001/*
002 * Copyright (C) 2008 The Guava Authors
003 *
004 * Licensed under the Apache License, Version 2.0 (the "License");
005 * you may not use this file except in compliance with the License.
006 * You may obtain a copy of the License at
007 *
008 * http://www.apache.org/licenses/LICENSE-2.0
009 *
010 * Unless required by applicable law or agreed to in writing, software
011 * distributed under the License is distributed on an "AS IS" BASIS,
012 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
013 * See the License for the specific language governing permissions and
014 * limitations under the License.
015 */
016
017package com.google.common.collect;
018
019import static com.google.common.base.Preconditions.checkArgument;
020import static com.google.common.base.Preconditions.checkNotNull;
021
022import com.google.common.annotations.GwtCompatible;
023import com.google.common.base.Equivalence;
024import com.google.common.base.Predicate;
025import com.google.errorprone.annotations.Immutable;
026import java.io.Serializable;
027import java.util.Comparator;
028import java.util.Iterator;
029import java.util.NoSuchElementException;
030import java.util.SortedSet;
031import javax.annotation.CheckForNull;
032
033/**
034 * A range (or "interval") defines the <i>boundaries</i> around a contiguous span of values of some
035 * {@code Comparable} type; for example, "integers from 1 to 100 inclusive." Note that it is not
036 * possible to <i>iterate</i> over these contained values. To do so, pass this range instance and an
037 * appropriate {@link DiscreteDomain} to {@link ContiguousSet#create}.
038 *
039 * <h3>Types of ranges</h3>
040 *
041 * <p>Each end of the range may be bounded or unbounded. If bounded, there is an associated
042 * <i>endpoint</i> value, and the range is considered to be either <i>open</i> (does not include the
043 * endpoint) or <i>closed</i> (includes the endpoint) on that side. With three possibilities on each
044 * side, this yields nine basic types of ranges, enumerated below. (Notation: a square bracket
045 * ({@code [ ]}) indicates that the range is closed on that side; a parenthesis ({@code ( )}) means
046 * it is either open or unbounded. The construct {@code {x | statement}} is read "the set of all
047 * <i>x</i> such that <i>statement</i>.")
048 *
049 * <blockquote>
050 *
051 * <table>
052 * <caption>Range Types</caption>
053 * <tr><th>Notation        <th>Definition               <th>Factory method
054 * <tr><td>{@code (a..b)}  <td>{@code {x | a < x < b}}  <td>{@link Range#open open}
055 * <tr><td>{@code [a..b]}  <td>{@code {x | a <= x <= b}}<td>{@link Range#closed closed}
056 * <tr><td>{@code (a..b]}  <td>{@code {x | a < x <= b}} <td>{@link Range#openClosed openClosed}
057 * <tr><td>{@code [a..b)}  <td>{@code {x | a <= x < b}} <td>{@link Range#closedOpen closedOpen}
058 * <tr><td>{@code (a..+∞)} <td>{@code {x | x > a}}      <td>{@link Range#greaterThan greaterThan}
059 * <tr><td>{@code [a..+∞)} <td>{@code {x | x >= a}}     <td>{@link Range#atLeast atLeast}
060 * <tr><td>{@code (-∞..b)} <td>{@code {x | x < b}}      <td>{@link Range#lessThan lessThan}
061 * <tr><td>{@code (-∞..b]} <td>{@code {x | x <= b}}     <td>{@link Range#atMost atMost}
062 * <tr><td>{@code (-∞..+∞)}<td>{@code {x}}              <td>{@link Range#all all}
063 * </table>
064 *
065 * </blockquote>
066 *
067 * <p>When both endpoints exist, the upper endpoint may not be less than the lower. The endpoints
068 * may be equal only if at least one of the bounds is closed:
069 *
070 * <ul>
071 *   <li>{@code [a..a]} : a singleton range
072 *   <li>{@code [a..a); (a..a]} : {@linkplain #isEmpty empty} ranges; also valid
073 *   <li>{@code (a..a)} : <b>invalid</b>; an exception will be thrown
074 * </ul>
075 *
076 * <h3>Warnings</h3>
077 *
078 * <ul>
079 *   <li>Use immutable value types only, if at all possible. If you must use a mutable type, <b>do
080 *       not</b> allow the endpoint instances to mutate after the range is created!
