EaglerForge/sources/main/java/com/google/common/collect/Ordering.java

/*
 * 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 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.TreeSet;

import javax.annotation.Nullable;

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

/**
 * 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}.
 *
 * <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>
 *
 * <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>
 *
 * <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>
 *
 * <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= "http://code.google.com/p/guava-libraries/wiki/OrderingExplained">
 * {@code Ordering}</a>.
 *
 * @author Jesse Wilson
 * @author Kevin Bourrillion
 * @since 2.0 (imported from Google Collections Library)
 */
@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.
	 */
	@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;
	}

	// 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;
}