path: root/guava/src/com/google/common/collect/ImmutableSortedSet.java

/*
 * Copyright (C) 2008 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 com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.GwtIncompatible;

import java.io.InvalidObjectException;
import java.io.ObjectInputStream;
import java.io.Serializable;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.Iterator;
import java.util.List;
import java.util.NavigableSet;
import java.util.SortedSet;

import javax.annotation.Nullable;

/**
 * An immutable {@code SortedSet} that stores its elements in a sorted array.
 * Some instances are ordered by an explicit comparator, while others follow the
 * natural sort ordering of their elements. Either way, null elements are not
 * supported.
 *
 * <p>Unlike {@link Collections#unmodifiableSortedSet}, which is a <i>view</i>
 * of a separate collection that can still change, an instance of {@code
 * ImmutableSortedSet} contains its own private data and will <i>never</i>
 * change. This class is convenient for {@code public static final} sets
 * ("constant sets") and also lets you easily make a "defensive copy" of a set
 * provided to your class by a caller.
 *
 * <p>The sets returned by the {@link #headSet}, {@link #tailSet}, and
 * {@link #subSet} methods share the same array as the original set, preventing
 * that array from being garbage collected. If this is a concern, the data may
 * be copied into a correctly-sized array by calling {@link #copyOfSorted}.
 *
 * <p><b>Note on element equivalence:</b> The {@link #contains(Object)},
 * {@link #containsAll(Collection)}, and {@link #equals(Object)}
 * implementations must check whether a provided object is equivalent to an
 * element in the collection. Unlike most collections, an
 * {@code ImmutableSortedSet} doesn't use {@link Object#equals} to determine if
 * two elements are equivalent. Instead, with an explicit comparator, the
 * following relation determines whether elements {@code x} and {@code y} are
 * equivalent: <pre>   {@code
 *
 *   {(x, y) | comparator.compare(x, y) == 0}}</pre>
 *
 * With natural ordering of elements, the following relation determines whether
 * two elements are equivalent: <pre>   {@code
 *
 *   {(x, y) | x.compareTo(y) == 0}}</pre>
 *
 * <b>Warning:</b> Like most sets, an {@code ImmutableSortedSet} will not
 * function correctly if an element is modified after being placed in the set.
 * For this reason, and to avoid general confusion, it is strongly recommended
 * to place only immutable objects into this collection.
 *
 * <p><b>Note:</b> Although this class is not final, it cannot be subclassed as
 * it has no public or protected constructors. Thus, instances of this type are
 * guaranteed to be immutable.
 *
 * <p>See the Guava User Guide article on <a href=
 * "http://code.google.com/p/guava-libraries/wiki/ImmutableCollectionsExplained">
 * immutable collections</a>.
 *
 * @see ImmutableSet
 * @author Jared Levy
 * @author Louis Wasserman
 * @since 2.0 (imported from Google Collections Library; implements {@code NavigableSet} since 12.0)
 */
// TODO(benyu): benchmark and optimize all creation paths, which are a mess now
@GwtCompatible(serializable = true, emulated = true)
@SuppressWarnings("serial") // we're overriding default serialization
public abstract class ImmutableSortedSet<E> extends ImmutableSortedSetFauxverideShim<E>
    implements NavigableSet<E>, SortedIterable<E> {

  private static final Comparator<Comparable> NATURAL_ORDER =
      Ordering.natural();

  private static final ImmutableSortedSet<Comparable> NATURAL_EMPTY_SET =
      new EmptyImmutableSortedSet<Comparable>(NATURAL_ORDER);

  @SuppressWarnings("unchecked")
  private static <E> ImmutableSortedSet<E> emptySet() {
    return (ImmutableSortedSet<E>) NATURAL_EMPTY_SET;
  }

  static <E> ImmutableSortedSet<E> emptySet(
      Comparator<? super E> comparator) {
    if (NATURAL_ORDER.equals(comparator)) {
      return emptySet();
    } else {
      return new EmptyImmutableSortedSet<E>(comparator);
    }
  }

  /**
   * Returns the empty immutable sorted set.
   */
  public static <E> ImmutableSortedSet<E> of() {
    return emptySet();
  }