081 *   <li>Your value type's comparison method should be {@linkplain Comparable consistent with
082 *       equals} if at all possible. Otherwise, be aware that concepts used throughout this
083 *       documentation such as "equal", "same", "unique" and so on actually refer to whether {@link
084 *       Comparable#compareTo compareTo} returns zero, not whether {@link Object#equals equals}
085 *       returns {@code true}.
086 *   <li>A class which implements {@code Comparable<UnrelatedType>} is very broken, and will cause
087 *       undefined horrible things to happen in {@code Range}. For now, the Range API does not
088 *       prevent its use, because this would also rule out all ungenerified (pre-JDK1.5) data types.
089 *       <b>This may change in the future.</b>
090 * </ul>
091 *
092 * <h3>Other notes</h3>
093 *
094 * <ul>
095 *   <li>All ranges are shallow-immutable.
096 *   <li>Instances of this type are obtained using the static factory methods in this class.
097 *   <li>Ranges are <i>convex</i>: whenever two values are contained, all values in between them
098 *       must also be contained. More formally, for any {@code c1 <= c2 <= c3} of type {@code C},
099 *       {@code r.contains(c1) && r.contains(c3)} implies {@code r.contains(c2)}). This means that a
100 *       {@code Range<Integer>} can never be used to represent, say, "all <i>prime</i> numbers from
101 *       1 to 100."
102 *   <li>When evaluated as a {@link Predicate}, a range yields the same result as invoking {@link
103 *       #contains}.
104 *   <li>Terminology note: a range {@code a} is said to be the <i>maximal</i> range having property
105 *       <i>P</i> if, for all ranges {@code b} also having property <i>P</i>, {@code a.encloses(b)}.
106 *       Likewise, {@code a} is <i>minimal</i> when {@code b.encloses(a)} for all {@code b} having
107 *       property <i>P</i>. See, for example, the definition of {@link #intersection intersection}.
108 *   <li>A {@code Range} is serializable if it has no bounds, or if each bound is serializable.
109 * </ul>
110 *
111 * <h3>Further reading</h3>
112 *
113 * <p>See the Guava User Guide article on <a
114 * href="https://github.com/google/guava/wiki/RangesExplained">{@code Range}</a>.
115 *
116 * @author Kevin Bourrillion
117 * @author Gregory Kick
118 * @since 10.0
119 */
120@GwtCompatible
121@SuppressWarnings("rawtypes") // https://github.com/google/guava/issues/989
122@Immutable(containerOf = "C")
123@ElementTypesAreNonnullByDefault
124public final class Range<C extends Comparable> extends RangeGwtSerializationDependencies
125    implements Predicate<C>, Serializable {
126  @SuppressWarnings("unchecked")
127  static <C extends Comparable<?>> Ordering<Range<C>> rangeLexOrdering() {
128    return (Ordering<Range<C>>) RangeLexOrdering.INSTANCE;
129  }
130
131  static <C extends Comparable<?>> Range<C> create(Cut<C> lowerBound, Cut<C> upperBound) {
132    return new Range<>(lowerBound, upperBound);
133  }
134
135  /**
136   * Returns a range that contains all values strictly greater than {@code lower} and strictly less
137   * than {@code upper}.
138   *
139   * @throws IllegalArgumentException if {@code lower} is greater than <i>or equal to</i> {@code
140   *     upper}
141   * @throws ClassCastException if {@code lower} and {@code upper} are not mutually comparable
142   * @since 14.0
143   */
144  public static <C extends Comparable<?>> Range<C> open(C lower, C upper) {
145    return create(Cut.aboveValue(lower), Cut.belowValue(upper));
146  }
147
148  /**
149   * Returns a range that contains all values greater than or equal to {@code lower} and less than
150   * or equal to {@code upper}.
