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   * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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  package java.util;
  
  import java.io.Serializable;
  import java.util.function.Function;
  import java.util.function.ToIntFunction;
  import java.util.function.ToLongFunction;
  import java.util.function.ToDoubleFunction;
  import java.util.Comparators;
  
  /**
   * A comparison function, which imposes a <i>total ordering</i> on some
   * collection of objects.  Comparators can be passed to a sort method (such
   * as {@link Collections#sort(List,Comparator) Collections.sort} or {@link
   * Arrays#sort(Object[],Comparator) Arrays.sort}) to allow precise control
   * over the sort order.  Comparators can also be used to control the order of
   * certain data structures (such as {@link SortedSet sorted sets} or {@link
   * SortedMap sorted maps}), or to provide an ordering for collections of
   * objects that don't have a {@link Comparable natural ordering}.<p>
   *
   * The ordering imposed by a comparator <tt>c</tt> on a set of elements
   * <tt>S</tt> is said to be <i>consistent with equals</i> if and only if
   * <tt>c.compare(e1, e2)==0</tt> has the same boolean value as
   * <tt>e1.equals(e2)</tt> for every <tt>e1</tt> and <tt>e2</tt> in
   * <tt>S</tt>.<p>
   *
   * Caution should be exercised when using a comparator capable of imposing an
   * ordering inconsistent with equals to order a sorted set (or sorted map).
   * Suppose a sorted set (or sorted map) with an explicit comparator <tt>c</tt>
   * is used with elements (or keys) drawn from a set <tt>S</tt>.  If the
   * ordering imposed by <tt>c</tt> on <tt>S</tt> is inconsistent with equals,
   * the sorted set (or sorted map) will behave "strangely."  In particular the
   * sorted set (or sorted map) will violate the general contract for set (or
   * map), which is defined in terms of <tt>equals</tt>.<p>
   *
   * For example, suppose one adds two elements {@code a} and {@code b} such that
   * {@code (a.equals(b) && c.compare(a, b) != 0)}
   * to an empty {@code TreeSet} with comparator {@code c}.
   * The second {@code add} operation will return
   * true (and the size of the tree set will increase) because {@code a} and
   * {@code b} are not equivalent from the tree set's perspective, even though
   * this is contrary to the specification of the
   * {@link Set#add Set.add} method.<p>
   *
   * Note: It is generally a good idea for comparators to also implement
   * <tt>java.io.Serializable</tt>, as they may be used as ordering methods in
   * serializable data structures (like {@link TreeSet}, {@link TreeMap}).  In
   * order for the data structure to serialize successfully, the comparator (if
   * provided) must implement <tt>Serializable</tt>.<p>
   *
   * For the mathematically inclined, the <i>relation</i> that defines the
   * <i>imposed ordering</i> that a given comparator <tt>c</tt> imposes on a
   * given set of objects <tt>S</tt> is:<pre>
   *       {(x, y) such that c.compare(x, y) &lt;= 0}.
   * </pre> The <i>quotient</i> for this total order is:<pre>
   *       {(x, y) such that c.compare(x, y) == 0}.
   * </pre>
   *
   * It follows immediately from the contract for <tt>compare</tt> that the
   * quotient is an <i>equivalence relation</i> on <tt>S</tt>, and that the
   * imposed ordering is a <i>total order</i> on <tt>S</tt>.  When we say that
   * the ordering imposed by <tt>c</tt> on <tt>S</tt> is <i>consistent with
   * equals</i>, we mean that the quotient for the ordering is the equivalence
   * relation defined by the objects' {@link Object#equals(Object)
   * equals(Object)} method(s):<pre>
   *     {(x, y) such that x.equals(y)}. </pre>
   *
   * <p>Unlike {@code Comparable}, a comparator may optionally permit
   * comparison of null arguments, while maintaining the requirements for
   * an equivalence relation.
   *
   * <p>This interface is a member of the
   * <a href="{@docRoot}/../technotes/guides/collections/index.html">
   * Java Collections Framework</a>.
   *
   * @param <T> the type of objects that may be compared by this comparator
   *
   * @author  Josh Bloch
   * @author  Neal Gafter
   * @see Comparable
   * @see Serializable
   * @since 1.2
   */
  @FunctionalInterface
  public interface Comparator<T> {
      /**
       * Compares its two arguments for order.  Returns a negative integer,
       * zero, or a positive integer as the first argument is less than, equal
       * to, or greater than the second.<p>
       *
       * In the foregoing description, the notation
       * <tt>sgn(</tt><i>expression</i><tt>)</tt> designates the mathematical
       * <i>signum</i> function, which is defined to return one of <tt>-1</tt>,
       * <tt>0</tt>, or <tt>1</tt> according to whether the value of
       * <i>expression</i> is negative, zero or positive.<p>
       *
       * The implementor must ensure that <tt>sgn(compare(x, y)) ==
       * -sgn(compare(y, x))</tt> for all <tt>x</tt> and <tt>y</tt>.  (This
       * implies that <tt>compare(x, y)</tt> must throw an exception if and only
       * if <tt>compare(y, x)</tt> throws an exception.)<p>
       *
       * The implementor must also ensure that the relation is transitive:
       * <tt>((compare(x, y)&gt;0) &amp;&amp; (compare(y, z)&gt;0))</tt> implies
       * <tt>compare(x, z)&gt;0</tt>.<p>
       *
       * Finally, the implementor must ensure that <tt>compare(x, y)==0</tt>
       * implies that <tt>sgn(compare(x, z))==sgn(compare(y, z))</tt> for all
       * <tt>z</tt>.<p>
       *
       * It is generally the case, but <i>not</i> strictly required that
       * <tt>(compare(x, y)==0) == (x.equals(y))</tt>.  Generally speaking,
       * any comparator that violates this condition should clearly indicate
       * this fact.  The recommended language is "Note: this comparator
       * imposes orderings that are inconsistent with equals."
       *
       * @param o1 the first object to be compared.
       * @param o2 the second object to be compared.
       * @return a negative integer, zero, or a positive integer as the
       *         first argument is less than, equal to, or greater than the
       *         second.
       * @throws NullPointerException if an argument is null and this
       *         comparator does not permit null arguments
       * @throws ClassCastException if the arguments' types prevent them from
       *         being compared by this comparator.
       */
      int compare(T o1, T o2);
  
