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/*
 * Copyright (C) 2007 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.checkNotNull;
import static com.google.common.collect.CollectPreconditions.checkNonnegative;

import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.VisibleForTesting;
import com.google.common.base.Function;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.SortedMap;
import java.util.SortedSet;
import java.util.TreeSet;
import java.util.concurrent.atomic.AtomicInteger;

import javax.annotation.Nullable;

/**
 * A comparator, with additional methods to support common operations. This is an "enriched"
 * version of {@code Comparator}, in the same sense that {@link FluentIterable} is an enriched
 * {@link Iterable}.
 *
 * <h3>Three types of methods</h3>
 *
 * Like other fluent types, there are three types of methods present: methods for <i>acquiring</i>,
 * <i>chaining</i>, and <i>using</i>.
 *
 * <h4>Acquiring</h4>
 *
 * <p>The common ways to get an instance of {@code Ordering} are:
 *
 * <ul>
 * <li>Subclass it and implement {@link #compare} instead of implementing {@link Comparator}
 *     directly
 * <li>Pass a <i>pre-existing</i> {@link Comparator} instance to {@link #from(Comparator)}
 * <li>Use the natural ordering, {@link Ordering#natural}
 * </ul>
 *
 * <h4>Chaining</h4>
 *
 * <p>Then you can use the <i>chaining</i> methods to get an altered version of that {@code
 * Ordering}, including:
 *
 * <ul>
 * <li>{@link #reverse}
 * <li>{@link #compound(Comparator)}
 * <li>{@link #onResultOf(Function)}
 * <li>{@link #nullsFirst} / {@link #nullsLast}
 * </ul>
 *
 * <h4>Using</h4>
 *
 * <p>Finally, use the resulting {@code Ordering} anywhere a {@link Comparator} is required, or use
 * any of its special operations, such as:</p>
 *
 * <ul>
 * <li>{@link #immutableSortedCopy}
 * <li>{@link #isOrdered} / {@link #isStrictlyOrdered}
 * <li>{@link #min} / {@link #max}
 * </ul>
 *
 * <h3>Understanding complex orderings</h3>
 *
 * <p>Complex chained orderings like the following example can be challenging to understand.
 * <pre>   {@code
 *
 *   Ordering<Foo> ordering =
 *       Ordering.natural()
 *           .nullsFirst()
 *           .onResultOf(getBarFunction)
 *           .nullsLast();}</pre>
 *
 * Note that each chaining method returns a new ordering instance which is backed by the previous
 * instance, but has the chance to act on values <i>before</i> handing off to that backing
 * instance. As a result, it usually helps to read chained ordering expressions <i>backwards</i>.
 * For example, when {@code compare} is called on the above ordering:
 *
 * <ol>
 * <li>First, if only one {@code Foo} is null, that null value is treated as <i>greater</i>
 * <li>Next, non-null {@code Foo} values are passed to {@code getBarFunction} (we will be
 *     comparing {@code Bar} values from now on)
 * <li>Next, if only one {@code Bar} is null, that null value is treated as <i>lesser</i>
 * <li>Finally, natural ordering is used (i.e. the result of {@code Bar.compareTo(Bar)} is
 *     returned)
 * </ol>
 *
 * <p>Alas, {@link #reverse} is a little different. As you read backwards through a chain and
 * encounter a call to {@code reverse}, continue working backwards until a result is determined,
 * and then reverse that result.
 *
 * <h3>Additional notes</h3>
 *
 * <p>Except as noted, the orderings returned by the factory methods of this
 * class are serializable if and only if the provided instances that back them
 * are. For example, if {@code ordering} and {@code function} can themselves be
 * serialized, then {@code ordering.onResultOf(function)} can as well.
 *
 * <p>See the Guava User Guide article on <a href=
 * "https://github.com/google/guava/wiki/OrderingExplained">
 * {@code Ordering}</a>.
 *
 * @author Jesse Wilson
 * @author Kevin Bourrillion
 * @since 2.0
 */
@GwtCompatible
public abstract class Ordering<T> implements Comparator<T> {
    // Natural order