151   *
152   * @throws IllegalArgumentException if {@code lower} is greater than {@code upper}
153   * @throws ClassCastException if {@code lower} and {@code upper} are not mutually comparable
154   * @since 14.0
155   */
156  public static <C extends Comparable<?>> Range<C> closed(C lower, C upper) {
157    return create(Cut.belowValue(lower), Cut.aboveValue(upper));
158  }
159
160  /**
161   * Returns a range that contains all values greater than or equal to {@code lower} and strictly
162   * less than {@code upper}.
163   *
164   * @throws IllegalArgumentException if {@code lower} is greater than {@code upper}
165   * @throws ClassCastException if {@code lower} and {@code upper} are not mutually comparable
166   * @since 14.0
167   */
168  public static <C extends Comparable<?>> Range<C> closedOpen(C lower, C upper) {
169    return create(Cut.belowValue(lower), Cut.belowValue(upper));
170  }
171
172  /**
173   * Returns a range that contains all values strictly greater than {@code lower} and less than or
174   * equal to {@code upper}.
175   *
176   * @throws IllegalArgumentException if {@code lower} is greater than {@code upper}
177   * @throws ClassCastException if {@code lower} and {@code upper} are not mutually comparable
178   * @since 14.0
179   */
180  public static <C extends Comparable<?>> Range<C> openClosed(C lower, C upper) {
181    return create(Cut.aboveValue(lower), Cut.aboveValue(upper));
182  }
183
184  /**
185   * Returns a range that contains any value from {@code lower} to {@code upper}, where each
186   * endpoint may be either inclusive (closed) or exclusive (open).
187   *
188   * @throws IllegalArgumentException if {@code lower} is greater than {@code upper}
189   * @throws ClassCastException if {@code lower} and {@code upper} are not mutually comparable
190   * @since 14.0
191   */
192  public static <C extends Comparable<?>> Range<C> range(
193      C lower, BoundType lowerType, C upper, BoundType upperType) {
194    checkNotNull(lowerType);
195    checkNotNull(upperType);
196
197    Cut<C> lowerBound =
198        (lowerType == BoundType.OPEN) ? Cut.aboveValue(lower) : Cut.belowValue(lower);
199    Cut<C> upperBound =
200        (upperType == BoundType.OPEN) ? Cut.belowValue(upper) : Cut.aboveValue(upper);
201    return create(lowerBound, upperBound);
202  }
203
204  /**
205   * Returns a range that contains all values strictly less than {@code endpoint}.
206   *
207   * @since 14.0
208   */
209  public static <C extends Comparable<?>> Range<C> lessThan(C endpoint) {
210    return create(Cut.<C>belowAll(), Cut.belowValue(endpoint));
211  }
212
213  /**
214   * Returns a range that contains all values less than or equal to {@code endpoint}.
215   *
216   * @since 14.0
217   */
218  public static <C extends Comparable<?>> Range<C> atMost(C endpoint) {
219    return create(Cut.<C>belowAll(), Cut.aboveValue(endpoint));
220  }
221
222  /**
223   * Returns a range with no lower bound up to the given endpoint, which may be either inclusive
224   * (closed) or exclusive (open).
225   *
226   * @since 14.0
227   */
228  public static <C extends Comparable<?>> Range<C> upTo(C endpoint, BoundType boundType) {
229    switch (boundType) {
230      case OPEN:
231        return lessThan(endpoint);
232      case CLOSED:
233        return atMost(endpoint);
234      default:
235        throw new AssertionError();
236    }
237  }
238
239  /**
240   * Returns a range that contains all values strictly greater than {@code endpoint}.
