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   * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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   * This code is free software; you can redistribute it and/or modify it
   * under the terms of the GNU General Public License version 2 only, as
   * published by the Free Software Foundation.  Oracle designates this
   * particular file as subject to the "Classpath" exception as provided
   * by Oracle in the LICENSE file that accompanied this code.
   *
   * This code is distributed in the hope that it will be useful, but WITHOUT
   * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
   * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
   * version 2 for more details (a copy is included in the LICENSE file that
   * accompanied this code).
   *
   * You should have received a copy of the GNU General Public License version
   * 2 along with this work; if not, write to the Free Software Foundation,
   * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
   *
   * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
   * or visit www.oracle.com if you need additional information or have any
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   */
  
  package java.util;
  
  /**
   * A {@link NavigableSet} implementation based on a {@link TreeMap}.
   * The elements are ordered using their {@linkplain Comparable natural
   * ordering}, or by a {@link Comparator} provided at set creation
   * time, depending on which constructor is used.
   *
   * <p>This implementation provides guaranteed log(n) time cost for the basic
   * operations ({@code add}, {@code remove} and {@code contains}).
   *
   * <p>Note that the ordering maintained by a set (whether or not an explicit
   * comparator is provided) must be <i>consistent with equals</i> if it is to
   * correctly implement the {@code Set} interface.  (See {@code Comparable}
   * or {@code Comparator} for a precise definition of <i>consistent with
   * equals</i>.)  This is so because the {@code Set} interface is defined in
   * terms of the {@code equals} operation, but a {@code TreeSet} instance
   * performs all element comparisons using its {@code compareTo} (or
   * {@code compare}) method, so two elements that are deemed equal by this method
   * are, from the standpoint of the set, equal.  The behavior of a set
   * <i>is</i> well-defined even if its ordering is inconsistent with equals; it
   * just fails to obey the general contract of the {@code Set} interface.
   *
   * <p><strong>Note that this implementation is not synchronized.</strong>
   * If multiple threads access a tree set concurrently, and at least one
   * of the threads modifies the set, it <i>must</i> be synchronized
   * externally.  This is typically accomplished by synchronizing on some
   * object that naturally encapsulates the set.
   * If no such object exists, the set should be "wrapped" using the
   * {@link Collections#synchronizedSortedSet Collections.synchronizedSortedSet}
   * method.  This is best done at creation time, to prevent accidental
   * unsynchronized access to the set: <pre>
   *   SortedSet s = Collections.synchronizedSortedSet(new TreeSet(...));</pre>
   *
   * <p>The iterators returned by this class's {@code iterator} method are
   * <i>fail-fast</i>: if the set is modified at any time after the iterator is
   * created, in any way except through the iterator's own {@code remove}
   * method, the iterator will throw a {@link ConcurrentModificationException}.
   * Thus, in the face of concurrent modification, the iterator fails quickly
   * and cleanly, rather than risking arbitrary, non-deterministic behavior at
   * an undetermined time in the future.
   *
   * <p>Note that the fail-fast behavior of an iterator cannot be guaranteed
   * as it is, generally speaking, impossible to make any hard guarantees in the
   * presence of unsynchronized concurrent modification.  Fail-fast iterators
   * throw {@code ConcurrentModificationException} on a best-effort basis.
   * Therefore, it would be wrong to write a program that depended on this
   * exception for its correctness:   <i>the fail-fast behavior of iterators
   * should be used only to detect bugs.</i>
   *
   * <p>This class is a member of the
   * <a href="{@docRoot}/../technotes/guides/collections/index.html">
   * Java Collections Framework</a>.
   *
   * @param <E> the type of elements maintained by this set
   *
   * @author  Josh Bloch
   * @see     Collection
   * @see     Set
   * @see     HashSet
   * @see     Comparable
   * @see     Comparator
   * @see     TreeMap
   * @since   1.2
   */
  
  public class TreeSet<E> extends AbstractSet<E>
      implements NavigableSet<E>, Cloneable, java.io.Serializable
  {
      /**
       * The backing map.
       */
      private transient NavigableMap<E,Object> m;
  
      // Dummy value to associate with an Object in the backing Map
      private static final Object PRESENT = new Object();
  
      /**
       * Constructs a set backed by the specified navigable map.
       */
      TreeSet(NavigableMap<E,Object> m) {
          this.m = m;
      }
  
      /**
       * Constructs a new, empty tree set, sorted according to the
       * natural ordering of its elements.  All elements inserted into
       * the set must implement the {@link Comparable} interface.
       * Furthermore, all such elements must be <i>mutually
       * comparable</i>: {@code e1.compareTo(e2)} must not throw a
       * {@code ClassCastException} for any elements {@code e1} and
       * {@code e2} in the set.  If the user attempts to add an element
       * to the set that violates this constraint (for example, the user
       * attempts to add a string element to a set whose elements are
       * integers), the {@code add} call will throw a
       * {@code ClassCastException}.
       */
      public TreeSet() {
          this(new TreeMap<E,Object>());
      }
  