    /**
     * Returns a serializable ordering that uses the natural order of the values.
     * The ordering throws a {@link NullPointerException} when passed a null
     * parameter.
     *
     * <p>The type specification is {@code <C extends Comparable>}, instead of
     * the technically correct {@code <C extends Comparable<? super C>>}, to
     * support legacy types from before Java 5.
     */
    @GwtCompatible(serializable = true)
    @SuppressWarnings("unchecked") // TODO(kevinb): right way to explain this??
    public static <C extends Comparable> Ordering<C> natural() {
        return (Ordering<C>) NaturalOrdering.INSTANCE;
    }

    // Static factories

    /**
     * Returns an ordering based on an <i>existing</i> comparator instance. Note
     * that it is unnecessary to create a <i>new</i> anonymous inner class
     * implementing {@code Comparator} just to pass it in here. Instead, simply
     * subclass {@code Ordering} and implement its {@code compare} method
     * directly.
     *
     * @param comparator the comparator that defines the order
     * @return comparator itself if it is already an {@code Ordering}; otherwise
     *     an ordering that wraps that comparator
     */
    @GwtCompatible(serializable = true)
    public static <T> Ordering<T> from(Comparator<T> comparator) {
        return (comparator instanceof Ordering) ? (Ordering<T>) comparator : new ComparatorOrdering<T>(comparator);
    }

    /**
     * Simply returns its argument.
     *
     * @deprecated no need to use this
     */
    @GwtCompatible(serializable = true)
    @Deprecated
    public static <T> Ordering<T> from(Ordering<T> ordering) {
        return checkNotNull(ordering);
    }

    /**
     * Returns an ordering that compares objects according to the order in
     * which they appear in the given list. Only objects present in the list
     * (according to {@link Object#equals}) may be compared. This comparator
     * imposes a "partial ordering" over the type {@code T}. Subsequent changes
     * to the {@code valuesInOrder} list will have no effect on the returned
     * comparator. Null values in the list are not supported.
     *
     * <p>The returned comparator throws an {@link ClassCastException} when it
     * receives an input parameter that isn't among the provided values.
     *
     * <p>The generated comparator is serializable if all the provided values are
     * serializable.
     *
     * @param valuesInOrder the values that the returned comparator will be able
     *     to compare, in the order the comparator should induce
     * @return the comparator described above
     * @throws NullPointerException if any of the provided values is null
     * @throws IllegalArgumentException if {@code valuesInOrder} contains any
     *     duplicate values (according to {@link Object#equals})
     */
    @GwtCompatible(serializable = true)
    public static <T> Ordering<T> explicit(List<T> valuesInOrder) {
        return new ExplicitOrdering<T>(valuesInOrder);
    }

    /**
     * Returns an ordering that compares objects according to the order in
     * which they are given to this method. Only objects present in the argument
     * list (according to {@link Object#equals}) may be compared. This comparator
     * imposes a "partial ordering" over the type {@code T}. Null values in the
     * argument list are not supported.
     *
     * <p>The returned comparator throws a {@link ClassCastException} when it
     * receives an input parameter that isn't among the provided values.
     *
     * <p>The generated comparator is serializable if all the provided values are
     * serializable.
     *
     * @param leastValue the value which the returned comparator should consider
     *     the "least" of all values
     * @param remainingValuesInOrder the rest of the values that the returned
     *     comparator will be able to compare, in the order the comparator should
     *     follow
     * @return the comparator described above
     * @throws NullPointerException if any of the provided values is null
     * @throws IllegalArgumentException if any duplicate values (according to
     *     {@link Object#equals(Object)}) are present among the method arguments
     */
    @GwtCompatible(serializable = true)
    public static <T> Ordering<T> explicit(T leastValue, T... remainingValuesInOrder) {
        return explicit(Lists.asList(leastValue, remainingValuesInOrder));
    }

