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  13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14  * version 2 for more details (a copy is included in the LICENSE file that
  15  * accompanied this code).
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  25 
  26 package java.util;
  27 
  28 import java.io.Serializable;
  29 import java.util.function.Function;
  30 import java.util.function.ToIntFunction;
  31 import java.util.function.ToLongFunction;
  32 import java.util.function.ToDoubleFunction;
  33 
  34 /**
  35  * A comparison function, which imposes a <i>total ordering</i> on some
  36  * collection of objects.  Comparators can be passed to a sort method (such
  37  * as {@link Collections#sort(List,Comparator) Collections.sort} or {@link
  38  * Arrays#sort(Object[],Comparator) Arrays.sort}) to allow precise control
  39  * over the sort order.  Comparators can also be used to control the order of
  40  * certain data structures (such as {@link SortedSet sorted sets} or {@link
  41  * SortedMap sorted maps}), or to provide an ordering for collections of
  42  * objects that don't have a {@link Comparable natural ordering}.<p>
  43  *
  44  * The ordering imposed by a comparator {@code c} on a set of elements
  45  * {@code S} is said to be <i>consistent with equals</i> if and only if
  46  * {@code c.compare(e1, e2)==0} has the same boolean value as
  47  * {@code e1.equals(e2)} for every {@code e1} and {@code e2} in
  48  * {@code S}.<p>
  49  *
  50  * Caution should be exercised when using a comparator capable of imposing an
  51  * ordering inconsistent with equals to order a sorted set (or sorted map).
  52  * Suppose a sorted set (or sorted map) with an explicit comparator {@code c}
  53  * is used with elements (or keys) drawn from a set {@code S}.  If the
  54  * ordering imposed by {@code c} on {@code S} is inconsistent with equals,
  55  * the sorted set (or sorted map) will behave "strangely."  In particular the
  56  * sorted set (or sorted map) will violate the general contract for set (or
  57  * map), which is defined in terms of {@code equals}.<p>
  58  *
  59  * For example, suppose one adds two elements {@code a} and {@code b} such that
  60  * {@code (a.equals(b) && c.compare(a, b) != 0)}
  61  * to an empty {@code TreeSet} with comparator {@code c}.
  62  * The second {@code add} operation will return
  63  * true (and the size of the tree set will increase) because {@code a} and
  64  * {@code b} are not equivalent from the tree set's perspective, even though
  65  * this is contrary to the specification of the
  66  * {@link Set#add Set.add} method.<p>
  67  *
  68  * Note: It is generally a good idea for comparators to also implement
  69  * {@code java.io.Serializable}, as they may be used as ordering methods in
  70  * serializable data structures (like {@link TreeSet}, {@link TreeMap}).  In
  71  * order for the data structure to serialize successfully, the comparator (if
  72  * provided) must implement {@code Serializable}.<p>
  73  *
  74  * For the mathematically inclined, the <i>relation</i> that defines the
  75  * <i>imposed ordering</i> that a given comparator {@code c} imposes on a
  76  * given set of objects {@code S} is:<pre>
  77  *       {(x, y) such that c.compare(x, y) &lt;= 0}.
  78  * </pre> The <i>quotient</i> for this total order is:<pre>
  79  *       {(x, y) such that c.compare(x, y) == 0}.
  80  * </pre>
  81  *
  82  * It follows immediately from the contract for {@code compare} that the
  83  * quotient is an <i>equivalence relation</i> on {@code S}, and that the
  84  * imposed ordering is a <i>total order</i> on {@code S}.  When we say that
  85  * the ordering imposed by {@code c} on {@code S} is <i>consistent with
  86  * equals</i>, we mean that the quotient for the ordering is the equivalence
  87  * relation defined by the objects' {@link Object#equals(Object)
  88  * equals(Object)} method(s):<pre>
  89  *     {(x, y) such that x.equals(y)}. </pre>
  90  *
  91  * <p>Unlike {@code Comparable}, a comparator may optionally permit
  92  * comparison of null arguments, while maintaining the requirements for
  93  * an equivalence relation.
  94  *
  95  * <p>This interface is a member of the
  96  * <a href="{@docRoot}/java/util/package-summary.html#CollectionsFramework">
  97  * Java Collections Framework</a>.
