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    
017    package com.google.common.collect;
018    
019    import static com.google.common.base.Preconditions.checkNotNull;
020    import static com.google.common.collect.Ranges.create;
021    
022    import com.google.common.annotations.Beta;
023    import com.google.common.annotations.GwtCompatible;
024    import com.google.common.base.Predicate;
025    
026    import java.io.Serializable;
027    import java.util.Collections;
028    import java.util.Comparator;
029    import java.util.NoSuchElementException;
030    import java.util.Set;
031    import java.util.SortedSet;
032    
033    import javax.annotation.Nullable;
034    
035    /**
036     * A range, sometimes known as an <i>interval</i>, is a <i>convex</i>
037     * (informally, "contiguous" or "unbroken") portion of a particular domain.
038     * Formally, convexity means that for any {@code a <= b <= c},
039     * {@code range.contains(a) && range.contains(c)} implies that {@code
040     * range.contains(b)}.
041     *
042     * <p>A range is characterized by its lower and upper <i>bounds</i> (extremes),
043     * each of which can <i>open</i> (exclusive of its endpoint), <i>closed</i>
044     * (inclusive of its endpoint), or <i>unbounded</i>. This yields nine basic
045     * types of ranges:
046     *
047     * <ul>
048     * <li>{@code (a..b) = {x | a < x < b}}
049     * <li>{@code [a..b] = {x | a <= x <= b}}
050     * <li>{@code [a..b) = {x | a <= x < b}}
051     * <li>{@code (a..b] = {x | a < x <= b}}
052     * <li>{@code (a..+∞) = {x | x > a}}
053     * <li>{@code [a..+∞) = {x | x >= a}}
054     * <li>{@code (-∞..b) = {x | x < b}}
055     * <li>{@code (-∞..b] = {x | x <= b}}
056     * <li>{@code (-∞..+∞) = all values}
057     * </ul>
058     *
059     * (The notation {@code {x | statement}} is read "the set of all <i>x</i> such
060     * that <i>statement</i>.")
061     *
062     * <p>Notice that we use a square bracket ({@code [ ]}) to denote that an range
063     * is closed on that end, and a parenthesis ({@code ( )}) when it is open or
064     * unbounded.
065     *
066     * <p>The values {@code a} and {@code b} used above are called <i>endpoints</i>.
067     * The upper endpoint may not be less than the lower endpoint. The endpoints may
068     * be equal only if at least one of the bounds is closed:
069     *
070     * <ul>
071     * <li>{@code [a..a]} : singleton range
072     * <li>{@code [a..a); (a..a]} : {@linkplain #isEmpty empty}, but valid
073     * <li>{@code (a..a)} : <b>invalid</b>
074     * </ul>
075     *
076     * <p>Instances of this type can be obtained using the static factory methods in
077     * the {@link Ranges} class.
078     *
079     * <p>Instances of {@code Range} are immutable. It is strongly encouraged to
080     * use this class only with immutable data types. When creating a range over a
081     * mutable type, take great care not to allow the value objects to mutate after
082     * the range is created.
083     *
084     * <p>In this and other range-related specifications, concepts like "equal",
085     * "same", "unique" and so on are based on {@link Comparable#compareTo}
086     * returning zero, not on {@link Object#equals} returning {@code true}. Of
087     * course, when these methods are kept <i>consistent</i> (as defined in {@link
088     * Comparable}), this is not an issue.
089     *
090     * <p>A range {@code a} is said to be the <i>maximal</i> range having property
091     * <i>P</i> if, for all ranges {@code b} also having property <i>P</i>, {@code
092     * a.encloses(b)}. Likewise, {@code a} is <i>minimal</i> when {@code
093     * b.encloses(a)} for all {@code b} having property <i>P</i>. See, for example,
094     * the definition of {@link #intersection}.
095     *
096     * <p>This class can be used with any type which implements {@code Comparable};
097     * it does not require {@code Comparable<? super C>} because this would be
098     * incompatible with pre-Java 5 types. If this class is used with a perverse
099     * {@code Comparable} type ({@code Foo implements Comparable<Bar>} where {@code
100     * Bar} is not a supertype of {@code Foo}), any of its methods may throw {@link
101     * ClassCastException}. (There is no good reason for such a type to exist.)