      /**
       * Indicates whether some other object is &quot;equal to&quot; this
       * comparator.  This method must obey the general contract of
       * {@link Object#equals(Object)}.  Additionally, this method can return
       * <tt>true</tt> <i>only</i> if the specified object is also a comparator
       * and it imposes the same ordering as this comparator.  Thus,
       * <code>comp1.equals(comp2)</code> implies that <tt>sgn(comp1.compare(o1,
       * o2))==sgn(comp2.compare(o1, o2))</tt> for every object reference
       * <tt>o1</tt> and <tt>o2</tt>.<p>
       *
       * Note that it is <i>always</i> safe <i>not</i> to override
       * <tt>Object.equals(Object)</tt>.  However, overriding this method may,
       * in some cases, improve performance by allowing programs to determine
       * that two distinct comparators impose the same order.
       *
       * @param   obj   the reference object with which to compare.
       * @return  <code>true</code> only if the specified object is also
       *          a comparator and it imposes the same ordering as this
       *          comparator.
       * @see Object#equals(Object)
       * @see Object#hashCode()
       */
      boolean equals(Object obj);
  
      /**
       * Returns a comparator that imposes the reverse ordering of this
       * comparator.
       *
       * @return a comparator that imposes the reverse ordering of this
       *         comparator.
       * @since 1.8
       */
      default Comparator<T> reversed() {
          return Collections.reverseOrder(this);
      }
  
      /**
       * Returns a lexicographic-order comparator with another comparator.
       * If this {@code Comparator} considers two elements equal, i.e.
       * {@code compare(a, b) == 0}, {@code other} is used to determine the order.
       *
       * <p>The returned comparator is serializable if the specified comparator
       * is also serializable.
       *
       * @apiNote
       * For example, to sort a collection of {@code String} based on the length
       * and then case-insensitive natural ordering, the comparator can be
       * composed using following code,
       *
       * <pre>{@code
       *     Comparator<String> cmp = Comparator.comparingInt(String::length)
       *             .thenComparing(String.CASE_INSENSITIVE_ORDER);
       * }</pre>
       *
       * @param  other the other comparator to be used when this comparator
       *         compares two objects that are equal.
       * @return a lexicographic-order comparator composed of this and then the
       *         other comparator
       * @throws NullPointerException if the argument is null.
       * @since 1.8
       */
      default Comparator<T> thenComparing(Comparator<? super T> other) {
          Objects.requireNonNull(other);
          return (Comparator<T> & Serializable) (c1, c2) -> {
              int res = compare(c1, c2);
              return (res != 0) ? res : other.compare(c1, c2);
          };
      }
  
