     * Configures this builder to build min-max priority queues with an initial expected size of
     * {@code expectedSize}.
     */
    @CanIgnoreReturnValue
    public Builder<B> expectedSize(int expectedSize) {
      checkArgument(expectedSize >= 0);
      this.expectedSize = expectedSize;
      return this;
    }

    /**
     * Configures this builder to build {@code MinMaxPriorityQueue} instances that are limited to
     * {@code maximumSize} elements. Each time a queue grows beyond this bound, it immediately
     * removes its greatest element (according to its comparator), which might be the element that
     * was just added.
     */
    @CanIgnoreReturnValue
    public Builder<B> maximumSize(int maximumSize) {
      checkArgument(maximumSize > 0);
      this.maximumSize = maximumSize;
      return this;
    }

    /**
     * Builds a new min-max priority queue using the previously specified options, and having no
     * initial contents.
     */
    public <T extends B> MinMaxPriorityQueue<T> create() {
      return create(Collections.<T>emptySet());
    }

    /**
     * Builds a new min-max priority queue using the previously specified options, and having the
     * given initial elements.
     */
    public <T extends B> MinMaxPriorityQueue<T> create(Iterable<? extends T> initialContents) {
      MinMaxPriorityQueue<T> queue =
          new MinMaxPriorityQueue<T>(
              this, initialQueueSize(expectedSize, maximumSize, initialContents));
      for (T element : initialContents) {
        queue.offer(element);
      }
      return queue;
    }

    @SuppressWarnings("unchecked") // safe "contravariant cast"
    private <T extends B> Ordering<T> ordering() {
      return Ordering.from((Comparator<T>) comparator);
    }
  }

  private final Heap minHeap;
  private final Heap maxHeap;
  @VisibleForTesting final int maximumSize;
  private Object[] queue;
  private int size;
  private int modCount;

  private MinMaxPriorityQueue(Builder<? super E> builder, int queueSize) {
    Ordering<E> ordering = builder.ordering();
    this.minHeap = new Heap(ordering);
    this.maxHeap = new Heap(ordering.reverse());
    minHeap.otherHeap = maxHeap;
    maxHeap.otherHeap = minHeap;

    this.maximumSize = builder.maximumSize;
    // TODO(kevinb): pad?
    this.queue = new Object[queueSize];
  }

  @Override
  public int size() {
    return size;
  }

  /**
   * Adds the given element to this queue. If this queue has a maximum size, after adding {@code
   * element} the queue will automatically evict its greatest element (according to its comparator),
   * which may be {@code element} itself.
   *
   * @return {@code true} always
   */
  @CanIgnoreReturnValue
  @Override
  public boolean add(E element) {
    offer(element);
    return true;
  }

  @CanIgnoreReturnValue
  @Override
  public boolean addAll(Collection<? extends E> newElements) {
    boolean modified = false;
    for (E element : newElements) {
      offer(element);
      modified = true;
    }
    return modified;
  }

  /**
   * Adds the given element to this queue. If this queue has a maximum size, after adding {@code
   * element} the queue will automatically evict its greatest element (according to its comparator),
   * which may be {@code element} itself.
   */
  @CanIgnoreReturnValue
  @Override
  public boolean offer(E element) {
    checkNotNull(element);
    modCount++;
    int insertIndex = size++;

    growIfNeeded();

    // Adds the element to the end of the heap and bubbles it up to the correct
    // position.
    heapForIndex(insertIndex).bubbleUp(insertIndex, element);
    return size <= maximumSize || pollLast() != element;
  }

  @CanIgnoreReturnValue
  @Override
  public E poll() {
    return isEmpty() ? null : removeAndGet(0);
  }

  @SuppressWarnings("unchecked") // we must carefully only allow Es to get in
  E elementData(int index) {
    return (E) queue[index];
  }

  @Override
  public E peek() {
    return isEmpty() ? null : elementData(0);
  }

  /** Returns the index of the max element. */
  private int getMaxElementIndex() {
    switch (size) {
      case 1:
        return 0; // The lone element in the queue is the maximum.
      case 2:
        return 1; // The lone element in the maxHeap is the maximum.
      default:
        // The max element must sit on the first level of the maxHeap. It is
        // actually the *lesser* of the two from the maxHeap's perspective.
        return (maxHeap.compareElements(1, 2) <= 0) ? 1 : 2;
    }
  }