102     *
103     * <p>When evaluated as a {@link Predicate}, a range yields the same result as
104     * invoking {@link #contains}.
105     *
106     * @author Kevin Bourrillion
107     * @author Gregory Kick
108     * @since 10.0
109     */
110    @GwtCompatible
111    @Beta
112    public final class Range<C extends Comparable>
113        implements Predicate<C>, Serializable {
114      final Cut<C> lowerBound;
115      final Cut<C> upperBound;
116    
117      Range(Cut<C> lowerBound, Cut<C> upperBound) {
118        if (lowerBound.compareTo(upperBound) > 0) {
119          throw new IllegalArgumentException(
120              "Invalid range: " + toString(lowerBound, upperBound));
121        }
122        this.lowerBound = lowerBound;
123        this.upperBound = upperBound;
124      }
125    
126      /**
127       * Returns {@code true} if this range has a lower endpoint.
128       */
129      public boolean hasLowerBound() {
130        return lowerBound != Cut.belowAll();
131      }
132    
133      /**
134       * Returns the lower endpoint of this range.
135       *
136       * @throws IllegalStateException if this range is unbounded below (that is,
137       *     {@link #hasLowerBound()} returns {@code false})
138       */
139      public C lowerEndpoint() {
140        return lowerBound.endpoint();
141      }
142    
143      /**
144       * Returns the type of this range's lower bound: {@link BoundType#CLOSED} if
145       * the range includes its lower endpoint, {@link BoundType#OPEN} if it does
146       * not.
147       *
148       * @throws IllegalStateException if this range is unbounded below (that is,
149       *     {@link #hasLowerBound()} returns {@code false})
150       */
151      public BoundType lowerBoundType() {
152        return lowerBound.typeAsLowerBound();
153      }
154    
155      /**
156       * Returns {@code true} if this range has an upper endpoint.
157       */
158      public boolean hasUpperBound() {
159        return upperBound != Cut.aboveAll();
160      }
161    
162      /**
163       * Returns the upper endpoint of this range.
164       *
165       * @throws IllegalStateException if this range is unbounded above (that is,
166       *     {@link #hasUpperBound()} returns {@code false})
167       */
168      public C upperEndpoint() {
169        return upperBound.endpoint();
170      }
171    
172      /**
173       * Returns the type of this range's upper bound: {@link BoundType#CLOSED} if
174       * the range includes its upper endpoint, {@link BoundType#OPEN} if it does
175       * not.
176       *
177       * @throws IllegalStateException if this range is unbounded above (that is,
178       *     {@link #hasUpperBound()} returns {@code false})
179       */
180      public BoundType upperBoundType() {
181        return upperBound.typeAsUpperBound();
182      }
183    
184      /**
185       * Returns {@code true} if this range is of the form {@code [v..v)} or {@code
186       * (v..v]}. (This does not encompass ranges of the form {@code (v..v)},
187       * because such ranges are <i>invalid</i> and can't be constructed at all.)
188       *
189       * <p>Note that certain discrete ranges such as the integer range {@code
190       * (3..4)} are <b>not</b> considered empty, even though they contain no actual
191       * values.
192       */
193      public boolean isEmpty() {
194        return lowerBound.equals(upperBound);
195      }
196    
197      /**
198       * Returns {@code true} if {@code value} is within the bounds of this
199       * range. For example, on the range {@code [0..2)}, {@code contains(1)}
200       * returns {@code true}, while {@code contains(2)} returns {@code false}.
201       */
202      public boolean contains(C value) {
203        checkNotNull(value);
204        // let this throw CCE if there is some trickery going on
205        return lowerBound.isLessThan(value) && !upperBound.isLessThan(value);
206      }
207    
208      /**
209       * Equivalent to {@link #contains}; provided only to satisfy the {@link
210       * Predicate} interface. When using a reference of type {@code Range}, always
211       * invoke {@link #contains} directly instead.
212       */
213      @Override public boolean apply(C input) {
214        return contains(input);
215      }
216    
217      /**
218       * Returns {@code true} if every element in {@code values} is {@linkplain
219       * #contains contained} in this range.