  98  *
  99  * @param <T> the type of objects that may be compared by this comparator
 100  *
 101  * @author  Josh Bloch
 102  * @author  Neal Gafter
 103  * @see Comparable
 104  * @see java.io.Serializable
 105  * @since 1.2
 106  */
 107 @FunctionalInterface
 108 public interface Comparator<T> {
 109     /**
 110      * Compares its two arguments for order.  Returns a negative integer,
 111      * zero, or a positive integer as the first argument is less than, equal
 112      * to, or greater than the second.<p>
 113      *
 114      * The implementor must ensure that {@code sgn(compare(x, y)) ==
 115      * -sgn(compare(y, x))} for all {@code x} and {@code y}.  (This
 116      * implies that {@code compare(x, y)} must throw an exception if and only
 117      * if {@code compare(y, x)} throws an exception.)<p>
 118      *
 119      * The implementor must also ensure that the relation is transitive:
 120      * {@code ((compare(x, y)>0) && (compare(y, z)>0))} implies
 121      * {@code compare(x, z)>0}.<p>
 122      *
 123      * Finally, the implementor must ensure that {@code compare(x, y)==0}
 124      * implies that {@code sgn(compare(x, z))==sgn(compare(y, z))} for all
 125      * {@code z}.<p>
 126      *
 127      * It is generally the case, but <i>not</i> strictly required that
 128      * {@code (compare(x, y)==0) == (x.equals(y))}.  Generally speaking,
 129      * any comparator that violates this condition should clearly indicate
 130      * this fact.  The recommended language is "Note: this comparator
 131      * imposes orderings that are inconsistent with equals."<p>
 132      *
 133      * In the foregoing description, the notation
 134      * {@code sgn(}<i>expression</i>{@code )} designates the mathematical
 135      * <i>signum</i> function, which is defined to return one of {@code -1},
 136      * {@code 0}, or {@code 1} according to whether the value of
 137      * <i>expression</i> is negative, zero, or positive, respectively.
 138      *
 139      * @param o1 the first object to be compared.
 140      * @param o2 the second object to be compared.
 141      * @return a negative integer, zero, or a positive integer as the
 142      *         first argument is less than, equal to, or greater than the
 143      *         second.
 144      * @throws NullPointerException if an argument is null and this
 145      *         comparator does not permit null arguments
 146      * @throws ClassCastException if the arguments' types prevent them from
 147      *         being compared by this comparator.
 148      */
 149     int compare(T o1, T o2);
 150 
 151     /**
 152      * Indicates whether some other object is &quot;equal to&quot; this
 153      * comparator.  This method must obey the general contract of
 154      * {@link Object#equals(Object)}.  Additionally, this method can return
 155      * {@code true} <i>only</i> if the specified object is also a comparator
 156      * and it imposes the same ordering as this comparator.  Thus,
 157      * {@code comp1.equals(comp2)} implies that {@code sgn(comp1.compare(o1,
 158      * o2))==sgn(comp2.compare(o1, o2))} for every object reference
 159      * {@code o1} and {@code o2}.<p>
 160      *
 161      * Note that it is <i>always</i> safe <i>not</i> to override
 162      * {@code Object.equals(Object)}.  However, overriding this method may,
 163      * in some cases, improve performance by allowing programs to determine
 164      * that two distinct comparators impose the same order.
 165      *
 166      * @param   obj   the reference object with which to compare.
 167      * @return  {@code true} only if the specified object is also
 168      *          a comparator and it imposes the same ordering as this
 169      *          comparator.
 170      * @see Object#equals(Object)
 171      * @see Object#hashCode()
 172      */
 173     boolean equals(Object obj);
 174 
 175     /**
 176      * Returns a comparator that imposes the reverse ordering of this
 177      * comparator.
 178      *
 179      * @return a comparator that imposes the reverse ordering of this
 180      *         comparator.
 181      * @since 1.8
 182      */
 183     default Comparator<T> reversed() {
 184         return Collections.reverseOrder(this);
 185     }
 186 
 187     /**
 188      * Returns a lexicographic-order comparator with another comparator.
 189      * If this {@code Comparator} considers two elements equal, i.e.
 190      * {@code compare(a, b) == 0}, {@code other} is used to determine the order.
 191      *
 192      * <p>The returned comparator is serializable if the specified comparator
 193      * is also serializable.