  /**
   * Removes and returns the least element of this queue, or returns {@code null} if the queue is
   * empty.
   */
  @CanIgnoreReturnValue
  public E pollFirst() {
    return poll();
  }

  /**
   * Removes and returns the least element of this queue.
   *
   * @throws NoSuchElementException if the queue is empty
   */
  @CanIgnoreReturnValue
  public E removeFirst() {
    return remove();
  }

  /**
   * Retrieves, but does not remove, the least element of this queue, or returns {@code null} if the
   * queue is empty.
   */
  public E peekFirst() {
    return peek();
  }

  /**
   * Removes and returns the greatest element of this queue, or returns {@code null} if the queue is
   * empty.
   */
  @CanIgnoreReturnValue
  public E pollLast() {
    return isEmpty() ? null : removeAndGet(getMaxElementIndex());
  }

  /**
   * Removes and returns the greatest element of this queue.
   *
   * @throws NoSuchElementException if the queue is empty
   */
  @CanIgnoreReturnValue
  public E removeLast() {
    if (isEmpty()) {
      throw new NoSuchElementException();
    }
    return removeAndGet(getMaxElementIndex());
  }

  /**
   * Retrieves, but does not remove, the greatest element of this queue, or returns {@code null} if
   * the queue is empty.
   */
  public E peekLast() {
    return isEmpty() ? null : elementData(getMaxElementIndex());
  }

  /**
   * Removes the element at position {@code index}.
   *
   * <p>Normally this method leaves the elements at up to {@code index - 1}, inclusive, untouched.
   * Under these circumstances, it returns {@code null}.
   *
   * <p>Occasionally, in order to maintain the heap invariant, it must swap a later element of the
   * list with one before {@code index}. Under these circumstances it returns a pair of elements as
   * a {@link MoveDesc}. The first one is the element that was previously at the end of the heap and
   * is now at some position before {@code index}. The second element is the one that was swapped
   * down to replace the element at {@code index}. This fact is used by iterator.remove so as to
   * visit elements during a traversal once and only once.
   */
  @VisibleForTesting
  @CanIgnoreReturnValue
  MoveDesc<E> removeAt(int index) {
    checkPositionIndex(index, size);
    modCount++;
    size--;
    if (size == index) {
      queue[size] = null;
      return null;
    }
    E actualLastElement = elementData(size);
    int lastElementAt = heapForIndex(size).swapWithConceptuallyLastElement(actualLastElement);
    if (lastElementAt == index) {
      // 'actualLastElement' is now at 'lastElementAt', and the element that was at 'lastElementAt'
      // is now at the end of queue. If that's the element we wanted to remove in the first place,
      // don't try to (incorrectly) trickle it. Instead, just delete it and we're done.
      queue[size] = null;
      return null;
    }
    E toTrickle = elementData(size);
    queue[size] = null;
    MoveDesc<E> changes = fillHole(index, toTrickle);
    if (lastElementAt < index) {
      // Last element is moved to before index, swapped with trickled element.
      if (changes == null) {
        // The trickled element is still after index.
        return new MoveDesc<E>(actualLastElement, toTrickle);
      } else {
        // The trickled element is back before index, but the replaced element
        // has now been moved after index.
        return new MoveDesc<E>(actualLastElement, changes.replaced);
      }
    }
    // Trickled element was after index to begin with, no adjustment needed.
    return changes;
  }

  private MoveDesc<E> fillHole(int index, E toTrickle) {
    Heap heap = heapForIndex(index);
    // We consider elementData(index) a "hole", and we want to fill it
    // with the last element of the heap, toTrickle.
    // Since the last element of the heap is from the bottom level, we
    // optimistically fill index position with elements from lower levels,
    // moving the hole down. In most cases this reduces the number of
    // comparisons with toTrickle, but in some cases we will need to bubble it
    // all the way up again.
    int vacated = heap.fillHoleAt(index);
    // Try to see if toTrickle can be bubbled up min levels.
    int bubbledTo = heap.bubbleUpAlternatingLevels(vacated, toTrickle);
    if (bubbledTo == vacated) {
      // Could not bubble toTrickle up min levels, try moving
      // it from min level to max level (or max to min level) and bubble up
      // there.
      return heap.tryCrossOverAndBubbleUp(index, vacated, toTrickle);
    } else {
      return (bubbledTo < index) ? new MoveDesc<E>(toTrickle, elementData(index)) : null;
    }
  }