220       */
221      public boolean containsAll(Iterable<? extends C> values) {
222        if (Iterables.isEmpty(values)) {
223          return true;
224        }
225    
226        // this optimizes testing equality of two range-backed sets
227        if (values instanceof SortedSet) {
228          SortedSet<? extends C> set = cast(values);
229          Comparator<?> comparator = set.comparator();
230          if (Ordering.natural().equals(comparator) || comparator == null) {
231            return contains(set.first()) && contains(set.last());
232          }
233        }
234    
235        for (C value : values) {
236          if (!contains(value)) {
237            return false;
238          }
239        }
240        return true;
241      }
242    
243      /**
244       * Returns {@code true} if the bounds of {@code other} do not extend outside
245       * the bounds of this range. Examples:
246       *
247       * <ul>
248       * <li>{@code [3..6]} encloses {@code [4..5]}
249       * <li>{@code (3..6)} encloses {@code (3..6)}
250       * <li>{@code [3..6]} encloses {@code [4..4)} (even though the latter is
251       *     empty)
252       * <li>{@code (3..6]} does not enclose {@code [3..6]}
253       * <li>{@code [4..5]} does not enclose {@code (3..6)} (even though it contains
254       *     every value contained by the latter range)
255       * <li>{@code [3..6]} does not enclose {@code (1..1]} (even though it contains
256       *     every value contained by the latter range)
257       * </ul>
258       *
259       * Note that if {@code a.encloses(b)}, then {@code b.contains(v)} implies
260       * {@code a.contains(v)}, but as the last two examples illustrate, the
261       * converse is not always true.
262       *
263       * <p>The encloses relation has the following properties:
264       *
265       * <ul>
266       * <li>reflexive: {@code a.encloses(a)} is always true
267       * <li>antisymmetric: {@code a.encloses(b) && b.encloses(a)} implies {@code
268       *     a.equals(b)}
269       * <li>transitive: {@code a.encloses(b) && b.encloses(c)} implies {@code
270       *     a.encloses(c)}
271       * <li>not a total ordering: {@code !a.encloses(b)} does not imply {@code
272       *     b.encloses(a)}
273       * <li>there exists a {@linkplain Ranges#all maximal} range, for which
274       *     {@code encloses} is always true
275       * <li>there also exist {@linkplain #isEmpty minimal} ranges, for
276       *     which {@code encloses(b)} is always false when {@code !equals(b)}
277       * <li>if {@code a.encloses(b)}, then {@link #isConnected a.isConnected(b)}
278       *     is {@code true}. 
279       * </ul>
280       */
281      public boolean encloses(Range<C> other) {
282        return lowerBound.compareTo(other.lowerBound) <= 0
283            && upperBound.compareTo(other.upperBound) >= 0;
284      }
285    
286      /**
287       * Returns the maximal range {@linkplain #encloses enclosed} by both this
288       * range and {@code other}, if such a range exists.
289       * 
290       * <p>For example, the intersection of {@code [1..5]} and {@code (3..7)} is
291       * {@code (3..5]}. The resulting range may be empty; for example, 
292       * {@code [1..5)} intersected with {@code [5..7)} yields the empty range
293       * {@code [5..5)}.
294       * 
295       * <p>Generally, the intersection exists if and only if this range and 
296       * {@code other} are {@linkplain #isConnected connected}.
297       *
298       * <p>The intersection operation has the following properties:
299       *
300       * <ul>
301       * <li>commutative: {@code a.intersection(b)} produces the same result as
302       *     {@code b.intersection(a)}
303       * <li>associative: {@code a.intersection(b).intersection(c)} produces the
304       *     same result as {@code a.intersection(b.intersection(c))}
305       * <li>idempotent: {@code a.intersection(a)} equals {@code a}
306       * <li>identity ({@link Ranges#all}): {@code a.intersection(Ranges.all())}
307       *     equals {@code a}
308       * </ul>
309       *
310       * @throws IllegalArgumentException if no range exists that is enclosed by
311       *     both these ranges
312       */
313      public Range<C> intersection(Range<C> other) {
314        Cut<C> newLower = Ordering.natural().max(lowerBound, other.lowerBound);
315        Cut<C> newUpper = Ordering.natural().min(upperBound, other.upperBound);
316        return create(newLower, newUpper);
317      }
318    
319      /**
320       * Returns {@code true} if there exists a (possibly empty) range which is
321       * {@linkplain #encloses enclosed} by both this range and {@code other}.