 194      *
 195      * @apiNote
 196      * For example, to sort a collection of {@code String} based on the length
 197      * and then case-insensitive natural ordering, the comparator can be
 198      * composed using following code,
 199      *
 200      * <pre>{@code
 201      *     Comparator<String> cmp = Comparator.comparingInt(String::length)
 202      *             .thenComparing(String.CASE_INSENSITIVE_ORDER);
 203      * }</pre>
 204      *
 205      * @param  other the other comparator to be used when this comparator
 206      *         compares two objects that are equal.
 207      * @return a lexicographic-order comparator composed of this and then the
 208      *         other comparator
 209      * @throws NullPointerException if the argument is null.
 210      * @since 1.8
 211      */
 212     default Comparator<T> thenComparing(Comparator<? super T> other) {
 213         Objects.requireNonNull(other);
 214         return (Comparator<T> & Serializable) (c1, c2) -> {
 215             int res = compare(c1, c2);
 216             return (res != 0) ? res : other.compare(c1, c2);
 217         };
 218     }
 219 
 220     /**
 221      * Returns a lexicographic-order comparator with a function that
 222      * extracts a key to be compared with the given {@code Comparator}.
 223      *
 224      * @implSpec This default implementation behaves as if {@code
 225      *           thenComparing(comparing(keyExtractor, cmp))}.
 226      *
 227      * @param  <U>  the type of the sort key
 228      * @param  keyExtractor the function used to extract the sort key
 229      * @param  keyComparator the {@code Comparator} used to compare the sort key
 230      * @return a lexicographic-order comparator composed of this comparator
 231      *         and then comparing on the key extracted by the keyExtractor function
 232      * @throws NullPointerException if either argument is null.
 233      * @see #comparing(Function, Comparator)
 234      * @see #thenComparing(Comparator)
 235      * @since 1.8
 236      */
 237     default <U> Comparator<T> thenComparing(
 238             Function<? super T, ? extends U> keyExtractor,
 239             Comparator<? super U> keyComparator)
 240     {
 241         return thenComparing(comparing(keyExtractor, keyComparator));
 242     }
 243 
 244     /**
 245      * Returns a lexicographic-order comparator with a function that
 246      * extracts a {@code Comparable} sort key.
 247      *
 248      * @implSpec This default implementation behaves as if {@code
 249      *           thenComparing(comparing(keyExtractor))}.
 250      *
 251      * @param  <U>  the type of the {@link Comparable} sort key
 252      * @param  keyExtractor the function used to extract the {@link
 253      *         Comparable} sort key
 254      * @return a lexicographic-order comparator composed of this and then the
 255      *         {@link Comparable} sort key.
 256      * @throws NullPointerException if the argument is null.
 257      * @see #comparing(Function)
 258      * @see #thenComparing(Comparator)
 259      * @since 1.8
 260      */
 261     default <U extends Comparable<? super U>> Comparator<T> thenComparing(
 262             Function<? super T, ? extends U> keyExtractor)
 263     {
 264         return thenComparing(comparing(keyExtractor));
 265     }
 266 
 267     /**
 268      * Returns a lexicographic-order comparator with a function that
 269      * extracts an {@code int} sort key.
 270      *
 271      * @implSpec This default implementation behaves as if {@code
 272      *           thenComparing(comparingInt(keyExtractor))}.
 273      *
 274      * @param  keyExtractor the function used to extract the integer sort key
 275      * @return a lexicographic-order comparator composed of this and then the
 276      *         {@code int} sort key
 277      * @throws NullPointerException if the argument is null.
 278      * @see #comparingInt(ToIntFunction)
 279      * @see #thenComparing(Comparator)
 280      * @since 1.8
 281      */
 282     default Comparator<T> thenComparingInt(ToIntFunction<? super T> keyExtractor) {
 283         return thenComparing(comparingInt(keyExtractor));
 284     }
 285 
 286     /**
 287      * Returns a lexicographic-order comparator with a function that
 288      * extracts a {@code long} sort key.
 289      *
 290      * @implSpec This default implementation behaves as if {@code
 291      *           thenComparing(comparingLong(keyExtractor))}.
 292      *
 293      * @param  keyExtractor the function used to extract the long sort key
 294      * @return a lexicographic-order comparator composed of this and then the
 295      *         {@code long} sort key
 296      * @throws NullPointerException if the argument is null.
 297      * @see #comparingLong(ToLongFunction)
 298      * @see #thenComparing(Comparator)
 299      * @since 1.8
 300      */
 301     default Comparator<T> thenComparingLong(ToLongFunction<? super T> keyExtractor) {
 302         return thenComparing(comparingLong(keyExtractor));
 303     }
 304 
 305     /**
 306      * Returns a lexicographic-order comparator with a function that
 307      * extracts a {@code double} sort key.