  // Returned from removeAt() to iterator.remove()
  static class MoveDesc<E> {
    final E toTrickle;
    final E replaced;

    MoveDesc(E toTrickle, E replaced) {
      this.toTrickle = toTrickle;
      this.replaced = replaced;
    }
  }

  /** Removes and returns the value at {@code index}. */
  private E removeAndGet(int index) {
    E value = elementData(index);
    removeAt(index);
    return value;
  }

  private Heap heapForIndex(int i) {
    return isEvenLevel(i) ? minHeap : maxHeap;
  }

  private static final int EVEN_POWERS_OF_TWO = 0x55555555;
  private static final int ODD_POWERS_OF_TWO = 0xaaaaaaaa;

  @VisibleForTesting
  static boolean isEvenLevel(int index) {
    int oneBased = ~~(index + 1); // for GWT
    checkState(oneBased > 0, "negative index");
    return (oneBased & EVEN_POWERS_OF_TWO) > (oneBased & ODD_POWERS_OF_TWO);
  }

  /**
   * Returns {@code true} if the MinMax heap structure holds. This is only used in testing.
   *
   * <p>TODO(kevinb): move to the test class?
   */
  @VisibleForTesting
  boolean isIntact() {
    for (int i = 1; i < size; i++) {
      if (!heapForIndex(i).verifyIndex(i)) {
        return false;
      }
    }
    return true;
  }

  /**
   * Each instance of MinMaxPriortyQueue encapsulates two instances of Heap: a min-heap and a
   * max-heap. Conceptually, these might each have their own array for storage, but for efficiency's
   * sake they are stored interleaved on alternate heap levels in the same array (MMPQ.queue).
   */
  @WeakOuter
  private class Heap {
    final Ordering<E> ordering;
    @MonotonicNonNull @Weak Heap otherHeap;

    Heap(Ordering<E> ordering) {
      this.ordering = ordering;
    }

    int compareElements(int a, int b) {
      return ordering.compare(elementData(a), elementData(b));
    }

    /**
     * Tries to move {@code toTrickle} from a min to a max level and bubble up there. If it moved
     * before {@code removeIndex} this method returns a pair as described in {@link #removeAt}.
     */
    MoveDesc<E> tryCrossOverAndBubbleUp(int removeIndex, int vacated, E toTrickle) {
      int crossOver = crossOver(vacated, toTrickle);
      if (crossOver == vacated) {
        return null;
      }
      // Successfully crossed over from min to max.
      // Bubble up max levels.
      E parent;
      // If toTrickle is moved up to a parent of removeIndex, the parent is
      // placed in removeIndex position. We must return that to the iterator so
      // that it knows to skip it.
      if (crossOver < removeIndex) {
        // We crossed over to the parent level in crossOver, so the parent
        // has already been moved.
        parent = elementData(removeIndex);
      } else {
        parent = elementData(getParentIndex(removeIndex));
      }
      // bubble it up the opposite heap
      if (otherHeap.bubbleUpAlternatingLevels(crossOver, toTrickle) < removeIndex) {
        return new MoveDesc<E>(toTrickle, parent);
      } else {
        return null;
      }
    }

    /** Bubbles a value from {@code index} up the appropriate heap if required. */
    void bubbleUp(int index, E x) {
      int crossOver = crossOverUp(index, x);

      Heap heap;
      if (crossOver == index) {
        heap = this;
      } else {
        index = crossOver;
        heap = otherHeap;
      }
      heap.bubbleUpAlternatingLevels(index, x);
    }

    /**
     * Bubbles a value from {@code index} up the levels of this heap, and returns the index the
     * element ended up at.
     */
    @CanIgnoreReturnValue
    int bubbleUpAlternatingLevels(int index, E x) {
      while (index > 2) {
        int grandParentIndex = getGrandparentIndex(index);
        E e = elementData(grandParentIndex);
        if (ordering.compare(e, x) <= 0) {
          break;
        }
        queue[index] = e;
        index = grandParentIndex;
      }
      queue[index] = x;
      return index;
    }

