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 }