 308      *
 309      * @implSpec This default implementation behaves as if {@code
 310      *           thenComparing(comparingDouble(keyExtractor))}.
 311      *
 312      * @param  keyExtractor the function used to extract the double sort key
 313      * @return a lexicographic-order comparator composed of this and then the
 314      *         {@code double} sort key
 315      * @throws NullPointerException if the argument is null.
 316      * @see #comparingDouble(ToDoubleFunction)
 317      * @see #thenComparing(Comparator)
 318      * @since 1.8
 319      */
 320     default Comparator<T> thenComparingDouble(ToDoubleFunction<? super T> keyExtractor) {
 321         return thenComparing(comparingDouble(keyExtractor));
 322     }
 323 
 324     /**
 325      * Returns a comparator that imposes the reverse of the <em>natural
 326      * ordering</em>.
 327      *
 328      * <p>The returned comparator is serializable and throws {@link
 329      * NullPointerException} when comparing {@code null}.
 330      *
 331      * @param  <T> the {@link Comparable} type of element to be compared
 332      * @return a comparator that imposes the reverse of the <i>natural
 333      *         ordering</i> on {@code Comparable} objects.
 334      * @see Comparable
 335      * @since 1.8
 336      */
 337     public static <T extends Comparable<? super T>> Comparator<T> reverseOrder() {
 338         return Collections.reverseOrder();
 339     }
 340 
 341     /**
 342      * Returns a comparator that compares {@link Comparable} objects in natural
 343      * order.
 344      *
 345      * <p>The returned comparator is serializable and throws {@link
 346      * NullPointerException} when comparing {@code null}.
 347      *
 348      * @param  <T> the {@link Comparable} type of element to be compared
 349      * @return a comparator that imposes the <i>natural ordering</i> on {@code
 350      *         Comparable} objects.
 351      * @see Comparable
 352      * @since 1.8
 353      */
 354     @SuppressWarnings("unchecked")
 355     public static <T extends Comparable<? super T>> Comparator<T> naturalOrder() {
 356         return (Comparator<T>) Comparators.NaturalOrderComparator.INSTANCE;
 357     }
 358 
 359     /**
 360      * Returns a null-friendly comparator that considers {@code null} to be
 361      * less than non-null. When both are {@code null}, they are considered
 362      * equal. If both are non-null, the specified {@code Comparator} is used
 363      * to determine the order. If the specified comparator is {@code null},
 364      * then the returned comparator considers all non-null values to be equal.
 365      *
 366      * <p>The returned comparator is serializable if the specified comparator
 367      * is serializable.
 368      *
 369      * @param  <T> the type of the elements to be compared
 370      * @param  comparator a {@code Comparator} for comparing non-null values
 371      * @return a comparator that considers {@code null} to be less than
 372      *         non-null, and compares non-null objects with the supplied
 373      *         {@code Comparator}.
 374      * @since 1.8
 375      */
 376     public static <T> Comparator<T> nullsFirst(Comparator<? super T> comparator) {
 377         return new Comparators.NullComparator<>(true, comparator);
 378     }
 379 
 380     /**
 381      * Returns a null-friendly comparator that considers {@code null} to be
 382      * greater than non-null. When both are {@code null}, they are considered
 383      * equal. If both are non-null, the specified {@code Comparator} is used
 384      * to determine the order. If the specified comparator is {@code null},
 385      * then the returned comparator considers all non-null values to be equal.
 386      *
 387      * <p>The returned comparator is serializable if the specified comparator
 388      * is serializable.
 389      *
 390      * @param  <T> the type of the elements to be compared
 391      * @param  comparator a {@code Comparator} for comparing non-null values
 392      * @return a comparator that considers {@code null} to be greater than
 393      *         non-null, and compares non-null objects with the supplied
 394      *         {@code Comparator}.
 395      * @since 1.8
 396      */
 397     public static <T> Comparator<T> nullsLast(Comparator<? super T> comparator) {
 398         return new Comparators.NullComparator<>(false, comparator);
 399     }
 400 
 401     /**
 402      * Accepts a function that extracts a sort key from a type {@code T}, and
 403      * returns a {@code Comparator<T>} that compares by that sort key using
 404      * the specified {@link Comparator}.
 405       *
 406      * <p>The returned comparator is serializable if the specified function
 407      * and comparator are both serializable.