      /**
       * Returns a lexicographic-order comparator with a function that
       * extracts a key to be compared with the given {@code Comparator}.
       *
       * @implSpec This default implementation behaves as if {@code
       *           thenComparing(comparing(keyExtractor, cmp))}.
       *
       * @param  <U>  the type of the sort key
       * @param  keyExtractor the function used to extract the sort key
       * @param  keyComparator the {@code Comparator} used to compare the sort key
       * @return a lexicographic-order comparator composed of this comparator
       *         and then comparing on the key extracted by the keyExtractor function
       * @throws NullPointerException if either argument is null.
       * @see #comparing(Function, Comparator)
       * @see #thenComparing(Comparator)
       * @since 1.8
       */
      default <U> Comparator<T> thenComparing(
              Function<? super T, ? extends U> keyExtractor,
              Comparator<? super U> keyComparator)
      {
          return thenComparing(comparing(keyExtractor, keyComparator));
      }
  
      /**
       * Returns a lexicographic-order comparator with a function that
       * extracts a {@code Comparable} sort key.
       *
       * @implSpec This default implementation behaves as if {@code
       *           thenComparing(comparing(keyExtractor))}.
       *
       * @param  <U>  the type of the {@link Comparable} sort key
       * @param  keyExtractor the function used to extract the {@link
       *         Comparable} sort key
       * @return a lexicographic-order comparator composed of this and then the
       *         {@link Comparable} sort key.
       * @throws NullPointerException if the argument is null.
       * @see #comparing(Function)
       * @see #thenComparing(Comparator)
       * @since 1.8
       */
      default <U extends Comparable<? super U>> Comparator<T> thenComparing(
              Function<? super T, ? extends U> keyExtractor)
      {
          return thenComparing(comparing(keyExtractor));
      }
  
      /**
       * Returns a lexicographic-order comparator with a function that
       * extracts a {@code int} sort key.
       *
       * @implSpec This default implementation behaves as if {@code
       *           thenComparing(comparingInt(keyExtractor))}.
       *
       * @param  keyExtractor the function used to extract the integer sort key
       * @return a lexicographic-order comparator composed of this and then the
       *         {@code int} sort key
       * @throws NullPointerException if the argument is null.
       * @see #comparingInt(ToIntFunction)
       * @see #thenComparing(Comparator)
       * @since 1.8
       */
      default Comparator<T> thenComparingInt(ToIntFunction<? super T> keyExtractor) {
          return thenComparing(comparingInt(keyExtractor));
      }
  
      /**
       * Returns a lexicographic-order comparator with a function that
       * extracts a {@code long} sort key.
       *
       * @implSpec This default implementation behaves as if {@code
       *           thenComparing(comparingLong(keyExtractor))}.
       *
       * @param  keyExtractor the function used to extract the long sort key
       * @return a lexicographic-order comparator composed of this and then the
       *         {@code long} sort key
       * @throws NullPointerException if the argument is null.
       * @see #comparingLong(ToLongFunction)
       * @see #thenComparing(Comparator)
       * @since 1.8
       */
      default Comparator<T> thenComparingLong(ToLongFunction<? super T> keyExtractor) {
          return thenComparing(comparingLong(keyExtractor));
      }
  
      /**
       * Returns a lexicographic-order comparator with a function that
       * extracts a {@code double} sort key.
       *
       * @implSpec This default implementation behaves as if {@code
       *           thenComparing(comparingDouble(keyExtractor))}.
       *
       * @param  keyExtractor the function used to extract the double sort key
       * @return a lexicographic-order comparator composed of this and then the
       *         {@code double} sort key
       * @throws NullPointerException if the argument is null.
       * @see #comparingDouble(ToDoubleFunction)
       * @see #thenComparing(Comparator)
       * @since 1.8
       */
      default Comparator<T> thenComparingDouble(ToDoubleFunction<? super T> keyExtractor) {
          return thenComparing(comparingDouble(keyExtractor));
      }
  