  /**
   * Returns an immutable sorted set containing a single element.
   */
  public static <E extends Comparable<? super E>> ImmutableSortedSet<E> of(
      E element) {
    return new RegularImmutableSortedSet<E>(
        ImmutableList.of(element), Ordering.natural());
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * their natural ordering. When multiple elements are equivalent according to
   * {@link Comparable#compareTo}, only the first one specified is included.
   *
   * @throws NullPointerException if any element is null
   */
  @SuppressWarnings("unchecked")
  public static <E extends Comparable<? super E>> ImmutableSortedSet<E> of(
      E e1, E e2) {
    return copyOf(Ordering.natural(), Arrays.asList(e1, e2));
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * their natural ordering. When multiple elements are equivalent according to
   * {@link Comparable#compareTo}, only the first one specified is included.
   *
   * @throws NullPointerException if any element is null
   */
  @SuppressWarnings("unchecked")
  public static <E extends Comparable<? super E>> ImmutableSortedSet<E> of(
      E e1, E e2, E e3) {
    return copyOf(Ordering.natural(), Arrays.asList(e1, e2, e3));
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * their natural ordering. When multiple elements are equivalent according to
   * {@link Comparable#compareTo}, only the first one specified is included.
   *
   * @throws NullPointerException if any element is null
   */
  @SuppressWarnings("unchecked")
  public static <E extends Comparable<? super E>> ImmutableSortedSet<E> of(
      E e1, E e2, E e3, E e4) {
    return copyOf(Ordering.natural(), Arrays.asList(e1, e2, e3, e4));
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * their natural ordering. When multiple elements are equivalent according to
   * {@link Comparable#compareTo}, only the first one specified is included.
   *
   * @throws NullPointerException if any element is null
   */
  @SuppressWarnings("unchecked")
  public static <E extends Comparable<? super E>> ImmutableSortedSet<E> of(
      E e1, E e2, E e3, E e4, E e5) {
    return copyOf(Ordering.natural(), Arrays.asList(e1, e2, e3, e4, e5));
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * their natural ordering. When multiple elements are equivalent according to
   * {@link Comparable#compareTo}, only the first one specified is included.
   *
   * @throws NullPointerException if any element is null
   * @since 3.0 (source-compatible since 2.0)
   */
  @SuppressWarnings("unchecked")
  public static <E extends Comparable<? super E>> ImmutableSortedSet<E> of(
      E e1, E e2, E e3, E e4, E e5, E e6, E... remaining) {
    int size = remaining.length + 6;
    List<E> all = new ArrayList<E>(size);
    Collections.addAll(all, e1, e2, e3, e4, e5, e6);
    Collections.addAll(all, remaining);
    return copyOf(Ordering.natural(), all);
  }

  // TODO(kevinb): Consider factory methods that reject duplicates

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * their natural ordering. When multiple elements are equivalent according to
   * {@link Comparable#compareTo}, only the first one specified is included.
   *
   * @throws NullPointerException if any of {@code elements} is null
   * @since 3.0
   */
  public static <E extends Comparable<? super E>> ImmutableSortedSet<E> copyOf(
      E[] elements) {
    return copyOf(Ordering.natural(), Arrays.asList(elements));
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * their natural ordering. When multiple elements are equivalent according to
   * {@code compareTo()}, only the first one specified is included. To create a
   * copy of a {@code SortedSet} that preserves the comparator, call {@link
   * #copyOfSorted} instead. This method iterates over {@code elements} at most
   * once.