241   *
242   * @since 14.0
243   */
244  public static <C extends Comparable<?>> Range<C> greaterThan(C endpoint) {
245    return create(Cut.aboveValue(endpoint), Cut.<C>aboveAll());
246  }
247
248  /**
249   * Returns a range that contains all values greater than or equal to {@code endpoint}.
250   *
251   * @since 14.0
252   */
253  public static <C extends Comparable<?>> Range<C> atLeast(C endpoint) {
254    return create(Cut.belowValue(endpoint), Cut.<C>aboveAll());
255  }
256
257  /**
258   * Returns a range from the given endpoint, which may be either inclusive (closed) or exclusive
259   * (open), with no upper bound.
260   *
261   * @since 14.0
262   */
263  public static <C extends Comparable<?>> Range<C> downTo(C endpoint, BoundType boundType) {
264    switch (boundType) {
265      case OPEN:
266        return greaterThan(endpoint);
267      case CLOSED:
268        return atLeast(endpoint);
269      default:
270        throw new AssertionError();
271    }
272  }
273
274  private static final Range<Comparable> ALL = new Range<>(Cut.belowAll(), Cut.aboveAll());
275
276  /**
277   * Returns a range that contains every value of type {@code C}.
278   *
279   * @since 14.0
280   */
281  @SuppressWarnings("unchecked")
282  public static <C extends Comparable<?>> Range<C> all() {
283    return (Range) ALL;
284  }
285
286  /**
287   * Returns a range that {@linkplain Range#contains(Comparable) contains} only the given value. The
288   * returned range is {@linkplain BoundType#CLOSED closed} on both ends.
289   *
290   * @since 14.0
291   */
292  public static <C extends Comparable<?>> Range<C> singleton(C value) {
293    return closed(value, value);
294  }
295
296  /**
297   * Returns the minimal range that {@linkplain Range#contains(Comparable) contains} all of the
298   * given values. The returned range is {@linkplain BoundType#CLOSED closed} on both ends.
299   *
300   * @throws ClassCastException if the values are not mutually comparable
301   * @throws NoSuchElementException if {@code values} is empty
302   * @throws NullPointerException if any of {@code values} is null
303   * @since 14.0
304   */
305  public static <C extends Comparable<?>> Range<C> encloseAll(Iterable<C> values) {
306    checkNotNull(values);
307    if (values instanceof SortedSet) {
308      SortedSet<C> set = (SortedSet<C>) values;
309      Comparator<?> comparator = set.comparator();
310      if (Ordering.<C>natural().equals(comparator) || comparator == null) {
311        return closed(set.first(), set.last());
312      }
313    }
314    Iterator<C> valueIterator = values.iterator();
315    C min = checkNotNull(valueIterator.next());
316    C max = min;
317    while (valueIterator.hasNext()) {
318      C value = checkNotNull(valueIterator.next());
319      min = Ordering.<C>natural().min(min, value);
320      max = Ordering.<C>natural().max(max, value);
321    }
322    return closed(min, max);
323  }
324
325  final Cut<C> lowerBound;
326  final Cut<C> upperBound;
327
328  private Range(Cut<C> lowerBound, Cut<C> upperBound) {
329    this.lowerBound = checkNotNull(lowerBound);
330    this.upperBound = checkNotNull(upperBound);
331    if (lowerBound.compareTo(upperBound) > 0
332        || lowerBound == Cut.<C>aboveAll()
333        || upperBound == Cut.<C>belowAll()) {
334      throw new IllegalArgumentException("Invalid range: " + toString(lowerBound, upperBound));
335    }
336  }
337
338  /** Returns {@code true} if this range has a lower endpoint. */
339  public boolean hasLowerBound() {
340    return lowerBound != Cut.belowAll();
341  }
342
343  /**
344   * Returns the lower endpoint of this range.
345   *
346   * @throws IllegalStateException if this range is unbounded below (that is, {@link
347   *     #hasLowerBound()} returns {@code false})
348   */
349  public C lowerEndpoint() {
350    return lowerBound.endpoint();
351  }
352
353  /**
354   * Returns the type of this range's lower bound: {@link BoundType#CLOSED} if the range includes
355   * its lower endpoint, {@link BoundType#OPEN} if it does not.