    // Ordering<Object> singletons

    /**
     * Returns an ordering which treats all values as equal, indicating "no
     * ordering." Passing this ordering to any <i>stable</i> sort algorithm
     * results in no change to the order of elements. Note especially that {@link
     * #sortedCopy} and {@link #immutableSortedCopy} are stable, and in the
     * returned instance these are implemented by simply copying the source list.
     *
     * <p>Example: <pre>   {@code
     *
     *   Ordering.allEqual().nullsLast().sortedCopy(
     *       asList(t, null, e, s, null, t, null))}</pre>
     *
     * <p>Assuming {@code t}, {@code e} and {@code s} are non-null, this returns
     * {@code [t, e, s, t, null, null, null]} regardlesss of the true comparison
     * order of those three values (which might not even implement {@link
     * Comparable} at all).
     *
     * <p><b>Warning:</b> by definition, this comparator is not <i>consistent with
     * equals</i> (as defined {@linkplain Comparator here}). Avoid its use in
     * APIs, such as {@link TreeSet#TreeSet(Comparator)}, where such consistency
     * is expected.
     *
     * <p>The returned comparator is serializable.
     *
     * @since 13.0
     */
    @GwtCompatible(serializable = true)
    @SuppressWarnings("unchecked")
    public static Ordering<Object> allEqual() {
        return AllEqualOrdering.INSTANCE;
    }

    /**
     * Returns an ordering that compares objects by the natural ordering of their
     * string representations as returned by {@code toString()}. It does not
     * support null values.
     *
     * <p>The comparator is serializable.
     */
    @GwtCompatible(serializable = true)
    public static Ordering<Object> usingToString() {
        return UsingToStringOrdering.INSTANCE;
    }

    /**
     * Returns an arbitrary ordering over all objects, for which {@code compare(a,
     * b) == 0} implies {@code a == b} (identity equality). There is no meaning
     * whatsoever to the order imposed, but it is constant for the life of the VM.
     *
     * <p>Because the ordering is identity-based, it is not "consistent with
     * {@link Object#equals(Object)}" as defined by {@link Comparator}. Use
     * caution when building a {@link SortedSet} or {@link SortedMap} from it, as
     * the resulting collection will not behave exactly according to spec.
     *
     * <p>This ordering is not serializable, as its implementation relies on
     * {@link System#identityHashCode(Object)}, so its behavior cannot be
     * preserved across serialization.
     *
     * @since 2.0
     */
    public static Ordering<Object> arbitrary() {
        return ArbitraryOrderingHolder.ARBITRARY_ORDERING;
    }

    private static class ArbitraryOrderingHolder {
        static final Ordering<Object> ARBITRARY_ORDERING = new ArbitraryOrdering();
    }

    @VisibleForTesting
    static class ArbitraryOrdering extends Ordering<Object> {

        @SuppressWarnings("deprecation") // TODO(kevinb): ?
        private Map<Object, Integer> uids = Platform.tryWeakKeys(new MapMaker())
                .makeComputingMap(new Function<Object, Integer>() {
                    final AtomicInteger counter = new AtomicInteger(0);

                    @Override
                    public Integer apply(Object from) {
                        return counter.getAndIncrement();
                    }
                });

        @Override
        public int compare(Object left, Object right) {
            if (left == right) {
                return 0;
            } else if (left == null) {
                return -1;
            } else if (right == null) {
                return 1;
            }
            int leftCode = identityHashCode(left);
            int rightCode = identityHashCode(right);
            if (leftCode != rightCode) {
                return leftCode < rightCode ? -1 : 1;
            }

            // identityHashCode collision (rare, but not as rare as you'd think)
            int result = uids.get(left).compareTo(uids.get(right));
            if (result == 0) {
                throw new AssertionError(); // extremely, extremely unlikely.
            }
            return result;
        }

        @Override
        public String toString() {
            return "Ordering.arbitrary()";
        }

        /*
         * We need to be able to mock identityHashCode() calls for tests, because it
         * can take 1-10 seconds to find colliding objects. Mocking frameworks that
         * can do magic to mock static method calls still can't do so for a system
         * class, so we need the indirection. In production, Hotspot should still
         * recognize that the call is 1-morphic and should still be willing to
         * inline it if necessary.
         */
        int identityHashCode(Object object) {
            return System.identityHashCode(object);
        }
    }

    // Constructor

    /**
     * Constructs a new instance of this class (only invokable by the subclass
     * constructor, typically implicit).
     */
    protected Ordering() {
    }

    // Instance-based factories (and any static equivalents)

    /**
     * Returns the reverse of this ordering; the {@code Ordering} equivalent to
     * {@link Collections#reverseOrder(Comparator)}.
     */
    // type parameter <S> lets us avoid the extra <String> in statements like:
    // Ordering<String> o = Ordering.<String>natural().reverse();
    @GwtCompatible(serializable = true)
    public <S extends T> Ordering<S> reverse() {
        return new ReverseOrdering<S>(this);
    }