   *
   * <p>Note that if {@code s} is a {@code Set<String>}, then {@code
   * ImmutableSortedSet.copyOf(s)} returns an {@code ImmutableSortedSet<String>}
   * containing each of the strings in {@code s}, while {@code
   * ImmutableSortedSet.of(s)} returns an {@code
   * ImmutableSortedSet<Set<String>>} containing one element (the given set
   * itself).
   *
   * <p>Despite the method name, this method attempts to avoid actually copying
   * the data when it is safe to do so. The exact circumstances under which a
   * copy will or will not be performed are undocumented and subject to change.
   *
   * <p>This method is not type-safe, as it may be called on elements that are
   * not mutually comparable.
   *
   * @throws ClassCastException if the elements are not mutually comparable
   * @throws NullPointerException if any of {@code elements} is null
   */
  public static <E> ImmutableSortedSet<E> copyOf(
      Iterable<? extends E> elements) {
    // Hack around E not being a subtype of Comparable.
    // Unsafe, see ImmutableSortedSetFauxverideShim.
    @SuppressWarnings("unchecked")
    Ordering<E> naturalOrder = (Ordering<E>) Ordering.<Comparable>natural();
    return copyOf(naturalOrder, elements);
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * their natural ordering. When multiple elements are equivalent according to
   * {@code compareTo()}, only the first one specified is included. To create a
   * copy of a {@code SortedSet} that preserves the comparator, call
   * {@link #copyOfSorted} instead. This method iterates over {@code elements}
   * at most once.
   *
   * <p>Note that if {@code s} is a {@code Set<String>}, then
   * {@code ImmutableSortedSet.copyOf(s)} returns an
   * {@code ImmutableSortedSet<String>} containing each of the strings in
   * {@code s}, while {@code ImmutableSortedSet.of(s)} returns an
   * {@code ImmutableSortedSet<Set<String>>} containing one element (the given
   * set itself).
   *
   * <p><b>Note:</b> Despite what the method name suggests, if {@code elements}
   * is an {@code ImmutableSortedSet}, it may be returned instead of a copy.
   *
   * <p>This method is not type-safe, as it may be called on elements that are
   * not mutually comparable.
   *
   * <p>This method is safe to use even when {@code elements} is a synchronized
   * or concurrent collection that is currently being modified by another
   * thread.
   *
   * @throws ClassCastException if the elements are not mutually comparable
   * @throws NullPointerException if any of {@code elements} is null
   * @since 7.0 (source-compatible since 2.0)
   */
  public static <E> ImmutableSortedSet<E> copyOf(
      Collection<? extends E> elements) {
    // Hack around E not being a subtype of Comparable.
    // Unsafe, see ImmutableSortedSetFauxverideShim.
    @SuppressWarnings("unchecked")
    Ordering<E> naturalOrder = (Ordering<E>) Ordering.<Comparable>natural();
    return copyOf(naturalOrder, elements);
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * their natural ordering. When multiple elements are equivalent according to
   * {@code compareTo()}, only the first one specified is included.
   *
   * <p>This method is not type-safe, as it may be called on elements that are
   * not mutually comparable.
   *
   * @throws ClassCastException if the elements are not mutually comparable
   * @throws NullPointerException if any of {@code elements} is null
   */
  public static <E> ImmutableSortedSet<E> copyOf(
      Iterator<? extends E> elements) {
    // Hack around E not being a subtype of Comparable.
    // Unsafe, see ImmutableSortedSetFauxverideShim.
    @SuppressWarnings("unchecked")
    Ordering<E> naturalOrder = (Ordering<E>) Ordering.<Comparable>natural();
    return copyOf(naturalOrder, elements);
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * the given {@code Comparator}. When multiple elements are equivalent
   * according to {@code compareTo()}, only the first one specified is
   * included.
   *
   * @throws NullPointerException if {@code comparator} or any of
   *     {@code elements} is null
   */
  public static <E> ImmutableSortedSet<E> copyOf(
      Comparator<? super E> comparator, Iterator<? extends E> elements) {
    return copyOf(comparator, Lists.newArrayList(elements));
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * the given {@code Comparator}. When multiple elements are equivalent
   * according to {@code compare()}, only the first one specified is
   * included. This method iterates over {@code elements} at most once.
   *
   * <p>Despite the method name, this method attempts to avoid actually copying
   * the data when it is safe to do so. The exact circumstances under which a
   * copy will or will not be performed are undocumented and subject to change.
   *
   * @throws NullPointerException if {@code comparator} or any of {@code
   *         elements} is null
   */
  public static <E> ImmutableSortedSet<E> copyOf(
      Comparator<? super E> comparator, Iterable<? extends E> elements) {
    checkNotNull(comparator);
    boolean hasSameComparator =
        SortedIterables.hasSameComparator(comparator, elements);

    if (hasSameComparator && (elements instanceof ImmutableSortedSet)) {
      @SuppressWarnings("unchecked")
      ImmutableSortedSet<E> original = (ImmutableSortedSet<E>) elements;
      if (!original.isPartialView()) {
        return original;
      }
    }
    @SuppressWarnings("unchecked") // elements only contains E's; it's safe.
    E[] array = (E[]) Iterables.toArray(elements);
    return construct(comparator, array.length, array);
  }