356   *
357   * @throws IllegalStateException if this range is unbounded below (that is, {@link
358   *     #hasLowerBound()} returns {@code false})
359   */
360  public BoundType lowerBoundType() {
361    return lowerBound.typeAsLowerBound();
362  }
363
364  /** Returns {@code true} if this range has an upper endpoint. */
365  public boolean hasUpperBound() {
366    return upperBound != Cut.aboveAll();
367  }
368
369  /**
370   * Returns the upper endpoint of this range.
371   *
372   * @throws IllegalStateException if this range is unbounded above (that is, {@link
373   *     #hasUpperBound()} returns {@code false})
374   */
375  public C upperEndpoint() {
376    return upperBound.endpoint();
377  }
378
379  /**
380   * Returns the type of this range's upper bound: {@link BoundType#CLOSED} if the range includes
381   * its upper endpoint, {@link BoundType#OPEN} if it does not.
382   *
383   * @throws IllegalStateException if this range is unbounded above (that is, {@link
384   *     #hasUpperBound()} returns {@code false})
385   */
386  public BoundType upperBoundType() {
387    return upperBound.typeAsUpperBound();
388  }
389
390  /**
391   * Returns {@code true} if this range is of the form {@code [v..v)} or {@code (v..v]}. (This does
392   * not encompass ranges of the form {@code (v..v)}, because such ranges are <i>invalid</i> and
393   * can't be constructed at all.)
394   *
395   * <p>Note that certain discrete ranges such as the integer range {@code (3..4)} are <b>not</b>
396   * considered empty, even though they contain no actual values. In these cases, it may be helpful
397   * to preprocess ranges with {@link #canonical(DiscreteDomain)}.
398   */
399  public boolean isEmpty() {
400    return lowerBound.equals(upperBound);
401  }
402
403  /**
404   * Returns {@code true} if {@code value} is within the bounds of this range. For example, on the
405   * range {@code [0..2)}, {@code contains(1)} returns {@code true}, while {@code contains(2)}
406   * returns {@code false}.
407   */
408  public boolean contains(C value) {
409    checkNotNull(value);
410    // let this throw CCE if there is some trickery going on
411    return lowerBound.isLessThan(value) && !upperBound.isLessThan(value);
412  }
413
414  /**
415   * @deprecated Provided only to satisfy the {@link Predicate} interface; use {@link #contains}
416   *     instead.
417   */
418  @Deprecated
419  @Override
420  public boolean apply(C input) {
421    return contains(input);
422  }
423
424  /**
425   * Returns {@code true} if every element in {@code values} is {@linkplain #contains contained} in
426   * this range.
427   */
428  public boolean containsAll(Iterable<? extends C> values) {
429    if (Iterables.isEmpty(values)) {
430      return true;
431    }
432
433    // this optimizes testing equality of two range-backed sets
434    if (values instanceof SortedSet) {
435      SortedSet<? extends C> set = (SortedSet<? extends C>) values;
436      Comparator<?> comparator = set.comparator();
437      if (Ordering.natural().equals(comparator) || comparator == null) {
438        return contains(set.first()) && contains(set.last());
439      }
440    }
441
442    for (C value : values) {
443      if (!contains(value)) {
444        return false;
445      }
446    }
447    return true;
448  }
449
450  /**
451   * Returns {@code true} if the bounds of {@code other} do not extend outside the bounds of this
452   * range. Examples:
453   *
454   * <ul>
455   *   <li>{@code [3..6]} encloses {@code [4..5]}
456   *   <li>{@code (3..6)} encloses {@code (3..6)}
457   *   <li>{@code [3..6]} encloses {@code [4..4)} (even though the latter is empty)
458   *   <li>{@code (3..6]} does not enclose {@code [3..6]}
459   *   <li>{@code [4..5]} does not enclose {@code (3..6)} (even though it contains every value
460   *       contained by the latter range)
461   *   <li>{@code [3..6]} does not enclose {@code (1..1]} (even though it contains every value
462   *       contained by the latter range)
463   * </ul>
464   *
465   * <p>Note that if {@code a.encloses(b)}, then {@code b.contains(v)} implies {@code
466   * a.contains(v)}, but as the last two examples illustrate, the converse is not always true.