    /**
     * Returns an ordering that treats {@code null} as less than all other values
     * and uses {@code this} to compare non-null values.
     */
    // type parameter <S> lets us avoid the extra <String> in statements like:
    // Ordering<String> o = Ordering.<String>natural().nullsFirst();
    @GwtCompatible(serializable = true)
    public <S extends T> Ordering<S> nullsFirst() {
        return new NullsFirstOrdering<S>(this);
    }

    /**
     * Returns an ordering that treats {@code null} as greater than all other
     * values and uses this ordering to compare non-null values.
     */
    // type parameter <S> lets us avoid the extra <String> in statements like:
    // Ordering<String> o = Ordering.<String>natural().nullsLast();
    @GwtCompatible(serializable = true)
    public <S extends T> Ordering<S> nullsLast() {
        return new NullsLastOrdering<S>(this);
    }

    /**
     * Returns a new ordering on {@code F} which orders elements by first applying
     * a function to them, then comparing those results using {@code this}. For
     * example, to compare objects by their string forms, in a case-insensitive
     * manner, use: <pre>   {@code
     *
     *   Ordering.from(String.CASE_INSENSITIVE_ORDER)
     *       .onResultOf(Functions.toStringFunction())}</pre>
     */
    @GwtCompatible(serializable = true)
    public <F> Ordering<F> onResultOf(Function<F, ? extends T> function) {
        return new ByFunctionOrdering<F, T>(function, this);
    }

    <T2 extends T> Ordering<Map.Entry<T2, ?>> onKeys() {
        return onResultOf(Maps.<T2>keyFunction());
    }

    /**
     * Returns an ordering which first uses the ordering {@code this}, but which
     * in the event of a "tie", then delegates to {@code secondaryComparator}.
     * For example, to sort a bug list first by status and second by priority, you
     * might use {@code byStatus.compound(byPriority)}. For a compound ordering
     * with three or more components, simply chain multiple calls to this method.
     *
     * <p>An ordering produced by this method, or a chain of calls to this method,
     * is equivalent to one created using {@link Ordering#compound(Iterable)} on
     * the same component comparators.
     */
    @GwtCompatible(serializable = true)
    public <U extends T> Ordering<U> compound(Comparator<? super U> secondaryComparator) {
        return new CompoundOrdering<U>(this, checkNotNull(secondaryComparator));
    }

    /**
     * Returns an ordering which tries each given comparator in order until a
     * non-zero result is found, returning that result, and returning zero only if
     * all comparators return zero. The returned ordering is based on the state of
     * the {@code comparators} iterable at the time it was provided to this
     * method.
     *
     * <p>The returned ordering is equivalent to that produced using {@code
     * Ordering.from(comp1).compound(comp2).compound(comp3) . . .}.
     *
     * <p><b>Warning:</b> Supplying an argument with undefined iteration order,
     * such as a {@link HashSet}, will produce non-deterministic results.
     *
     * @param comparators the comparators to try in order
     */
    @GwtCompatible(serializable = true)
    public static <T> Ordering<T> compound(Iterable<? extends Comparator<? super T>> comparators) {
        return new CompoundOrdering<T>(comparators);
    }

    /**
     * Returns a new ordering which sorts iterables by comparing corresponding
     * elements pairwise until a nonzero result is found; imposes "dictionary
     * order". If the end of one iterable is reached, but not the other, the
     * shorter iterable is considered to be less than the longer one. For example,
     * a lexicographical natural ordering over integers considers {@code
     * [] < [1] < [1, 1] < [1, 2] < [2]}.
     *
     * <p>Note that {@code ordering.lexicographical().reverse()} is not
     * equivalent to {@code ordering.reverse().lexicographical()} (consider how
     * each would order {@code [1]} and {@code [1, 1]}).
     *
     * @since 2.0
     */
    @GwtCompatible(serializable = true)
    // type parameter <S> lets us avoid the extra <String> in statements like:
    // Ordering<Iterable<String>> o =
    //     Ordering.<String>natural().lexicographical();
    public <S extends T> Ordering<Iterable<S>> lexicographical() {
        /*
         * Note that technically the returned ordering should be capable of
         * handling not just {@code Iterable<S>} instances, but also any {@code
         * Iterable<? extends S>}. However, the need for this comes up so rarely
         * that it doesn't justify making everyone else deal with the very ugly
         * wildcard.
         */
        return new LexicographicalOrdering<S>(this);
    }