  /**
   * Returns an immutable sorted set containing the given elements sorted by
   * the given {@code Comparator}. When multiple elements are equivalent
   * according to {@code compareTo()}, only the first one specified is
   * included.
   *
   * <p>Despite the method name, this method attempts to avoid actually copying
   * the data when it is safe to do so. The exact circumstances under which a
   * copy will or will not be performed are undocumented and subject to change.
   *
   * <p>This method is safe to use even when {@code elements} is a synchronized
   * or concurrent collection that is currently being modified by another
   * thread.
   *
   * @throws NullPointerException if {@code comparator} or any of
   *     {@code elements} is null
   * @since 7.0 (source-compatible since 2.0)
   */
  public static <E> ImmutableSortedSet<E> copyOf(
      Comparator<? super E> comparator, Collection<? extends E> elements) {
    return copyOf(comparator, (Iterable<? extends E>) elements);
  }

  /**
   * Returns an immutable sorted set containing the elements of a sorted set,
   * sorted by the same {@code Comparator}. That behavior differs from {@link
   * #copyOf(Iterable)}, which always uses the natural ordering of the
   * elements.
   *
   * <p>Despite the method name, this method attempts to avoid actually copying
   * the data when it is safe to do so. The exact circumstances under which a
   * copy will or will not be performed are undocumented and subject to change.
   *
   * <p>This method is safe to use even when {@code sortedSet} is a synchronized
   * or concurrent collection that is currently being modified by another
   * thread.
   *
   * @throws NullPointerException if {@code sortedSet} or any of its elements
   *     is null
   */
  public static <E> ImmutableSortedSet<E> copyOfSorted(SortedSet<E> sortedSet) {
    Comparator<? super E> comparator = SortedIterables.comparator(sortedSet);
    Object[] elements = sortedSet.toArray();
    if (elements.length == 0) {
      return emptySet(comparator);
    } else {
      return new RegularImmutableSortedSet<E>(
          ImmutableList.<E>asImmutableList(elements), comparator);
    }
  }

  /**
   * Sorts and eliminates duplicates from the first {@code n} positions in {@code contents}.
   * Returns the number of unique elements.  If this returns {@code k}, then the first {@code k}
   * elements of {@code contents} will be the sorted, unique elements, and {@code
   * contents[i] == null} for {@code k <= i < n}.
   *
   * @throws NullPointerException if any of the first {@code n} elements of {@code contents} is
   *          null
   */
  static <E> int sortAndUnique(
      Comparator<? super E> comparator, int n, E... contents) {
    if (n == 0) {
      return 0;
    }
    for (int i = 0; i < n; i++) {
      ObjectArrays.checkElementNotNull(contents[i], i);
    }
    Arrays.sort(contents, 0, n, comparator);
    int uniques = 1;
    for (int i = 1; i < n; i++) {
      E cur = contents[i];
      E prev = contents[uniques - 1];
      if (comparator.compare(cur, prev) != 0) {
        contents[uniques++] = cur;
      }
    }
    Arrays.fill(contents, uniques, n, null);
    return uniques;
  }

  /**
   * Constructs an {@code ImmutableSortedSet} from the first {@code n} elements of
   * {@code contents}.  If {@code k} is the size of the returned {@code ImmutableSortedSet}, then
   * the sorted unique elements are in the first {@code k} positions of {@code contents}, and
   * {@code contents[i] == null} for {@code k <= i < n}.
   *
   * <p>If {@code k == contents.length}, then {@code contents} may no longer be safe for
   * modification.
   *
   * @throws NullPointerException if any of the first {@code n} elements of {@code contents} is
   *          null
   */
  static <E> ImmutableSortedSet<E> construct(
      Comparator<? super E> comparator, int n, E... contents) {
    int uniques = sortAndUnique(comparator, n, contents);
    if (uniques == 0) {
      return emptySet(comparator);
    } else if (uniques < contents.length) {
      contents = ObjectArrays.arraysCopyOf(contents, uniques);
    }
    return new RegularImmutableSortedSet<E>(
        ImmutableList.<E>asImmutableList(contents), comparator);
  }