      /**
       * Constructs a new, empty tree set, sorted according to the specified
       * comparator.  All elements inserted into the set must be <i>mutually
       * comparable</i> by the specified comparator: {@code comparator.compare(e1,
       * e2)} must not throw a {@code ClassCastException} for any elements
       * {@code e1} and {@code e2} in the set.  If the user attempts to add
       * an element to the set that violates this constraint, the
       * {@code add} call will throw a {@code ClassCastException}.
       *
       * @param comparator the comparator that will be used to order this set.
       *        If {@code null}, the {@linkplain Comparable natural
       *        ordering} of the elements will be used.
       */
      public TreeSet(Comparator<? super E> comparator) {
          this(new TreeMap<>(comparator));
      }
  
      /**
       * Constructs a new tree set containing the elements in the specified
       * collection, sorted according to the <i>natural ordering</i> of its
       * elements.  All elements inserted into the set must implement the
       * {@link Comparable} interface.  Furthermore, all such elements must be
       * <i>mutually comparable</i>: {@code e1.compareTo(e2)} must not throw a
       * {@code ClassCastException} for any elements {@code e1} and
       * {@code e2} in the set.
       *
       * @param c collection whose elements will comprise the new set
       * @throws ClassCastException if the elements in {@code c} are
       *         not {@link Comparable}, or are not mutually comparable
       * @throws NullPointerException if the specified collection is null
       */
      public TreeSet(Collection<? extends E> c) {
          this();
          addAll(c);
      }
  
      /**
       * Constructs a new tree set containing the same elements and
       * using the same ordering as the specified sorted set.
       *
       * @param s sorted set whose elements will comprise the new set
       * @throws NullPointerException if the specified sorted set is null
       */
      public TreeSet(SortedSet<E> s) {
          this(s.comparator());
          addAll(s);
      }
  
      /**
       * Returns an iterator over the elements in this set in ascending order.
       *
       * @return an iterator over the elements in this set in ascending order
       */
      public Iterator<E> iterator() {
          return m.navigableKeySet().iterator();
      }
  
      /**
       * Returns an iterator over the elements in this set in descending order.
       *
       * @return an iterator over the elements in this set in descending order
       * @since 1.6
       */
      public Iterator<E> descendingIterator() {
          return m.descendingKeySet().iterator();
      }
  
      /**
       * @since 1.6
       */
      public NavigableSet<E> descendingSet() {
          return new TreeSet<>(m.descendingMap());
      }
  
      /**
       * Returns the number of elements in this set (its cardinality).
       *
       * @return the number of elements in this set (its cardinality)
       */
      public int size() {
          return m.size();
      }
  
      /**
       * Returns {@code true} if this set contains no elements.
       *
       * @return {@code true} if this set contains no elements
       */
      public boolean isEmpty() {
          return m.isEmpty();
      }
  
      /**
       * Returns {@code true} if this set contains the specified element.
       * More formally, returns {@code true} if and only if this set
       * contains an element {@code e} such that
       * <tt>(o==null&nbsp;?&nbsp;e==null&nbsp;:&nbsp;o.equals(e))</tt>.
       *
       * @param o object to be checked for containment in this set
       * @return {@code true} if this set contains the specified element
       * @throws ClassCastException if the specified object cannot be compared
       *         with the elements currently in the set
       * @throws NullPointerException if the specified element is null
       *         and this set uses natural ordering, or its comparator
       *         does not permit null elements
       */
      public boolean contains(Object o) {
          return m.containsKey(o);
      }
  
      /**
       * Adds the specified element to this set if it is not already present.
       * More formally, adds the specified element {@code e} to this set if
       * the set contains no element {@code e2} such that
       * <tt>(e==null&nbsp;?&nbsp;e2==null&nbsp;:&nbsp;e.equals(e2))</tt>.
       * If this set already contains the element, the call leaves the set
       * unchanged and returns {@code false}.
       *
       * @param e element to be added to this set
       * @return {@code true} if this set did not already contain the specified
       *         element
       * @throws ClassCastException if the specified object cannot be compared
       *         with the elements currently in this set
       * @throws NullPointerException if the specified element is null
       *         and this set uses natural ordering, or its comparator
       *         does not permit null elements
       */
      public boolean add(E e) {
          return m.put(e, PRESENT)==null;
      }
  