    // Regular instance methods

    // Override to add @Nullable
    @Override
    public abstract int compare(@Nullable T left, @Nullable T right);

    /**
     * Returns the least of the specified values according to this ordering. If
     * there are multiple least values, the first of those is returned. The
     * iterator will be left exhausted: its {@code hasNext()} method will return
     * {@code false}.
     *
     * @param iterator the iterator whose minimum element is to be determined
     * @throws NoSuchElementException if {@code iterator} is empty
     * @throws ClassCastException if the parameters are not <i>mutually
     *     comparable</i> under this ordering.
     *
     * @since 11.0
     */
    public <E extends T> E min(Iterator<E> iterator) {
        // let this throw NoSuchElementException as necessary
        E minSoFar = iterator.next();

        while (iterator.hasNext()) {
            minSoFar = min(minSoFar, iterator.next());
        }

        return minSoFar;
    }

    /**
     * Returns the least of the specified values according to this ordering. If
     * there are multiple least values, the first of those is returned.
     *
     * @param iterable the iterable whose minimum element is to be determined
     * @throws NoSuchElementException if {@code iterable} is empty
     * @throws ClassCastException if the parameters are not <i>mutually
     *     comparable</i> under this ordering.
     */
    public <E extends T> E min(Iterable<E> iterable) {
        return min(iterable.iterator());
    }

    /**
     * Returns the lesser of the two values according to this ordering. If the
     * values compare as 0, the first is returned.
     *
     * <p><b>Implementation note:</b> this method is invoked by the default
     * implementations of the other {@code min} overloads, so overriding it will
     * affect their behavior.
     *
     * @param a value to compare, returned if less than or equal to b.
     * @param b value to compare.
     * @throws ClassCastException if the parameters are not <i>mutually
     *     comparable</i> under this ordering.
     */
    public <E extends T> E min(@Nullable E a, @Nullable E b) {
        return (compare(a, b) <= 0) ? a : b;
    }

    /**
     * Returns the least of the specified values according to this ordering. If
     * there are multiple least values, the first of those is returned.
     *
     * @param a value to compare, returned if less than or equal to the rest.
     * @param b value to compare
     * @param c value to compare
     * @param rest values to compare
     * @throws ClassCastException if the parameters are not <i>mutually
     *     comparable</i> under this ordering.
     */
    public <E extends T> E min(@Nullable E a, @Nullable E b, @Nullable E c, E... rest) {
        E minSoFar = min(min(a, b), c);

        for (E r : rest) {
            minSoFar = min(minSoFar, r);
        }

        return minSoFar;
    }

    /**
     * Returns the greatest of the specified values according to this ordering. If
     * there are multiple greatest values, the first of those is returned. The
     * iterator will be left exhausted: its {@code hasNext()} method will return
     * {@code false}.
     *
     * @param iterator the iterator whose maximum element is to be determined
     * @throws NoSuchElementException if {@code iterator} is empty
     * @throws ClassCastException if the parameters are not <i>mutually
     *     comparable</i> under this ordering.
     *
     * @since 11.0
     */
    public <E extends T> E max(Iterator<E> iterator) {
        // let this throw NoSuchElementException as necessary
        E maxSoFar = iterator.next();

        while (iterator.hasNext()) {
            maxSoFar = max(maxSoFar, iterator.next());
        }

        return maxSoFar;
    }

    /**
     * Returns the greatest of the specified values according to this ordering. If
     * there are multiple greatest values, the first of those is returned.
     *
     * @param iterable the iterable whose maximum element is to be determined
     * @throws NoSuchElementException if {@code iterable} is empty
     * @throws ClassCastException if the parameters are not <i>mutually
     *     comparable</i> under this ordering.
     */
    public <E extends T> E max(Iterable<E> iterable) {
        return max(iterable.iterator());
    }