  /**
   * Returns a builder that creates immutable sorted sets with an explicit
   * comparator. If the comparator has a more general type than the set being
   * generated, such as creating a {@code SortedSet<Integer>} with a
   * {@code Comparator<Number>}, use the {@link Builder} constructor instead.
   *
   * @throws NullPointerException if {@code comparator} is null
   */
  public static <E> Builder<E> orderedBy(Comparator<E> comparator) {
    return new Builder<E>(comparator);
  }

  /**
   * Returns a builder that creates immutable sorted sets whose elements are
   * ordered by the reverse of their natural ordering.
   */
  public static <E extends Comparable<?>> Builder<E> reverseOrder() {
    return new Builder<E>(Ordering.natural().reverse());
  }

  /**
   * Returns a builder that creates immutable sorted sets whose elements are
   * ordered by their natural ordering. The sorted sets use {@link
   * Ordering#natural()} as the comparator. This method provides more
   * type-safety than {@link #builder}, as it can be called only for classes
   * that implement {@link Comparable}.
   */
  public static <E extends Comparable<?>> Builder<E> naturalOrder() {
    return new Builder<E>(Ordering.natural());
  }

  /**
   * A builder for creating immutable sorted set instances, especially {@code
   * public static final} sets ("constant sets"), with a given comparator.
   * Example: <pre>   {@code
   *
   *   public static final ImmutableSortedSet<Number> LUCKY_NUMBERS =
   *       new ImmutableSortedSet.Builder<Number>(ODDS_FIRST_COMPARATOR)
   *           .addAll(SINGLE_DIGIT_PRIMES)
   *           .add(42)
   *           .build();}</pre>
   *
   * Builder instances can be reused; it is safe to call {@link #build} multiple
   * times to build multiple sets in series. Each set is a superset of the set
   * created before it.
   *
   * @since 2.0 (imported from Google Collections Library)
   */
  public static final class Builder<E> extends ImmutableSet.Builder<E> {
    private final Comparator<? super E> comparator;

    /**
     * Creates a new builder. The returned builder is equivalent to the builder
     * generated by {@link ImmutableSortedSet#orderedBy}.
     */
    public Builder(Comparator<? super E> comparator) {
      this.comparator = checkNotNull(comparator);
    }

    /**
     * Adds {@code element} to the {@code ImmutableSortedSet}.  If the
     * {@code ImmutableSortedSet} already contains {@code element}, then
     * {@code add} has no effect. (only the previously added element
     * is retained).
     *
     * @param element the element to add
     * @return this {@code Builder} object
     * @throws NullPointerException if {@code element} is null
     */
    @Override public Builder<E> add(E element) {
      super.add(element);
      return this;
    }

    /**
     * Adds each element of {@code elements} to the {@code ImmutableSortedSet},
     * ignoring duplicate elements (only the first duplicate element is added).
     *
     * @param elements the elements to add
     * @return this {@code Builder} object
     * @throws NullPointerException if {@code elements} contains a null element
     */
    @Override public Builder<E> add(E... elements) {
      super.add(elements);
      return this;
    }

    /**
     * Adds each element of {@code elements} to the {@code ImmutableSortedSet},
     * ignoring duplicate elements (only the first duplicate element is added).
     *
     * @param elements the elements to add to the {@code ImmutableSortedSet}
     * @return this {@code Builder} object
     * @throws NullPointerException if {@code elements} contains a null element
     */
    @Override public Builder<E> addAll(Iterable<? extends E> elements) {
      super.addAll(elements);
      return this;
    }

    /**
     * Adds each element of {@code elements} to the {@code ImmutableSortedSet},
     * ignoring duplicate elements (only the first duplicate element is added).
     *
     * @param elements the elements to add to the {@code ImmutableSortedSet}
     * @return this {@code Builder} object
     * @throws NullPointerException if {@code elements} contains a null element
     */
    @Override public Builder<E> addAll(Iterator<? extends E> elements) {
      super.addAll(elements);
      return this;
    }