    /**
     * Returns the index of minimum value between {@code index} and {@code index + len}, or {@code
     * -1} if {@code index} is greater than {@code size}.
     */
    int findMin(int index, int len) {
      if (index >= size) {
        return -1;
      }
      checkState(index > 0);
      int limit = Math.min(index, size - len) + len;
      int minIndex = index;
      for (int i = index + 1; i < limit; i++) {
        if (compareElements(i, minIndex) < 0) {
          minIndex = i;
        }
      }
      return minIndex;
    }

    /** Returns the minimum child or {@code -1} if no child exists. */
    int findMinChild(int index) {
      return findMin(getLeftChildIndex(index), 2);
    }

    /** Returns the minimum grand child or -1 if no grand child exists. */
    int findMinGrandChild(int index) {
      int leftChildIndex = getLeftChildIndex(index);
      if (leftChildIndex < 0) {
        return -1;
      }
      return findMin(getLeftChildIndex(leftChildIndex), 4);
    }

    /**
     * Moves an element one level up from a min level to a max level (or vice versa). Returns the
     * new position of the element.
     */
    int crossOverUp(int index, E x) {
      if (index == 0) {
        queue[0] = x;
        return 0;
      }
      int parentIndex = getParentIndex(index);
      E parentElement = elementData(parentIndex);
      if (parentIndex != 0) {
        // This is a guard for the case of the childless uncle.
        // Since the end of the array is actually the middle of the heap,
        // a smaller childless uncle can become a child of x when we
        // bubble up alternate levels, violating the invariant.
        int grandparentIndex = getParentIndex(parentIndex);
        int uncleIndex = getRightChildIndex(grandparentIndex);
        if (uncleIndex != parentIndex && getLeftChildIndex(uncleIndex) >= size) {
          E uncleElement = elementData(uncleIndex);
          if (ordering.compare(uncleElement, parentElement) < 0) {
            parentIndex = uncleIndex;
            parentElement = uncleElement;
          }
        }
      }
      if (ordering.compare(parentElement, x) < 0) {
        queue[index] = parentElement;
        queue[parentIndex] = x;
        return parentIndex;
      }
      queue[index] = x;
      return index;
    }

    /**
     * Swap {@code actualLastElement} with the conceptually correct last element of the heap.
     * Returns the index that {@code actualLastElement} now resides in.
     *
     * <p>Since the last element of the array is actually in the middle of the sorted structure, a
     * childless uncle node could be smaller, which would corrupt the invariant if this element
     * becomes the new parent of the uncle. In that case, we first switch the last element with its
     * uncle, before returning.
     */
    int swapWithConceptuallyLastElement(E actualLastElement) {
      int parentIndex = getParentIndex(size);
      if (parentIndex != 0) {
        int grandparentIndex = getParentIndex(parentIndex);
        int uncleIndex = getRightChildIndex(grandparentIndex);
        if (uncleIndex != parentIndex && getLeftChildIndex(uncleIndex) >= size) {
          E uncleElement = elementData(uncleIndex);
          if (ordering.compare(uncleElement, actualLastElement) < 0) {
            queue[uncleIndex] = actualLastElement;
            queue[size] = uncleElement;
            return uncleIndex;
          }
        }
      }
      return size;
    }

    /**
     * Crosses an element over to the opposite heap by moving it one level down (or up if there are
     * no elements below it).
     *
     * <p>Returns the new position of the element.
     */
    int crossOver(int index, E x) {
      int minChildIndex = findMinChild(index);
      // TODO(kevinb): split the && into two if's and move crossOverUp so it's
      // only called when there's no child.
      if ((minChildIndex > 0) && (ordering.compare(elementData(minChildIndex), x) < 0)) {
        queue[index] = elementData(minChildIndex);
        queue[minChildIndex] = x;
        return minChildIndex;
      }
      return crossOverUp(index, x);
    }