467   *
468   * <p>Being reflexive, antisymmetric and transitive, the {@code encloses} relation defines a
469   * <i>partial order</i> over ranges. There exists a unique {@linkplain Range#all maximal} range
470   * according to this relation, and also numerous {@linkplain #isEmpty minimal} ranges. Enclosure
471   * also implies {@linkplain #isConnected connectedness}.
472   */
473  public boolean encloses(Range<C> other) {
474    return lowerBound.compareTo(other.lowerBound) <= 0
475        && upperBound.compareTo(other.upperBound) >= 0;
476  }
477
478  /**
479   * Returns {@code true} if there exists a (possibly empty) range which is {@linkplain #encloses
480   * enclosed} by both this range and {@code other}.
481   *
482   * <p>For example,
483   *
484   * <ul>
485   *   <li>{@code [2, 4)} and {@code [5, 7)} are not connected
486   *   <li>{@code [2, 4)} and {@code [3, 5)} are connected, because both enclose {@code [3, 4)}
487   *   <li>{@code [2, 4)} and {@code [4, 6)} are connected, because both enclose the empty range
488   *       {@code [4, 4)}
489   * </ul>
490   *
491   * <p>Note that this range and {@code other} have a well-defined {@linkplain #span union} and
492   * {@linkplain #intersection intersection} (as a single, possibly-empty range) if and only if this
493   * method returns {@code true}.
494   *
495   * <p>The connectedness relation is both reflexive and symmetric, but does not form an {@linkplain
496   * Equivalence equivalence relation} as it is not transitive.
497   *
498   * <p>Note that certain discrete ranges are not considered connected, even though there are no
499   * elements "between them." For example, {@code [3, 5]} is not considered connected to {@code [6,
500   * 10]}. In these cases, it may be desirable for both input ranges to be preprocessed with {@link
501   * #canonical(DiscreteDomain)} before testing for connectedness.
502   */
503  public boolean isConnected(Range<C> other) {
504    return lowerBound.compareTo(other.upperBound) <= 0
505        && other.lowerBound.compareTo(upperBound) <= 0;
506  }
507
508  /**
509   * Returns the maximal range {@linkplain #encloses enclosed} by both this range and {@code
510   * connectedRange}, if such a range exists.
511   *
512   * <p>For example, the intersection of {@code [1..5]} and {@code (3..7)} is {@code (3..5]}. The
513   * resulting range may be empty; for example, {@code [1..5)} intersected with {@code [5..7)}
514   * yields the empty range {@code [5..5)}.
515   *
516   * <p>The intersection exists if and only if the two ranges are {@linkplain #isConnected
517   * connected}.
518   *
519   * <p>The intersection operation is commutative, associative and idempotent, and its identity
520   * element is {@link Range#all}).
521   *
522   * @throws IllegalArgumentException if {@code isConnected(connectedRange)} is {@code false}
523   */
524  public Range<C> intersection(Range<C> connectedRange) {
525    int lowerCmp = lowerBound.compareTo(connectedRange.lowerBound);
526    int upperCmp = upperBound.compareTo(connectedRange.upperBound);
527    if (lowerCmp >= 0 && upperCmp <= 0) {
528      return this;
529    } else if (lowerCmp <= 0 && upperCmp >= 0) {
530      return connectedRange;
531    } else {
532      Cut<C> newLower = (lowerCmp >= 0) ? lowerBound : connectedRange.lowerBound;
533      Cut<C> newUpper = (upperCmp <= 0) ? upperBound : connectedRange.upperBound;
534
535      // create() would catch this, but give a confusing error message
536      checkArgument(
537          newLower.compareTo(newUpper) <= 0,
538          "intersection is undefined for disconnected ranges %s and %s",
539          this,
540          connectedRange);
541
542      // TODO(kevinb): all the precondition checks in the constructor are redundant...