      /**
       * Removes the specified element from this set if it is present.
       * More formally, removes an element {@code e} such that
       * <tt>(o==null&nbsp;?&nbsp;e==null&nbsp;:&nbsp;o.equals(e))</tt>,
       * if this set contains such an element.  Returns {@code true} if
       * this set contained the element (or equivalently, if this set
       * changed as a result of the call).  (This set will not contain the
       * element once the call returns.)
       *
       * @param o object to be removed from this set, if present
       * @return {@code true} if this set contained the specified element
       * @throws ClassCastException if the specified object cannot be compared
       *         with the elements currently in this set
       * @throws NullPointerException if the specified element is null
       *         and this set uses natural ordering, or its comparator
       *         does not permit null elements
       */
      public boolean remove(Object o) {
          return m.remove(o)==PRESENT;
      }
  
      /**
       * Removes all of the elements from this set.
       * The set will be empty after this call returns.
       */
      public void clear() {
          m.clear();
      }
  
      /**
       * Adds all of the elements in the specified collection to this set.
       *
       * @param c collection containing elements to be added to this set
       * @return {@code true} if this set changed as a result of the call
       * @throws ClassCastException if the elements provided cannot be compared
       *         with the elements currently in the set
       * @throws NullPointerException if the specified collection is null or
       *         if any element is null and this set uses natural ordering, or
       *         its comparator does not permit null elements
       */
      public  boolean addAll(Collection<? extends E> c) {
          // Use linear-time version if applicable
          if (m.size()==0 && c.size() > 0 &&
              c instanceof SortedSet &&
              m instanceof TreeMap) {
              SortedSet<? extends E> set = (SortedSet<? extends E>) c;
              TreeMap<E,Object> map = (TreeMap<E, Object>) m;
              Comparator<?> cc = set.comparator();
              Comparator<? super E> mc = map.comparator();
              if (cc==mc || (cc != null && cc.equals(mc))) {
                  map.addAllForTreeSet(set, PRESENT);
                  return true;
              }
          }
          return super.addAll(c);
      }
  
      /**
       * @throws ClassCastException {@inheritDoc}
       * @throws NullPointerException if {@code fromElement} or {@code toElement}
       *         is null and this set uses natural ordering, or its comparator
       *         does not permit null elements
       * @throws IllegalArgumentException {@inheritDoc}
       * @since 1.6
       */
      public NavigableSet<E> subSet(E fromElement, boolean fromInclusive,
                                    E toElement,   boolean toInclusive) {
          return new TreeSet<>(m.subMap(fromElement, fromInclusive,
                                         toElement,   toInclusive));
      }
  
      /**
       * @throws ClassCastException {@inheritDoc}
       * @throws NullPointerException if {@code toElement} is null and
       *         this set uses natural ordering, or its comparator does
       *         not permit null elements
       * @throws IllegalArgumentException {@inheritDoc}
       * @since 1.6
       */
      public NavigableSet<E> headSet(E toElement, boolean inclusive) {
          return new TreeSet<>(m.headMap(toElement, inclusive));
      }
  
      /**
       * @throws ClassCastException {@inheritDoc}
       * @throws NullPointerException if {@code fromElement} is null and
       *         this set uses natural ordering, or its comparator does
       *         not permit null elements
       * @throws IllegalArgumentException {@inheritDoc}
       * @since 1.6
       */
      public NavigableSet<E> tailSet(E fromElement, boolean inclusive) {
          return new TreeSet<>(m.tailMap(fromElement, inclusive));
      }
  
      /**
       * @throws ClassCastException {@inheritDoc}
       * @throws NullPointerException if {@code fromElement} or
       *         {@code toElement} is null and this set uses natural ordering,
       *         or its comparator does not permit null elements
       * @throws IllegalArgumentException {@inheritDoc}
       */
      public SortedSet<E> subSet(E fromElement, E toElement) {
          return subSet(fromElement, true, toElement, false);
      }
  
      /**
       * @throws ClassCastException {@inheritDoc}
       * @throws NullPointerException if {@code toElement} is null
       *         and this set uses natural ordering, or its comparator does
       *         not permit null elements
       * @throws IllegalArgumentException {@inheritDoc}
       */
      public SortedSet<E> headSet(E toElement) {
          return headSet(toElement, false);
      }
  
      /**
       * @throws ClassCastException {@inheritDoc}
       * @throws NullPointerException if {@code fromElement} is null
       *         and this set uses natural ordering, or its comparator does
       *         not permit null elements
       * @throws IllegalArgumentException {@inheritDoc}
       */
      public SortedSet<E> tailSet(E fromElement) {
          return tailSet(fromElement, true);
      }
  
      public Comparator<? super E> comparator() {
          return m.comparator();
      }
  
      /**
       * @throws NoSuchElementException {@inheritDoc}
       */
      public E first() {
          return m.firstKey();
      }
  
