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Java Source Code / Java Documentation  » 6.0 JDK Core » Collections Jar Zip Logging regex » java.util 
Source Cross Referenced  Class Diagram Java Document (Java Doc) 


        /*
         * Copyright 1997-2007 Sun Microsystems, Inc.  All Rights Reserved.
         * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
         *
         * 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.  Sun designates this
         * particular file as subject to the "Classpath" exception as provided
         * by Sun 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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
         * CA 95054 USA or visit www.sun.com if you need additional information or
         * have any questions.
         */

        package java.util;

        /**
         * A Red-Black tree based {@link NavigableMap} implementation.
         * The map is sorted according to the {@linkplain Comparable natural
         * ordering} of its keys, or by a {@link Comparator} provided at map
         * creation time, depending on which constructor is used.
         *
         * <p>This implementation provides guaranteed log(n) time cost for the
         * <tt>containsKey</tt>, <tt>get</tt>, <tt>put</tt> and <tt>remove</tt>
         * operations.  Algorithms are adaptations of those in Cormen, Leiserson, and
         * Rivest's <I>Introduction to Algorithms</I>.
         *
         * <p>Note that the ordering maintained by a sorted map (whether or not an
         * explicit comparator is provided) must be <i>consistent with equals</i> if
         * this sorted map is to correctly implement the <tt>Map</tt> interface.  (See
         * <tt>Comparable</tt> or <tt>Comparator</tt> for a precise definition of
         * <i>consistent with equals</i>.)  This is so because the <tt>Map</tt>
         * interface is defined in terms of the equals operation, but a map performs
         * all key comparisons using its <tt>compareTo</tt> (or <tt>compare</tt>)
         * method, so two keys that are deemed equal by this method are, from the
         * standpoint of the sorted map, equal.  The behavior of a sorted map
         * <i>is</i> well-defined even if its ordering is inconsistent with equals; it
         * just fails to obey the general contract of the <tt>Map</tt> interface.
         *
         * <p><strong>Note that this implementation is not synchronized.</strong>
         * If multiple threads access a map concurrently, and at least one of the
         * threads modifies the map structurally, it <i>must</i> be synchronized
         * externally.  (A structural modification is any operation that adds or
         * deletes one or more mappings; merely changing the value associated
         * with an existing key is not a structural modification.)  This is
         * typically accomplished by synchronizing on some object that naturally
         * encapsulates the map.
         * If no such object exists, the map should be "wrapped" using the
         * {@link Collections#synchronizedSortedMap Collections.synchronizedSortedMap}
         * method.  This is best done at creation time, to prevent accidental
         * unsynchronized access to the map: <pre>
         *   SortedMap m = Collections.synchronizedSortedMap(new TreeMap(...));</pre>
         *
         * <p>The iterators returned by the <tt>iterator</tt> method of the collections
         * returned by all of this class's "collection view methods" are
         * <i>fail-fast</i>: if the map is structurally modified at any time after the
         * iterator is created, in any way except through the iterator's own
         * <tt>remove</tt> 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 <tt>ConcurrentModificationException</tt> 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>All <tt>Map.Entry</tt> pairs returned by methods in this class
         * and its views represent snapshots of mappings at the time they were
         * produced. They do <em>not</em> support the <tt>Entry.setValue</tt>
         * method. (Note however that it is possible to change mappings in the
         * associated map using <tt>put</tt>.)
         *
         * <p>This class is a member of the
         * <a href="{@docRoot}/../technotes/guides/collections/index.html">
         * Java Collections Framework</a>.
         *
         * @param <K> the type of keys maintained by this map
         * @param <V> the type of mapped values
         *
         * @author  Josh Bloch and Doug Lea
         * @version 1.73, 05/10/06
         * @see Map
         * @see HashMap
         * @see Hashtable
         * @see Comparable
         * @see Comparator
         * @see Collection
         * @since 1.2
         */

        public class TreeMap<K, V> extends AbstractMap<K, V> implements 
                NavigableMap<K, V>, Cloneable, java.io.Serializable {
            /**
             * The comparator used to maintain order in this tree map, or
             * null if it uses the natural ordering of its keys.
             *
             * @serial
             */
            private final Comparator<? super  K> comparator;

            private transient Entry<K, V> root = null;