543      return create(newLower, newUpper);
544    }
545  }
546
547  /**
548   * Returns the maximal range lying between this range and {@code otherRange}, if such a range
549   * exists. The resulting range may be empty if the two ranges are adjacent but non-overlapping.
550   *
551   * <p>For example, the gap of {@code [1..5]} and {@code (7..10)} is {@code (5..7]}. The resulting
552   * range may be empty; for example, the gap between {@code [1..5)} {@code [5..7)} yields the empty
553   * range {@code [5..5)}.
554   *
555   * <p>The gap exists if and only if the two ranges are either disconnected or immediately adjacent
556   * (any intersection must be an empty range).
557   *
558   * <p>The gap operation is commutative.
559   *
560   * @throws IllegalArgumentException if this range and {@code otherRange} have a nonempty
561   *     intersection
562   * @since 27.0
563   */
564  public Range<C> gap(Range<C> otherRange) {
565    /*
566     * For an explanation of the basic principle behind this check, see
567     * https://stackoverflow.com/a/35754308/28465
568     *
569     * In that explanation's notation, our `overlap` check would be `x1 < y2 && y1 < x2`. We've
570     * flipped one part of the check so that we're using "less than" in both cases (rather than a
571     * mix of "less than" and "greater than"). We've also switched to "strictly less than" rather
572     * than "less than or equal to" because of *handwave* the difference between "endpoints of
573     * inclusive ranges" and "Cuts."
574     */
575    if (lowerBound.compareTo(otherRange.upperBound) < 0
576        && otherRange.lowerBound.compareTo(upperBound) < 0) {
577      throw new IllegalArgumentException(
578          "Ranges have a nonempty intersection: " + this + ", " + otherRange);
579    }
580
581    boolean isThisFirst = this.lowerBound.compareTo(otherRange.lowerBound) < 0;
582    Range<C> firstRange = isThisFirst ? this : otherRange;
583    Range<C> secondRange = isThisFirst ? otherRange : this;
584    return create(firstRange.upperBound, secondRange.lowerBound);
585  }
586
587  /**
588   * Returns the minimal range that {@linkplain #encloses encloses} both this range and {@code
589   * other}. For example, the span of {@code [1..3]} and {@code (5..7)} is {@code [1..7)}.
590   *
591   * <p><i>If</i> the input ranges are {@linkplain #isConnected connected}, the returned range can
592   * also be called their <i>union</i>. If they are not, note that the span might contain values
593   * that are not contained in either input range.
594   *
595   * <p>Like {@link #intersection(Range) intersection}, this operation is commutative, associative
596   * and idempotent. Unlike it, it is always well-defined for any two input ranges.