 408      *
 409      * @apiNote
 410      * For example, to obtain a {@code Comparator} that compares {@code
 411      * Person} objects by their last name ignoring case differences,
 412      *
 413      * <pre>{@code
 414      *     Comparator<Person> cmp = Comparator.comparing(
 415      *             Person::getLastName,
 416      *             String.CASE_INSENSITIVE_ORDER);
 417      * }</pre>
 418      *
 419      * @param  <T> the type of element to be compared
 420      * @param  <U> the type of the sort key
 421      * @param  keyExtractor the function used to extract the sort key
 422      * @param  keyComparator the {@code Comparator} used to compare the sort key
 423      * @return a comparator that compares by an extracted key using the
 424      *         specified {@code Comparator}
 425      * @throws NullPointerException if either argument is null
 426      * @since 1.8
 427      */
 428     public static <T, U> Comparator<T> comparing(
 429             Function<? super T, ? extends U> keyExtractor,
 430             Comparator<? super U> keyComparator)
 431     {
 432         Objects.requireNonNull(keyExtractor);
 433         Objects.requireNonNull(keyComparator);
 434         return (Comparator<T> & Serializable)
 435             (c1, c2) -> keyComparator.compare(keyExtractor.apply(c1),
 436                                               keyExtractor.apply(c2));
 437     }
 438 
 439     /**
 440      * Accepts a function that extracts a {@link java.lang.Comparable
 441      * Comparable} sort key from a type {@code T}, and returns a {@code
 442      * Comparator<T>} that compares by that sort key.
 443      *
 444      * <p>The returned comparator is serializable if the specified function
 445      * is also serializable.
 446      *
 447      * @apiNote
 448      * For example, to obtain a {@code Comparator} that compares {@code
 449      * Person} objects by their last name,
 450      *
 451      * <pre>{@code
 452      *     Comparator<Person> byLastName = Comparator.comparing(Person::getLastName);
 453      * }</pre>
 454      *
 455      * @param  <T> the type of element to be compared
 456      * @param  <U> the type of the {@code Comparable} sort key
 457      * @param  keyExtractor the function used to extract the {@link
 458      *         Comparable} sort key
 459      * @return a comparator that compares by an extracted key
 460      * @throws NullPointerException if the argument is null
 461      * @since 1.8
 462      */
 463     public static <T, U extends Comparable<? super U>> Comparator<T> comparing(
 464             Function<? super T, ? extends U> keyExtractor)
 465     {
 466         Objects.requireNonNull(keyExtractor);
 467         return (Comparator<T> & Serializable)
 468             (c1, c2) -> keyExtractor.apply(c1).compareTo(keyExtractor.apply(c2));
 469     }
 470 
 471     /**
 472      * Accepts a function that extracts an {@code int} sort key from a type
 473      * {@code T}, and returns a {@code Comparator<T>} that compares by that
 474      * sort key.
 475      *
 476      * <p>The returned comparator is serializable if the specified function
 477      * is also serializable.
 478      *
 479      * @param  <T> the type of element to be compared
 480      * @param  keyExtractor the function used to extract the integer sort key
 481      * @return a comparator that compares by an extracted key
 482      * @see #comparing(Function)
 483      * @throws NullPointerException if the argument is null
 484      * @since 1.8
 485      */
 486     public static <T> Comparator<T> comparingInt(ToIntFunction<? super T> keyExtractor) {
 487         Objects.requireNonNull(keyExtractor);
 488         return (Comparator<T> & Serializable)
 489             (c1, c2) -> Integer.compare(keyExtractor.applyAsInt(c1), keyExtractor.applyAsInt(c2));
 490     }
 491 
 492     /**
 493      * Accepts a function that extracts a {@code long} sort key from a type
 494      * {@code T}, and returns a {@code Comparator<T>} that compares by that
 495      * sort key.
 496      *
 497      * <p>The returned comparator is serializable if the specified function is
 498      * also serializable.
 499      *
 500      * @param  <T> the type of element to be compared
 501      * @param  keyExtractor the function used to extract the long sort key
 502      * @return a comparator that compares by an extracted key
 503      * @see #comparing(Function)
 504      * @throws NullPointerException if the argument is null
 505      * @since 1.8
 506      */
 507     public static <T> Comparator<T> comparingLong(ToLongFunction<? super T> keyExtractor) {
 508         Objects.requireNonNull(keyExtractor);
 509         return (Comparator<T> & Serializable)
 510             (c1, c2) -> Long.compare(keyExtractor.applyAsLong(c1), keyExtractor.applyAsLong(c2));
 511     }
 512 
 513     /**
 514      * Accepts a function that extracts a {@code double} sort key from a type
 515      * {@code T}, and returns a {@code Comparator<T>} that compares by that
 516      * sort key.