      /**
       * @throws NoSuchElementException {@inheritDoc}
       */
      public E last() {
          return m.lastKey();
      }
  
      // NavigableSet API methods
  
      /**
       * @throws ClassCastException {@inheritDoc}
       * @throws NullPointerException if the specified element is null
       *         and this set uses natural ordering, or its comparator
       *         does not permit null elements
       * @since 1.6
       */
      public E lower(E e) {
          return m.lowerKey(e);
      }
  
      /**
       * @throws ClassCastException {@inheritDoc}
       * @throws NullPointerException if the specified element is null
       *         and this set uses natural ordering, or its comparator
       *         does not permit null elements
       * @since 1.6
       */
      public E floor(E e) {
          return m.floorKey(e);
      }
  
      /**
       * @throws ClassCastException {@inheritDoc}
       * @throws NullPointerException if the specified element is null
       *         and this set uses natural ordering, or its comparator
       *         does not permit null elements
       * @since 1.6
       */
      public E ceiling(E e) {
          return m.ceilingKey(e);
      }
  
      /**
       * @throws ClassCastException {@inheritDoc}
       * @throws NullPointerException if the specified element is null
       *         and this set uses natural ordering, or its comparator
       *         does not permit null elements
       * @since 1.6
       */
      public E higher(E e) {
          return m.higherKey(e);
      }
  
      /**
       * @since 1.6
       */
      public E pollFirst() {
          Map.Entry<E,?> e = m.pollFirstEntry();
          return (e == null) ? null : e.getKey();
      }
  
      /**
       * @since 1.6
       */
      public E pollLast() {
          Map.Entry<E,?> e = m.pollLastEntry();
          return (e == null) ? null : e.getKey();
      }
  
      /**
       * Returns a shallow copy of this {@code TreeSet} instance. (The elements
       * themselves are not cloned.)
       *
       * @return a shallow copy of this set
       */
      @SuppressWarnings("unchecked")
      public Object clone() {
          TreeSet<E> clone;
          try {
              clone = (TreeSet<E>) super.clone();
          } catch (CloneNotSupportedException e) {
              throw new InternalError(e);
          }
  
          clone.m = new TreeMap<>(m);
          return clone;
      }
  
      /**
       * Save the state of the {@code TreeSet} instance to a stream (that is,
       * serialize it).
       *
       * @serialData Emits the comparator used to order this set, or
       *             {@code null} if it obeys its elements' natural ordering
       *             (Object), followed by the size of the set (the number of
       *             elements it contains) (int), followed by all of its
       *             elements (each an Object) in order (as determined by the
       *             set's Comparator, or by the elements' natural ordering if
       *             the set has no Comparator).
       */
      private void writeObject(java.io.ObjectOutputStream s)
          throws java.io.IOException {
          // Write out any hidden stuff
          s.defaultWriteObject();
  
          // Write out Comparator
          s.writeObject(m.comparator());
  
          // Write out size
          s.writeInt(m.size());
  
          // Write out all elements in the proper order.
          for (E e : m.keySet())
              s.writeObject(e);
      }
  
      /**
       * Reconstitute the {@code TreeSet} instance from a stream (that is,
       * deserialize it).
       */
      private void readObject(java.io.ObjectInputStream s)
          throws java.io.IOException, ClassNotFoundException {
          // Read in any hidden stuff
          s.defaultReadObject();
  
          // Read in Comparator
          @SuppressWarnings("unchecked")
              Comparator<? super E> c = (Comparator<? super E>) s.readObject();
  
          // Create backing TreeMap
          TreeMap<E,Object> tm = new TreeMap<>(c);
          m = tm;
  
          // Read in size
          int size = s.readInt();
  
          tm.readTreeSet(size, s, PRESENT);
      }
  
      /**
       * Creates a <em><a href="Spliterator.html#binding">late-binding</a></em>
       * and <em>fail-fast</em> {@link Spliterator} over the elements in this
       * set.
       *
       * <p>The {@code Spliterator} reports {@link Spliterator#SIZED},
       * {@link Spliterator#DISTINCT}, {@link Spliterator#SORTED}, and
       * {@link Spliterator#ORDERED}.  Overriding implementations should document
       * the reporting of additional characteristic values.
       *
       * <p>The spliterator's comparator (see
       * {@link Spliterator#getComparator()}) is {@code null} if
       * the tree set's comparator (see {@link #comparator()}) is {@code null}.
       * Otherwise, the spliterator's comparator is the same as or imposes the
       * same total ordering as the tree set's comparator.
       *
       * @return a {@code Spliterator} over the elements in this set
       * @since 1.8
       */
      public Spliterator<E> spliterator() {
          return TreeMap.keySpliteratorFor(m);
      }
  
      private static final long serialVersionUID = -2479143000061671589L;
  }
  