    /**
     * Returns a newly-created {@code ImmutableSortedSet} based on the contents
     * of the {@code Builder} and its comparator.
     */
    @Override public ImmutableSortedSet<E> build() {
      @SuppressWarnings("unchecked") // we're careful to put only E's in here
      E[] contentsArray = (E[]) contents;
      ImmutableSortedSet<E> result = construct(comparator, size, contentsArray);
      this.size = result.size(); // we eliminated duplicates in-place in contentsArray
      return result;
    }
  }

  int unsafeCompare(Object a, Object b) {
    return unsafeCompare(comparator, a, b);
  }

  static int unsafeCompare(
      Comparator<?> comparator, Object a, Object b) {
    // Pretend the comparator can compare anything. If it turns out it can't
    // compare a and b, we should get a CCE on the subsequent line. Only methods
    // that are spec'd to throw CCE should call this.
    @SuppressWarnings("unchecked")
    Comparator<Object> unsafeComparator = (Comparator<Object>) comparator;
    return unsafeComparator.compare(a, b);
  }

  final transient Comparator<? super E> comparator;

  ImmutableSortedSet(Comparator<? super E> comparator) {
    this.comparator = comparator;
  }

  /**
   * Returns the comparator that orders the elements, which is
   * {@link Ordering#natural()} when the natural ordering of the
   * elements is used. Note that its behavior is not consistent with
   * {@link SortedSet#comparator()}, which returns {@code null} to indicate
   * natural ordering.
   */
  @Override
  public Comparator<? super E> comparator() {
    return comparator;
  }

  @Override // needed to unify the iterator() methods in Collection and SortedIterable
  public abstract UnmodifiableIterator<E> iterator();

  /**
   * {@inheritDoc}
   *
   * <p>This method returns a serializable {@code ImmutableSortedSet}.
   *
   * <p>The {@link SortedSet#headSet} documentation states that a subset of a
   * subset throws an {@link IllegalArgumentException} if passed a
   * {@code toElement} greater than an earlier {@code toElement}. However, this
   * method doesn't throw an exception in that situation, but instead keeps the
   * original {@code toElement}.
   */
  @Override
  public ImmutableSortedSet<E> headSet(E toElement) {
    return headSet(toElement, false);
  }

  /**
   * @since 12.0
   */
  @GwtIncompatible("NavigableSet")
  @Override
  public ImmutableSortedSet<E> headSet(E toElement, boolean inclusive) {
    return headSetImpl(checkNotNull(toElement), inclusive);
  }

  /**
   * {@inheritDoc}
   *
   * <p>This method returns a serializable {@code ImmutableSortedSet}.
   *
   * <p>The {@link SortedSet#subSet} documentation states that a subset of a
   * subset throws an {@link IllegalArgumentException} if passed a
   * {@code fromElement} smaller than an earlier {@code fromElement}. However,
   * this method doesn't throw an exception in that situation, but instead keeps
   * the original {@code fromElement}. Similarly, this method keeps the
   * original {@code toElement}, instead of throwing an exception, if passed a
   * {@code toElement} greater than an earlier {@code toElement}.
   */
  @Override
  public ImmutableSortedSet<E> subSet(E fromElement, E toElement) {
    return subSet(fromElement, true, toElement, false);
  }

  /**
   * @since 12.0
   */
  @GwtIncompatible("NavigableSet")
  @Override
  public ImmutableSortedSet<E> subSet(
      E fromElement, boolean fromInclusive, E toElement, boolean toInclusive) {
    checkNotNull(fromElement);
    checkNotNull(toElement);
    checkArgument(comparator.compare(fromElement, toElement) <= 0);
    return subSetImpl(fromElement, fromInclusive, toElement, toInclusive);
  }

  /**
   * {@inheritDoc}
   *
   * <p>This method returns a serializable {@code ImmutableSortedSet}.
   *
   * <p>The {@link SortedSet#tailSet} documentation states that a subset of a
   * subset throws an {@link IllegalArgumentException} if passed a
   * {@code fromElement} smaller than an earlier {@code fromElement}. However,
   * this method doesn't throw an exception in that situation, but instead keeps
   * the original {@code fromElement}.
   */
  @Override
  public ImmutableSortedSet<E> tailSet(E fromElement) {
    return tailSet(fromElement, true);
  }