      /**
       * Returns a comparator that imposes the reverse of the <em>natural
       * ordering</em>.
       *
       * <p>The returned comparator is serializable and throws {@link
       * NullPointerException} when comparing {@code null}.
       *
       * @param  <T> the {@link Comparable} type of element to be compared
       * @return a comparator that imposes the reverse of the <i>natural
       *         ordering</i> on {@code Comparable} objects.
       * @see Comparable
       * @since 1.8
       */
      public static <T extends Comparable<? super T>> Comparator<T> reverseOrder() {
          return Collections.reverseOrder();
      }
  
      /**
       * Returns a comparator that compares {@link Comparable} objects in natural
       * order.
       *
       * <p>The returned comparator is serializable and throws {@link
       * NullPointerException} when comparing {@code null}.
       *
       * @param  <T> the {@link Comparable} type of element to be compared
       * @return a comparator that imposes the <i>natural ordering</i> on {@code
       *         Comparable} objects.
       * @see Comparable
       * @since 1.8
       */
      @SuppressWarnings("unchecked")
      public static <T extends Comparable<? super T>> Comparator<T> naturalOrder() {
          return (Comparator<T>) Comparators.NaturalOrderComparator.INSTANCE;
      }
  
      /**
       * Returns a null-friendly comparator that considers {@code null} to be
       * less than non-null. When both are {@code null}, they are considered
       * equal. If both are non-null, the specified {@code Comparator} is used
       * to determine the order. If the specified comparator is {@code null},
       * then the returned comparator considers all non-null values to be equal.
       *
       * <p>The returned comparator is serializable if the specified comparator
       * is serializable.
       *
       * @param  <T> the type of the elements to be compared
       * @param  comparator a {@code Comparator} for comparing non-null values
       * @return a comparator that considers {@code null} to be less than
       *         non-null, and compares non-null objects with the supplied
       *         {@code Comparator}.
       * @since 1.8
       */
      public static <T> Comparator<T> nullsFirst(Comparator<? super T> comparator) {
          return new Comparators.NullComparator<>(true, comparator);
      }
  
      /**
       * Returns a null-friendly comparator that considers {@code null} to be
       * greater than non-null. When both are {@code null}, they are considered
       * equal. If both are non-null, the specified {@code Comparator} is used
       * to determine the order. If the specified comparator is {@code null},
       * then the returned comparator considers all non-null values to be equal.
       *
       * <p>The returned comparator is serializable if the specified comparator
       * is serializable.
       *
       * @param  <T> the type of the elements to be compared
       * @param  comparator a {@code Comparator} for comparing non-null values
       * @return a comparator that considers {@code null} to be greater than
       *         non-null, and compares non-null objects with the supplied
       *         {@code Comparator}.
       * @since 1.8
       */
      public static <T> Comparator<T> nullsLast(Comparator<? super T> comparator) {
          return new Comparators.NullComparator<>(false, comparator);
      }
  
      /**
       * Accepts a function that extracts a sort key from a type {@code T}, and
       * returns a {@code Comparator<T>} that compares by that sort key using
       * the specified {@link Comparator}.
        *
       * <p>The returned comparator is serializable if the specified function
       * and comparator are both serializable.
       *
       * @apiNote
       * For example, to obtain a {@code Comparator} that compares {@code
       * Person} objects by their last name ignoring case differences,
       *
       * <pre>{@code
       *     Comparator<Person> cmp = Comparator.comparing(
       *             Person::getLastName,
       *             String.CASE_INSENSITIVE_ORDER);
       * }</pre>
       *
       * @param  <T> the type of element to be compared
       * @param  <U> the type of the sort key
       * @param  keyExtractor the function used to extract the sort key
       * @param  keyComparator the {@code Comparator} used to compare the sort key
       * @return a comparator that compares by an extracted key using the
       *         specified {@code Comparator}
       * @throws NullPointerException if either argument is null
       * @since 1.8
       */
      public static <T, U> Comparator<T> comparing(
              Function<? super T, ? extends U> keyExtractor,
              Comparator<? super U> keyComparator)
      {
          Objects.requireNonNull(keyExtractor);
          Objects.requireNonNull(keyComparator);
          return (Comparator<T> & Serializable)
              (c1, c2) -> keyComparator.compare(keyExtractor.apply(c1),
                                                keyExtractor.apply(c2));
      }
  