    /**
     * Returns the greater of the two values according to this ordering. If the
     * values compare as 0, the first is returned.
     *
     * <p><b>Implementation note:</b> this method is invoked by the default
     * implementations of the other {@code max} overloads, so overriding it will
     * affect their behavior.
     *
     * @param a value to compare, returned if greater than or equal to b.
     * @param b value to compare.
     * @throws ClassCastException if the parameters are not <i>mutually
     *     comparable</i> under this ordering.
     */
    public <E extends T> E max(@Nullable E a, @Nullable E b) {
        return (compare(a, b) >= 0) ? a : b;
    }

    /**
     * Returns the greatest of the specified values according to this ordering. If
     * there are multiple greatest values, the first of those is returned.
     *
     * @param a value to compare, returned if greater than or equal to the rest.
     * @param b value to compare
     * @param c value to compare
     * @param rest values to compare
     * @throws ClassCastException if the parameters are not <i>mutually
     *     comparable</i> under this ordering.
     */
    public <E extends T> E max(@Nullable E a, @Nullable E b, @Nullable E c, E... rest) {
        E maxSoFar = max(max(a, b), c);

        for (E r : rest) {
            maxSoFar = max(maxSoFar, r);
        }

        return maxSoFar;
    }

    /**
     * Returns the {@code k} least elements of the given iterable according to
     * this ordering, in order from least to greatest.  If there are fewer than
     * {@code k} elements present, all will be included.
     *
     * <p>The implementation does not necessarily use a <i>stable</i> sorting
     * algorithm; when multiple elements are equivalent, it is undefined which
     * will come first.
     *
     * @return an immutable {@code RandomAccess} list of the {@code k} least
     *     elements in ascending order
     * @throws IllegalArgumentException if {@code k} is negative
     * @since 8.0
     */
    public <E extends T> List<E> leastOf(Iterable<E> iterable, int k) {
        if (iterable instanceof Collection) {
            Collection<E> collection = (Collection<E>) iterable;
            if (collection.size() <= 2L * k) {
                // In this case, just dumping the collection to an array and sorting is
                // faster than using the implementation for Iterator, which is
                // specialized for k much smaller than n.

                @SuppressWarnings("unchecked") // c only contains E's and doesn't escape
                E[] array = (E[]) collection.toArray();
                Arrays.sort(array, this);
                if (array.length > k) {
                    array = ObjectArrays.arraysCopyOf(array, k);
                }
                return Collections.unmodifiableList(Arrays.asList(array));
            }
        }
        return leastOf(iterable.iterator(), k);
    }

    /**
     * Returns the {@code k} least elements from the given iterator according to
     * this ordering, in order from least to greatest.  If there are fewer than
     * {@code k} elements present, all will be included.
     *
     * <p>The implementation does not necessarily use a <i>stable</i> sorting
     * algorithm; when multiple elements are equivalent, it is undefined which
     * will come first.
     *
     * @return an immutable {@code RandomAccess} list of the {@code k} least
     *     elements in ascending order
     * @throws IllegalArgumentException if {@code k} is negative
     * @since 14.0
     */
    public <E extends T> List<E> leastOf(Iterator<E> elements, int k) {
        checkNotNull(elements);
        checkNonnegative(k, "k");

        if (k == 0 || !elements.hasNext()) {
            return ImmutableList.of();
        } else if (k >= Integer.MAX_VALUE / 2) {
            // k is really large; just do a straightforward sorted-copy-and-sublist
            ArrayList<E> list = Lists.newArrayList(elements);
            Collections.sort(list, this);
            if (list.size() > k) {
                list.subList(k, list.size()).clear();
            }
            list.trimToSize();
            return Collections.unmodifiableList(list);
        }

        /*
         * Our goal is an O(n) algorithm using only one pass and O(k) additional
         * memory.
         *
         * We use the following algorithm: maintain a buffer of size 2*k. Every time
         * the buffer gets full, find the median and partition around it, keeping
         * only the lowest k elements.  This requires n/k find-median-and-partition
         * steps, each of which take O(k) time with a traditional quickselect.
         *
         * After sorting the output, the whole algorithm is O(n + k log k). It
         * degrades gracefully for worst-case input (descending order), performs
         * competitively or wins outright for randomly ordered input, and doesn't
         * require the whole collection to fit into memory.
         */
        int bufferCap = k * 2;
        @SuppressWarnings("unchecked") // we'll only put E's in
        E[] buffer = (E[]) new Object[bufferCap];
        E threshold = elements.next();
        buffer[0] = threshold;
        int bufferSize = 1;
        // threshold is the kth smallest element seen so far.  Once bufferSize >= k,
        // anything larger than threshold can be ignored immediately.