 517      *
 518      * <p>The returned comparator is serializable if the specified function
 519      * is also serializable.
 520      *
 521      * @param  <T> the type of element to be compared
 522      * @param  keyExtractor the function used to extract the double sort key
 523      * @return a comparator that compares by an extracted key
 524      * @see #comparing(Function)
 525      * @throws NullPointerException if the argument is null
 526      * @since 1.8
 527      */
 528     public static <T> Comparator<T> comparingDouble(ToDoubleFunction<? super T> keyExtractor) {
 529         Objects.requireNonNull(keyExtractor);
 530         return (Comparator<T> & Serializable)
 531             (c1, c2) -> Double.compare(keyExtractor.applyAsDouble(c1), keyExtractor.applyAsDouble(c2));
 532     }
 533 
 534     /**
 535      * The returned comparator compares two character sequences as though each
 536      * of them would be first transformed into a tuple of the form:
 537      * <pre>{@code (A0, N0, A1, N1, ..., An-1, Nn-1, An, Nn)}</pre>
 538      * where:
 539      * <p>{@code A0} and {@code An} are (possibly empty) sub-sequences
 540      * consisting of non-decimal-digit characters,
 541      * <p>{@code A1 ... An-1} are non-empty sub-sequences consisting of
 542      * non-decimal-digit characters,
 543      * <p>{@code N0 ... Nn-1} are non-empty sub-sequences consisting of
 544      * decimal-digit characters, and
 545      * <p>{@code Nn} is a (possibly empty) sub-sequence consisting of
 546      * decimal-digit characters.
 547      *
 548      * <p>All sub-sequences concatenated together in order as they appear in the
 549      * tuple yield the original character sequence.
 550      *
 551      * After transformation, the tuples are compared by their elements (from
 552      * left to right) so that corresponding {@code Ax} elements are compared
 553      * using the provided comparator {@code alphaComparator} and {@code Nx}
 554      * elements are compared as non negative decimal integers.
 555      *
 556      * The first pair of compared elements that is different with respect to the
 557      * used comparator (either {@code alphaComparator}, or special decimal
 558      * comparator) if any, provides the result produced by this comparator.
 559      * The arguments are treated equal, if and only if all the subsequences,
 560      * both decimal and non-decimal, compare equal.
 561      *
 562      * <p>For example, the following array was sorted using such comparator:
 563      * <pre>{@code
 564      * { "1ab", "5ab", "10ab",
 565      *   "a1b", "a5b", "a10b",
 566      *   "ab1", "ab5", "ab10" };}</pre>
 567      *
 568      * <p>When comparing numerical parts, an empty character sequence is
 569      * considered less than any non-empty sequence of decimal digits.
 570      *
 571      * <p>If the numeric values of two compared character sub-sequences are
 572      * equal, but their string representations have different number of leading
 573      * zeroes, the comparator treats the number with less leading zeros as
 574      * smaller.
 575      * For example, {@code "abc 1" < "abc 01" < "abc 001"}.
 576      *
 577      * @apiNote  For example, to sort a collection of {@code String} based on
 578      * case-insensitive ordering, and treating numbers with more leading
 579      * zeroes as greater, one could use
 580      *
 581      * <pre>{@code
 582      *     Comparator<String> cmp = Comparator.comparingAlphaDecimal(
 583      *             Comparator.comparing(CharSequence::toString,
 584      *                                  String::compareToIgnoreCase));
 585      * }</pre>
 586      *
 587      * @implSpec  To test if the given code point represents a decimal digit,
 588      * the comparator checks if {@link java.lang.Character#getType(int)}
 589      * returns value {@link java.lang.Character#DECIMAL_DIGIT_NUMBER}.
 590      * The comparator uses {@link java.lang.Character#digit(int, int)} with
 591      * the second argument set to {@code 10} to determine the numeric
 592      * value of a digit represented by the given code point.