597   */
598  public Range<C> span(Range<C> other) {
599    int lowerCmp = lowerBound.compareTo(other.lowerBound);
600    int upperCmp = upperBound.compareTo(other.upperBound);
601    if (lowerCmp <= 0 && upperCmp >= 0) {
602      return this;
603    } else if (lowerCmp >= 0 && upperCmp <= 0) {
604      return other;
605    } else {
606      Cut<C> newLower = (lowerCmp <= 0) ? lowerBound : other.lowerBound;
607      Cut<C> newUpper = (upperCmp >= 0) ? upperBound : other.upperBound;
608      return create(newLower, newUpper);
609    }
610  }
611
612  /**
613   * Returns the canonical form of this range in the given domain. The canonical form has the
614   * following properties:
615   *
616   * <ul>
617   *   <li>equivalence: {@code a.canonical().contains(v) == a.contains(v)} for all {@code v} (in
618   *       other words, {@code ContiguousSet.create(a.canonical(domain), domain).equals(
619   *       ContiguousSet.create(a, domain))}
620   *   <li>uniqueness: unless {@code a.isEmpty()}, {@code ContiguousSet.create(a,
621   *       domain).equals(ContiguousSet.create(b, domain))} implies {@code
622   *       a.canonical(domain).equals(b.canonical(domain))}
623   *   <li>idempotence: {@code a.canonical(domain).canonical(domain).equals(a.canonical(domain))}
624   * </ul>
625   *
626   * <p>Furthermore, this method guarantees that the range returned will be one of the following
627   * canonical forms:
628   *
629   * <ul>
630   *   <li>[start..end)
631   *   <li>[start..+∞)
632   *   <li>(-∞..end) (only if type {@code C} is unbounded below)
633   *   <li>(-∞..+∞) (only if type {@code C} is unbounded below)
634   * </ul>
635   */
636  public Range<C> canonical(DiscreteDomain<C> domain) {
637    checkNotNull(domain);
638    Cut<C> lower = lowerBound.canonical(domain);
639    Cut<C> upper = upperBound.canonical(domain);
640    return (lower == lowerBound && upper == upperBound) ? this : create(lower, upper);
641  }
642
643  /**
644   * Returns {@code true} if {@code object} is a range having the same endpoints and bound types as
645   * this range. Note that discrete ranges such as {@code (1..4)} and {@code [2..3]} are <b>not</b>
646   * equal to one another, despite the fact that they each contain precisely the same set of values.
647   * Similarly, empty ranges are not equal unless they have exactly the same representation, so
648   * {@code [3..3)}, {@code (3..3]}, {@code (4..4]} are all unequal.
649   */
650  @Override
651  public boolean equals(@CheckForNull Object object) {
652    if (object instanceof Range) {
653      Range<?> other = (Range<?>) object;
654      return lowerBound.equals(other.lowerBound) && upperBound.equals(other.upperBound);
655    }
656    return false;
657  }
658
659  /** Returns a hash code for this range. */
660  @Override
661  public int hashCode() {
662    return lowerBound.hashCode() * 31 + upperBound.hashCode();
663  }
664
665  /**
666   * Returns a string representation of this range, such as {@code "[3..5)"} (other examples are
667   * listed in the class documentation).
668   */
669  @Override
670  public String toString() {
671    return toString(lowerBound, upperBound);
672  }
673
674  // We declare accessors so that we can use method references like `Range::lowerBound`.
675
676  Cut<C> lowerBound() {
677    return lowerBound;
678  }
679
680  Cut<C> upperBound() {
681    return upperBound;
682  }
683
684  private static String toString(Cut<?> lowerBound, Cut<?> upperBound) {
685    StringBuilder sb = new StringBuilder(16);
686    lowerBound.describeAsLowerBound(sb);
687    sb.append("..");
688    upperBound.describeAsUpperBound(sb);
689    return sb.toString();
690  }
691
692  Object readResolve() {
693    if (this.equals(ALL)) {
694      return all();
695    } else {
696      return this;
697    }
698  }
699
700  @SuppressWarnings("unchecked") // this method may throw CCE
701  static int compareOrThrow(Comparable left, Comparable right) {
702    return left.compareTo(right);
703  }
704
705  /** Needed to serialize sorted collections of Ranges. */
706  private static class RangeLexOrdering extends Ordering<Range<?>> implements Serializable {
707    static final Ordering<?> INSTANCE = new RangeLexOrdering();
708
709    @Override
710    public int compare(Range<?> left, Range<?> right) {
711      return ComparisonChain.start()
712          .compare(left.lowerBound, right.lowerBound)
713          .compare(left.upperBound, right.upperBound)
714          .result();
715    }
716
717    private static final long serialVersionUID = 0;
718  }
719
720  private static final long serialVersionUID = 0;
721}