        while (bufferSize < k && elements.hasNext()) {
            E e = elements.next();
            buffer[bufferSize++] = e;
            threshold = max(threshold, e);
        }

        while (elements.hasNext()) {
            E e = elements.next();
            if (compare(e, threshold) >= 0) {
                continue;
            }

            buffer[bufferSize++] = e;
            if (bufferSize == bufferCap) {
                // We apply the quickselect algorithm to partition about the median,
                // and then ignore the last k elements.
                int left = 0;
                int right = bufferCap - 1;

                int minThresholdPosition = 0;
                // The leftmost position at which the greatest of the k lower elements
                // -- the new value of threshold -- might be found.

                while (left < right) {
                    int pivotIndex = (left + right + 1) >>> 1;
                    int pivotNewIndex = partition(buffer, left, right, pivotIndex);
                    if (pivotNewIndex > k) {
                        right = pivotNewIndex - 1;
                    } else if (pivotNewIndex < k) {
                        left = Math.max(pivotNewIndex, left + 1);
                        minThresholdPosition = pivotNewIndex;
                    } else {
                        break;
                    }
                }
                bufferSize = k;

                threshold = buffer[minThresholdPosition];
                for (int i = minThresholdPosition + 1; i < bufferSize; i++) {
                    threshold = max(threshold, buffer[i]);
                }
            }
        }

        Arrays.sort(buffer, 0, bufferSize, this);

        bufferSize = Math.min(bufferSize, k);
        return Collections.unmodifiableList(Arrays.asList(ObjectArrays.arraysCopyOf(buffer, bufferSize)));
        // We can't use ImmutableList; we have to be null-friendly!
    }

    private <E extends T> int partition(E[] values, int left, int right, int pivotIndex) {
        E pivotValue = values[pivotIndex];

        values[pivotIndex] = values[right];
        values[right] = pivotValue;

        int storeIndex = left;
        for (int i = left; i < right; i++) {
            if (compare(values[i], pivotValue) < 0) {
                ObjectArrays.swap(values, storeIndex, i);
                storeIndex++;
            }
        }
        ObjectArrays.swap(values, right, storeIndex);
        return storeIndex;
    }

    /**
     * Returns the {@code k} greatest elements of the given iterable according to
     * this ordering, in order from greatest to least. If there are fewer than
     * {@code k} elements present, all will be included.
     *
     * <p>The implementation does not necessarily use a <i>stable</i> sorting
     * algorithm; when multiple elements are equivalent, it is undefined which
     * will come first.
     *
     * @return an immutable {@code RandomAccess} list of the {@code k} greatest
     *     elements in <i>descending order</i>
     * @throws IllegalArgumentException if {@code k} is negative
     * @since 8.0
     */
    public <E extends T> List<E> greatestOf(Iterable<E> iterable, int k) {
        // TODO(kevinb): see if delegation is hurting performance noticeably
        // TODO(kevinb): if we change this implementation, add full unit tests.
        return reverse().leastOf(iterable, k);
    }

    /**
     * Returns the {@code k} greatest elements from the given iterator according to
     * this ordering, in order from greatest to least. If there are fewer than
     * {@code k} elements present, all will be included.
     *
     * <p>The implementation does not necessarily use a <i>stable</i> sorting
     * algorithm; when multiple elements are equivalent, it is undefined which
     * will come first.
     *
     * @return an immutable {@code RandomAccess} list of the {@code k} greatest
     *     elements in <i>descending order</i>
     * @throws IllegalArgumentException if {@code k} is negative
     * @since 14.0
     */
    public <E extends T> List<E> greatestOf(Iterator<E> iterator, int k) {
        return reverse().leastOf(iterator, k);
    }