    /**
     * Fills the hole at {@code index} by moving in the least of its grandchildren to this position,
     * then recursively filling the new hole created.
     *
     * @return the position of the new hole (where the lowest grandchild moved from, that had no
     *     grandchild to replace it)
     */
    int fillHoleAt(int index) {
      int minGrandchildIndex;
      while ((minGrandchildIndex = findMinGrandChild(index)) > 0) {
        queue[index] = elementData(minGrandchildIndex);
        index = minGrandchildIndex;
      }
      return index;
    }

    private boolean verifyIndex(int i) {
      if ((getLeftChildIndex(i) < size) && (compareElements(i, getLeftChildIndex(i)) > 0)) {
        return false;
      }
      if ((getRightChildIndex(i) < size) && (compareElements(i, getRightChildIndex(i)) > 0)) {
        return false;
      }
      if ((i > 0) && (compareElements(i, getParentIndex(i)) > 0)) {
        return false;
      }
      if ((i > 2) && (compareElements(getGrandparentIndex(i), i) > 0)) {
        return false;
      }
      return true;
    }

    // These would be static if inner classes could have static members.

    private int getLeftChildIndex(int i) {
      return i * 2 + 1;
    }

    private int getRightChildIndex(int i) {
      return i * 2 + 2;
    }

    private int getParentIndex(int i) {
      return (i - 1) / 2;
    }

    private int getGrandparentIndex(int i) {
      return getParentIndex(getParentIndex(i)); // (i - 3) / 4
    }
  }

  /**
   * Iterates the elements of the queue in no particular order.
   *
   * <p>If the underlying queue is modified during iteration an exception will be thrown.
   */
  private class QueueIterator implements Iterator<E> {
    private int cursor = -1;
    private int nextCursor = -1;
    private int expectedModCount = modCount;
    // The same element is not allowed in both forgetMeNot and skipMe, but duplicates are allowed in
    // either of them, up to the same multiplicity as the queue.
    @MonotonicNonNull private Queue<E> forgetMeNot;
    @MonotonicNonNull private List<E> skipMe;
    private @Nullable E lastFromForgetMeNot;
    private boolean canRemove;

    @Override
    public boolean hasNext() {
      checkModCount();
      nextNotInSkipMe(cursor + 1);
      return (nextCursor < size()) || ((forgetMeNot != null) && !forgetMeNot.isEmpty());
    }

    @Override
    public E next() {
      checkModCount();
      nextNotInSkipMe(cursor + 1);
      if (nextCursor < size()) {
        cursor = nextCursor;
        canRemove = true;
        return elementData(cursor);
      } else if (forgetMeNot != null) {
        cursor = size();
        lastFromForgetMeNot = forgetMeNot.poll();
        if (lastFromForgetMeNot != null) {
          canRemove = true;
          return lastFromForgetMeNot;
        }
      }
      throw new NoSuchElementException("iterator moved past last element in queue.");
    }

    @Override
    public void remove() {
      checkRemove(canRemove);
      checkModCount();
      canRemove = false;
      expectedModCount++;
      if (cursor < size()) {
        MoveDesc<E> moved = removeAt(cursor);
        if (moved != null) {
          if (forgetMeNot == null) {
            forgetMeNot = new ArrayDeque<E>();
            skipMe = new ArrayList<E>(3);
          }
          if (!foundAndRemovedExactReference(skipMe, moved.toTrickle)) {
            forgetMeNot.add(moved.toTrickle);
          }
          if (!foundAndRemovedExactReference(forgetMeNot, moved.replaced)) {
            skipMe.add(moved.replaced);
          }
        }
        cursor--;
        nextCursor--;
      } else { // we must have set lastFromForgetMeNot in next()
        checkState(removeExact(lastFromForgetMeNot));
        lastFromForgetMeNot = null;
      }
    }

    /** Returns true if an exact reference (==) was found and removed from the supplied iterable. */
    private boolean foundAndRemovedExactReference(Iterable<E> elements, E target) {
      for (Iterator<E> it = elements.iterator(); it.hasNext(); ) {
        E element = it.next();
        if (element == target) {
          it.remove();
          return true;
        }
      }
      return false;
    }