322       * 
323       * <p>For example,
324       * <ul>
325       * <li>{@code [2, 4)} and {@code [5, 7)} are not connected
326       * <li>{@code [2, 4)} and {@code [3, 5)} are connected, because both enclose
327       *     {@code [3, 4)}
328       * <li>{@code [2, 4)} and {@code [4, 6)} are connected, because both enclose
329       *     the empty range {@code [4, 4)}
330       * </ul>
331       * 
332       * <p>Note that this range and {@code other} have a well-defined {@linkplain
333       * #span union} and {@linkplain #intersection intersection} (as a single,
334       * possibly-empty range) if and only if this method returns {@code true}.
335       * 
336       * <p>The connectedness relation has the following properties:
337       *
338       * <ul>
339       * <li>symmetric: {@code a.isConnected(b)} produces the same result as
340       *     {@code b.isConnected(a)}
341       * <li>reflexive: {@code a.isConnected(a)} returns {@code true}
342       * </ul>
343       */
344      public boolean isConnected(Range<C> other) {
345        return lowerBound.compareTo(other.upperBound) <= 0
346            && other.lowerBound.compareTo(upperBound) <= 0;
347      }
348    
349      /**
350       * Returns the minimal range that {@linkplain #encloses encloses} both this
351       * range and {@code other}. For example, the span of {@code [1..3]} and
352       * {@code (5..7)} is {@code [1..7)}. Note that the span may contain values
353       * that are not contained by either original range.
354       *
355       * <p>The span operation has the following properties:
356       *
357       * <ul>
358       * <li>closed: the range {@code a.span(b)} exists for all ranges {@code a} and
359       *     {@code b}
360       * <li>commutative: {@code a.span(b)} equals {@code b.span(a)}
361       * <li>associative: {@code a.span(b).span(c)} equals {@code a.span(b.span(c))}
362       * <li>idempotent: {@code a.span(a)} equals {@code a}
363       * </ul>
364       * 
365       * <p>Note that the returned range is also called the <i>union</i> of this
366       * range and {@code other} if and only if the ranges are 
367       * {@linkplain #isConnected connected}.
368       */
369      public Range<C> span(Range<C> other) {
370        Cut<C> newLower = Ordering.natural().min(lowerBound, other.lowerBound);
371        Cut<C> newUpper = Ordering.natural().max(upperBound, other.upperBound);
372        return create(newLower, newUpper);
373      }
374    
375      /**
376       * Returns an {@link ImmutableSortedSet} containing the same values in the
377       * given domain {@linkplain Range#contains contained} by this range.
378       *
379       * <p><b>Note:</b> {@code a.asSet().equals(b.asSet())} does not imply {@code
380       * a.equals(b)}! For example, {@code a} and {@code b} could be {@code [2..4]}
381       * and {@code (1..5)}, or the empty ranges {@code [3..3)} and {@code [4..4)}.
382       *
383       * <p><b>Warning:</b> Be extremely careful what you do with the {@code asSet}
384       * view of a large range (such as {@code Ranges.greaterThan(0)}). Certain
385       * operations on such a set can be performed efficiently, but others (such as
386       * {@link Set#hashCode} or {@link Collections#frequency}) can cause major
387       * performance problems.
388       *
389       * <p>The returned set's {@link Object#toString} method returns a short-hand
390       * form of set's contents such as {@code "[1..100]}"}.
391       *
392       * @throws IllegalArgumentException if neither this range nor the domain has a
393       *     lower bound, or if neither has an upper bound
394       */
395      // TODO(kevinb): commit in spec to which methods are efficient?