 593      *
 594      * @param  alphaComparator the comparator that compares sub-sequences
 595      *                         consisting of non-decimal-digits
 596      * @param  <T> the type of elements to be compared; normally
 597      *                         {@link java.lang.CharSequence}
 598      * @return a comparator that compares character sequences, following the
 599      *                         rules described above
 600      * @throws NullPointerException if the argument is null
 601      *
 602      * @since 10
 603      */
 604     public static <T extends CharSequence> Comparator<T>
 605     comparingAlphaDecimal(Comparator<? super CharSequence> alphaComparator) {
 606         return new Comparators.AlphaDecimalComparator<>(
 607                 Objects.requireNonNull(alphaComparator), false);
 608     }
 609 
 610     /**
 611      * The returned comparator compares two character sequences as though each
 612      * of them would be first transformed into a tuple of the form:
 613      * <pre>{@code (A0, N0, A1, N1, ..., An-1, Nn-1, An, Nn)}</pre>
 614      * where:
 615      * <p>{@code A0} and {@code An} are (possibly empty) sub-sequences
 616      * consisting of non-decimal-digit characters,
 617      * <p>{@code A1 ... An-1} are non-empty sub-sequences consisting of
 618      * non-decimal-digit characters,
 619      * <p>{@code N0 ... Nn-1} are non-empty sub-sequences consisting of
 620      * decimal-digit characters, and
 621      * <p>{@code Nn} is a (possibly empty) sub-sequence consisting of
 622      * decimal-digit characters.
 623      *
 624      * <p>All sub-sequences concatenated together in order as they appear in the
 625      * tuple yield the original character sequence.
 626      *
 627      * After transformation, the tuples are compared by their elements (from
 628      * left to right) so that corresponding {@code Ax} elements are compared
 629      * using the provided comparator {@code alphaComparator} and {@code Nx}
 630      * elements are compared as non negative decimal integers.
 631      *
 632      * The first pair of compared elements that is different with respect to the
 633      * used comparator (either {@code alphaComparator}, or special decimal
 634      * comparator) if any, provides the result produced by this comparator.
 635      * The arguments are treated equal, if and only if all the subsequences,
 636      * both decimal and non-decimal, compare equal.
 637      *
 638      * <p>For example, the following array was sorted using such comparator:
 639      * <pre>{@code
 640      * { "1ab", "5ab", "10ab",
 641      *   "a1b", "a5b", "a10b",
 642      *   "ab1", "ab5", "ab10" };}</pre>
 643      *
 644      * <p>When comparing numerical parts, an empty character sequence is
 645      * considered less than any non-empty sequence of decimal digits.
 646      *
 647      * <p>If the numeric values of two compared character sub-sequences are
 648      * equal, but their string representations have different number of leading
 649      * zeroes, the comparator treats the number with more leading zeros as
 650      * smaller.
 651      * For example, {@code "abc 001" < "abc 01" < "abc 1"}.
 652      *
 653      * @apiNote  For example, to sort a collection of {@code String} based on
 654      * case-insensitive ordering, and treating numbers with less leading
 655      * zeroes as greater, one could use
 656      *
 657      * <pre>{@code
 658      *       Comparator<String> cmp = Comparator.comparingAlphaDecimalLeadingZeroesFirst(
 659      *             Comparator.comparing(CharSequence::toString,
 660      *                                  String::compareToIgnoreCase));
 661      * }</pre>
 662      *
 663      * @implSpec  To test if the given code point represents a decimal digit,
 664      * the comparator checks if {@link java.lang.Character#getType(int)}
 665      * returns value {@link java.lang.Character#DECIMAL_DIGIT_NUMBER}.
 666      * The comparator uses {@link java.lang.Character#digit(int, int)} with
 667      * the second argument set to {@code 10} to determine the numeric
 668      * value of a digit represented by the given code point.
 669      *
 670      * @param  alphaComparator the comparator that compares sub-sequences
 671      *                         consisting of non-decimal-digits
 672      * @param  <T> the type of elements to be compared; normally
 673      *                         {@link java.lang.CharSequence}
 674      * @return a comparator that compares character sequences, following the
 675      *                         rules described above
 676      * @throws NullPointerException if the argument is null
 677      *
 678      * @since 10
 679      */
 680     public static <T extends CharSequence> Comparator<T>
 681     comparingAlphaDecimalLeadingZeroesFirst(
 682             Comparator<? super CharSequence> alphaComparator) {
 683         return new Comparators.AlphaDecimalComparator<>(
 684                 Objects.requireNonNull(alphaComparator), true);
 685     }
 686 }