    /** Removes only this exact instance, not others that are equals() */
    private boolean removeExact(Object target) {
      for (int i = 0; i < size; i++) {
        if (queue[i] == target) {
          removeAt(i);
          return true;
        }
      }
      return false;
    }

    private void checkModCount() {
      if (modCount != expectedModCount) {
        throw new ConcurrentModificationException();
      }
    }

    /**
     * Advances nextCursor to the index of the first element after {@code c} that is not in {@code
     * skipMe} and returns {@code size()} if there is no such element.
     */
    private void nextNotInSkipMe(int c) {
      if (nextCursor < c) {
        if (skipMe != null) {
          while (c < size() && foundAndRemovedExactReference(skipMe, elementData(c))) {
            c++;
          }
        }
        nextCursor = c;
      }
    }
  }

  /**
   * Returns an iterator over the elements contained in this collection, <i>in no particular
   * order</i>.
   *
   * <p>The iterator is <i>fail-fast</i>: If the MinMaxPriorityQueue is modified at any time after
   * the iterator is created, in any way except through the iterator's own remove method, the
   * iterator will generally throw a {@link ConcurrentModificationException}. Thus, in the face of
   * concurrent modification, the iterator fails quickly and cleanly, rather than risking arbitrary,
   * non-deterministic behavior at an undetermined time in the future.
   *
   * <p>Note that the fail-fast behavior of an iterator cannot be guaranteed as it is, generally
   * speaking, impossible to make any hard guarantees in the presence of unsynchronized concurrent
   * modification. Fail-fast iterators throw {@code ConcurrentModificationException} on a
   * best-effort basis. Therefore, it would be wrong to write a program that depended on this
   * exception for its correctness: <i>the fail-fast behavior of iterators should be used only to
   * detect bugs.</i>
   *
   * @return an iterator over the elements contained in this collection
   */
  @Override
  public Iterator<E> iterator() {
    return new QueueIterator();
  }

  @Override
  public void clear() {
    for (int i = 0; i < size; i++) {
      queue[i] = null;
    }
    size = 0;
  }

  @Override
  public Object[] toArray() {
    Object[] copyTo = new Object[size];
    System.arraycopy(queue, 0, copyTo, 0, size);
    return copyTo;
  }

  /**
   * Returns the comparator used to order the elements in this queue. Obeys the general contract of
   * {@link PriorityQueue#comparator}, but returns {@link Ordering#natural} instead of {@code null}
   * to indicate natural ordering.
   */
  public Comparator<? super E> comparator() {
    return minHeap.ordering;
  }

  @VisibleForTesting
  int capacity() {
    return queue.length;
  }

  // Size/capacity-related methods

  private static final int DEFAULT_CAPACITY = 11;

  @VisibleForTesting
  static int initialQueueSize(
      int configuredExpectedSize, int maximumSize, Iterable<?> initialContents) {
    // Start with what they said, if they said it, otherwise DEFAULT_CAPACITY
    int result =
        (configuredExpectedSize == Builder.UNSET_EXPECTED_SIZE)
            ? DEFAULT_CAPACITY
            : configuredExpectedSize;

    // Enlarge to contain initial contents
    if (initialContents instanceof Collection) {
      int initialSize = ((Collection<?>) initialContents).size();
      result = Math.max(result, initialSize);
    }

    // Now cap it at maxSize + 1
    return capAtMaximumSize(result, maximumSize);
  }

  private void growIfNeeded() {
    if (size > queue.length) {
      int newCapacity = calculateNewCapacity();
      Object[] newQueue = new Object[newCapacity];
      System.arraycopy(queue, 0, newQueue, 0, queue.length);
      queue = newQueue;
    }
  }

  /** Returns ~2x the old capacity if small; ~1.5x otherwise. */
  private int calculateNewCapacity() {
    int oldCapacity = queue.length;
    int newCapacity =
        (oldCapacity < 64) ? (oldCapacity + 1) * 2 : IntMath.checkedMultiply(oldCapacity / 2, 3);
    return capAtMaximumSize(newCapacity, maximumSize);
  }

  /** There's no reason for the queueSize to ever be more than maxSize + 1 */
  private static int capAtMaximumSize(int queueSize, int maximumSize) {
    return Math.min(queueSize - 1, maximumSize) + 1; // don't overflow
  }
}