    /**
     * Returns a <b>mutable</b> list containing {@code elements} sorted by this
     * ordering; use this only when the resulting list may need further
     * modification, or may contain {@code null}. The input is not modified. The
     * returned list is serializable and has random access.
     *
     * <p>Unlike {@link Sets#newTreeSet(Iterable)}, this method does not discard
     * elements that are duplicates according to the comparator. The sort
     * performed is <i>stable</i>, meaning that such elements will appear in the
     * returned list in the same order they appeared in {@code elements}.
     *
     * <p><b>Performance note:</b> According to our
     * benchmarking
     * on Open JDK 7, {@link #immutableSortedCopy} generally performs better (in
     * both time and space) than this method, and this method in turn generally
     * performs better than copying the list and calling {@link
     * Collections#sort(List)}.
     */
    public <E extends T> List<E> sortedCopy(Iterable<E> elements) {
        @SuppressWarnings("unchecked") // does not escape, and contains only E's
        E[] array = (E[]) Iterables.toArray(elements);
        Arrays.sort(array, this);
        return Lists.newArrayList(Arrays.asList(array));
    }

    /**
     * Returns an <b>immutable</b> list containing {@code elements} sorted by this
     * ordering. The input is not modified.
     *
     * <p>Unlike {@link Sets#newTreeSet(Iterable)}, this method does not discard
     * elements that are duplicates according to the comparator. The sort
     * performed is <i>stable</i>, meaning that such elements will appear in the
     * returned list in the same order they appeared in {@code elements}.
     *
     * <p><b>Performance note:</b> According to our
     * benchmarking
     * on Open JDK 7, this method is the most efficient way to make a sorted copy
     * of a collection.
     *
     * @throws NullPointerException if any of {@code elements} (or {@code
     *     elements} itself) is null
     * @since 3.0
     */
    public <E extends T> ImmutableList<E> immutableSortedCopy(Iterable<E> elements) {
        @SuppressWarnings("unchecked") // we'll only ever have E's in here
        E[] array = (E[]) Iterables.toArray(elements);
        for (E e : array) {
            checkNotNull(e);
        }
        Arrays.sort(array, this);
        return ImmutableList.asImmutableList(array);
    }

    /**
     * Returns {@code true} if each element in {@code iterable} after the first is
     * greater than or equal to the element that preceded it, according to this
     * ordering. Note that this is always true when the iterable has fewer than
     * two elements.
     */
    public boolean isOrdered(Iterable<? extends T> iterable) {
        Iterator<? extends T> it = iterable.iterator();
        if (it.hasNext()) {
            T prev = it.next();
            while (it.hasNext()) {
                T next = it.next();
                if (compare(prev, next) > 0) {
                    return false;
                }
                prev = next;
            }
        }
        return true;
    }

    /**
     * Returns {@code true} if each element in {@code iterable} after the first is
     * <i>strictly</i> greater than the element that preceded it, according to
     * this ordering. Note that this is always true when the iterable has fewer
     * than two elements.
     */
    public boolean isStrictlyOrdered(Iterable<? extends T> iterable) {
        Iterator<? extends T> it = iterable.iterator();
        if (it.hasNext()) {
            T prev = it.next();
            while (it.hasNext()) {
                T next = it.next();
                if (compare(prev, next) >= 0) {
                    return false;
                }
                prev = next;
            }
        }
        return true;
    }

    /**
     * {@link Collections#binarySearch(List, Object, Comparator) Searches}
     * {@code sortedList} for {@code key} using the binary search algorithm. The
     * list must be sorted using this ordering.
     *
     * @param sortedList the list to be searched
     * @param key the key to be searched for
     */
    public int binarySearch(List<? extends T> sortedList, @Nullable T key) {
        return Collections.binarySearch(sortedList, key, this);
    }

    /**
     * Exception thrown by a {@link Ordering#explicit(List)} or {@link
     * Ordering#explicit(Object, Object[])} comparator when comparing a value
     * outside the set of values it can compare. Extending {@link
     * ClassCastException} may seem odd, but it is required.
     */
    // TODO(kevinb): make this public, document it right
    @VisibleForTesting
    static class IncomparableValueException extends ClassCastException {
        final Object value;

        IncomparableValueException(Object value) {
            super("Cannot compare value: " + value);
            this.value = value;
        }

        private static final long serialVersionUID = 0;
    }

    // Never make these public
    static final int LEFT_IS_GREATER = 1;
    static final int RIGHT_IS_GREATER = -1;
}