      /**
       * Accepts a function that extracts a {@link Comparable
       * Comparable} sort key from a type {@code T}, and returns a {@code
       * Comparator<T>} that compares by that sort key.
       *
       * <p>The returned comparator is serializable if the specified function
       * is also serializable.
       *
       * @apiNote
       * For example, to obtain a {@code Comparator} that compares {@code
       * Person} objects by their last name,
       *
       * <pre>{@code
       *     Comparator<Person> byLastName = Comparator.comparing(Person::getLastName);
       * }</pre>
       *
       * @param  <T> the type of element to be compared
       * @param  <U> the type of the {@code Comparable} sort key
       * @param  keyExtractor the function used to extract the {@link
       *         Comparable} sort key
       * @return a comparator that compares by an extracted key
       * @throws NullPointerException if the argument is null
       * @since 1.8
       */
      public static <T, U extends Comparable<? super U>> Comparator<T> comparing(
              Function<? super T, ? extends U> keyExtractor)
      {
          Objects.requireNonNull(keyExtractor);
          return (Comparator<T> & Serializable)
              (c1, c2) -> keyExtractor.apply(c1).compareTo(keyExtractor.apply(c2));
      }
  
      /**
       * Accepts a function that extracts an {@code int} sort key from a type
       * {@code T}, and returns a {@code Comparator<T>} that compares by that
       * sort key.
       *
       * <p>The returned comparator is serializable if the specified function
       * is also serializable.
       *
       * @param  <T> the type of element to be compared
       * @param  keyExtractor the function used to extract the integer sort key
       * @return a comparator that compares by an extracted key
       * @see #comparing(Function)
       * @throws NullPointerException if the argument is null
       * @since 1.8
       */
      public static <T> Comparator<T> comparingInt(ToIntFunction<? super T> keyExtractor) {
          Objects.requireNonNull(keyExtractor);
          return (Comparator<T> & Serializable)
              (c1, c2) -> Integer.compare(keyExtractor.applyAsInt(c1), keyExtractor.applyAsInt(c2));
      }
  
      /**
       * Accepts a function that extracts a {@code long} sort key from a type
       * {@code T}, and returns a {@code Comparator<T>} that compares by that
       * sort key.
       *
       * <p>The returned comparator is serializable if the specified function is
       * also serializable.
       *
       * @param  <T> the type of element to be compared
       * @param  keyExtractor the function used to extract the long sort key
       * @return a comparator that compares by an extracted key
       * @see #comparing(Function)
       * @throws NullPointerException if the argument is null
       * @since 1.8
       */
      public static <T> Comparator<T> comparingLong(ToLongFunction<? super T> keyExtractor) {
          Objects.requireNonNull(keyExtractor);
          return (Comparator<T> & Serializable)
              (c1, c2) -> Long.compare(keyExtractor.applyAsLong(c1), keyExtractor.applyAsLong(c2));
      }
  
      /**
       * Accepts a function that extracts a {@code double} sort key from a type
       * {@code T}, and returns a {@code Comparator<T>} that compares by that
       * sort key.
       *
       * <p>The returned comparator is serializable if the specified function
       * is also serializable.
       *
       * @param  <T> the type of element to be compared
       * @param  keyExtractor the function used to extract the double sort key
       * @return a comparator that compares by an extracted key
       * @see #comparing(Function)
       * @throws NullPointerException if the argument is null
       * @since 1.8
       */
      public static<T> Comparator<T> comparingDouble(ToDoubleFunction<? super T> keyExtractor) {
          Objects.requireNonNull(keyExtractor);
          return (Comparator<T> & Serializable)
              (c1, c2) -> Double.compare(keyExtractor.applyAsDouble(c1), keyExtractor.applyAsDouble(c2));
      }
  }
  