396      @GwtCompatible(serializable = false)
397      public ContiguousSet<C> asSet(DiscreteDomain<C> domain) {
398        checkNotNull(domain);
399        Range<C> effectiveRange = this;
400        try {
401          if (!hasLowerBound()) {
402            effectiveRange = effectiveRange.intersection(
403                Ranges.atLeast(domain.minValue()));
404          }
405          if (!hasUpperBound()) {
406            effectiveRange = effectiveRange.intersection(
407                Ranges.atMost(domain.maxValue()));
408          }
409        } catch (NoSuchElementException e) {
410          throw new IllegalArgumentException(e);
411        }
412    
413        // Per class spec, we are allowed to throw CCE if necessary
414        boolean empty = effectiveRange.isEmpty()
415            || compareOrThrow(
416                lowerBound.leastValueAbove(domain),
417                upperBound.greatestValueBelow(domain)) > 0;
418    
419        return empty
420            ? new EmptyContiguousSet<C>(domain)
421            : new RegularContiguousSet<C>(effectiveRange, domain);
422      }
423    
424      /**
425       * Returns the canonical form of this range in the given domain. The canonical
426       * form has the following properties:
427       *
428       * <ul>
429       * <li>equivalence: {@code a.canonical().contains(v) == a.contains(v)} for
430       *     all {@code v} (in other words, {@code
431       *     a.canonical(domain).asSet(domain).equals(a.asSet(domain))}
432       * <li>uniqueness: unless {@code a.isEmpty()},
433       *     {@code a.asSet(domain).equals(b.asSet(domain))} implies
434       *     {@code a.canonical(domain).equals(b.canonical(domain))}
435       * <li>idempotence: {@code
436       *     a.canonical(domain).canonical(domain).equals(a.canonical(domain))}
437       * </ul>
438       *
439       * Furthermore, this method guarantees that the range returned will be one
440       * of the following canonical forms:
441       *
442       * <ul>
443       * <li>[start..end)
444       * <li>[start..+∞)
445       * <li>(-∞..end) (only if type {@code C} is unbounded below)
446       * <li>(-∞..+∞) (only if type {@code C} is unbounded below)
447       * </ul>
448       */
449      public Range<C> canonical(DiscreteDomain<C> domain) {
450        checkNotNull(domain);
451        Cut<C> lower = lowerBound.canonical(domain);
452        Cut<C> upper = upperBound.canonical(domain);
453        return (lower == lowerBound && upper == upperBound)
454            ? this : create(lower, upper);
455      }
456    
457      /**
458       * Returns {@code true} if {@code object} is a range having the same
459       * endpoints and bound types as this range. Note that discrete ranges
460       * such as {@code (1..4)} and {@code [2..3]} are <b>not</b> equal to one
461       * another, despite the fact that they each contain precisely the same set of
462       * values. Similarly, empty ranges are not equal unless they have exactly
463       * the same representation, so {@code [3..3)}, {@code (3..3]}, {@code (4..4]}
464       * are all unequal.
465       */
466      @Override public boolean equals(@Nullable Object object) {
467        if (object instanceof Range) {
468          Range<?> other = (Range<?>) object;
469          return lowerBound.equals(other.lowerBound)
470              && upperBound.equals(other.upperBound);
471        }
472        return false;
473      }
474    
475      /** Returns a hash code for this range. */
476      @Override public int hashCode() {
477        return lowerBound.hashCode() * 31 + upperBound.hashCode();
478      }
479    
480      /**
481       * Returns a string representation of this range, such as {@code "[3..5)"}
482       * (other examples are listed in the class documentation).
483       */
484      @Override public String toString() {
485        return toString(lowerBound, upperBound);
486      }
487    
488      private static String toString(Cut<?> lowerBound, Cut<?> upperBound) {
489        StringBuilder sb = new StringBuilder(16);
490        lowerBound.describeAsLowerBound(sb);
491        sb.append('\u2025');
492        upperBound.describeAsUpperBound(sb);
493        return sb.toString();
494      }
495    
496      /**
497       * Used to avoid http://bugs.sun.com/view_bug.do?bug_id=6558557
498       */
499      private static <T> SortedSet<T> cast(Iterable<T> iterable) {
500        return (SortedSet<T>) iterable;
501      }
502    
503      @SuppressWarnings("unchecked") // this method may throw CCE
504      static int compareOrThrow(Comparable left, Comparable right) {
505        return left.compareTo(right);
506      }
507    
508      private static final long serialVersionUID = 0;
509    }