  /**
   * @since 12.0
   */
  @GwtIncompatible("NavigableSet")
  @Override
  public ImmutableSortedSet<E> tailSet(E fromElement, boolean inclusive) {
    return tailSetImpl(checkNotNull(fromElement), inclusive);
  }

  /*
   * These methods perform most headSet, subSet, and tailSet logic, besides
   * parameter validation.
   */
  abstract ImmutableSortedSet<E> headSetImpl(E toElement, boolean inclusive);

  abstract ImmutableSortedSet<E> subSetImpl(
      E fromElement, boolean fromInclusive, E toElement, boolean toInclusive);

  abstract ImmutableSortedSet<E> tailSetImpl(E fromElement, boolean inclusive);

  /**
   * @since 12.0
   */
  @GwtIncompatible("NavigableSet")
  @Override
  public E lower(E e) {
    return Iterators.getNext(headSet(e, false).descendingIterator(), null);
  }

  /**
   * @since 12.0
   */
  @GwtIncompatible("NavigableSet")
  @Override
  public E floor(E e) {
    return Iterators.getNext(headSet(e, true).descendingIterator(), null);
  }

  /**
   * @since 12.0
   */
  @GwtIncompatible("NavigableSet")
  @Override
  public E ceiling(E e) {
    return Iterables.getFirst(tailSet(e, true), null);
  }

  /**
   * @since 12.0
   */
  @GwtIncompatible("NavigableSet")
  @Override
  public E higher(E e) {
    return Iterables.getFirst(tailSet(e, false), null);
  }

  @Override
  public E first() {
    return iterator().next();
  }

  @Override
  public E last() {
    return descendingIterator().next();
  }

  /**
   * Guaranteed to throw an exception and leave the set unmodified.
   *
   * @since 12.0
   * @throws UnsupportedOperationException always
   * @deprecated Unsupported operation.
   */
  @Deprecated
  @GwtIncompatible("NavigableSet")
  @Override
  public final E pollFirst() {
    throw new UnsupportedOperationException();
  }

  /**
   * Guaranteed to throw an exception and leave the set unmodified.
   *
   * @since 12.0
   * @throws UnsupportedOperationException always
   * @deprecated Unsupported operation.
   */
  @Deprecated
  @GwtIncompatible("NavigableSet")
  @Override
  public final E pollLast() {
    throw new UnsupportedOperationException();
  }

  @GwtIncompatible("NavigableSet")
  transient ImmutableSortedSet<E> descendingSet;

  /**
   * @since 12.0
   */
  @GwtIncompatible("NavigableSet")
  @Override
  public ImmutableSortedSet<E> descendingSet() {
    // racy single-check idiom
    ImmutableSortedSet<E> result = descendingSet;
    if (result == null) {
      result = descendingSet = createDescendingSet();
      result.descendingSet = this;
    }
    return result;
  }

  @GwtIncompatible("NavigableSet")
  ImmutableSortedSet<E> createDescendingSet() {
    return new DescendingImmutableSortedSet<E>(this);
  }

  /**
   * @since 12.0
   */
  @GwtIncompatible("NavigableSet")
  @Override
  public abstract UnmodifiableIterator<E> descendingIterator();

  /**
   * Returns the position of an element within the set, or -1 if not present.
   */
  abstract int indexOf(@Nullable Object target);

  /*
   * This class is used to serialize all ImmutableSortedSet instances,
   * regardless of implementation type. It captures their "logical contents"
   * only. This is necessary to ensure that the existence of a particular
   * implementation type is an implementation detail.
   */
  private static class SerializedForm<E> implements Serializable {
    final Comparator<? super E> comparator;
    final Object[] elements;

    public SerializedForm(Comparator<? super E> comparator, Object[] elements) {
      this.comparator = comparator;
      this.elements = elements;
    }

    @SuppressWarnings("unchecked")
    Object readResolve() {
      return new Builder<E>(comparator).add((E[]) elements).build();
    }

    private static final long serialVersionUID = 0;
  }

  private void readObject(ObjectInputStream stream)
      throws InvalidObjectException {
    throw new InvalidObjectException("Use SerializedForm");
  }

  @Override Object writeReplace() {
    return new SerializedForm<E>(comparator, toArray());
  }
}