            /**
             * The number of entries in the tree
             */
            private transient int size = 0;

            /**
             * The number of structural modifications to the tree.
             */
            private transient int modCount = 0;

            /**
             * Constructs a new, empty tree map, using the natural ordering of its
             * keys.  All keys inserted into the map must implement the {@link
             * Comparable} interface.  Furthermore, all such keys must be
             * <i>mutually comparable</i>: <tt>k1.compareTo(k2)</tt> must not throw
             * a <tt>ClassCastException</tt> for any keys <tt>k1</tt> and
             * <tt>k2</tt> in the map.  If the user attempts to put a key into the
             * map that violates this constraint (for example, the user attempts to
             * put a string key into a map whose keys are integers), the
             * <tt>put(Object key, Object value)</tt> call will throw a
             * <tt>ClassCastException</tt>.
             */
            public TreeMap() {
                comparator = null;
            }

            /**
             * Constructs a new, empty tree map, ordered according to the given
             * comparator.  All keys inserted into the map must be <i>mutually
             * comparable</i> by the given comparator: <tt>comparator.compare(k1,
             * k2)</tt> must not throw a <tt>ClassCastException</tt> for any keys
             * <tt>k1</tt> and <tt>k2</tt> in the map.  If the user attempts to put
             * a key into the map that violates this constraint, the <tt>put(Object
             * key, Object value)</tt> call will throw a
             * <tt>ClassCastException</tt>.
             *
             * @param comparator the comparator that will be used to order this map.
             *        If <tt>null</tt>, the {@linkplain Comparable natural
             *        ordering} of the keys will be used.
             */
            public TreeMap(Comparator<? super  K> comparator) {
                this .comparator = comparator;
            }

            /**
             * Constructs a new tree map containing the same mappings as the given
             * map, ordered according to the <i>natural ordering</i> of its keys.
             * All keys inserted into the new map must implement the {@link
             * Comparable} interface.  Furthermore, all such keys must be
             * <i>mutually comparable</i>: <tt>k1.compareTo(k2)</tt> must not throw
             * a <tt>ClassCastException</tt> for any keys <tt>k1</tt> and
             * <tt>k2</tt> in the map.  This method runs in n*log(n) time.
             *
             * @param  m the map whose mappings are to be placed in this map
             * @throws ClassCastException if the keys in m are not {@link Comparable},
             *         or are not mutually comparable
             * @throws NullPointerException if the specified map is null
             */
            public TreeMap(Map<? extends K, ? extends V> m) {
                comparator = null;
                putAll(m);
            }

            /**
             * Constructs a new tree map containing the same mappings and
             * using the same ordering as the specified sorted map.  This
             * method runs in linear time.
             *
             * @param  m the sorted map whose mappings are to be placed in this map,
             *         and whose comparator is to be used to sort this map
             * @throws NullPointerException if the specified map is null
             */
            public TreeMap(SortedMap<K, ? extends V> m) {
                comparator = m.comparator();
                try {
                    buildFromSorted(m.size(), m.entrySet().iterator(), null,
                            null);
                } catch (java.io.IOException cannotHappen) {
                } catch (ClassNotFoundException cannotHappen) {
                }
            }

            // Query Operations

            /**
             * Returns the number of key-value mappings in this map.
             *
             * @return the number of key-value mappings in this map
             */
            public int size() {
                return size;
            }

            /**
             * Returns <tt>true</tt> if this map contains a mapping for the specified
             * key.
             *
             * @param key key whose presence in this map is to be tested
             * @return <tt>true</tt> if this map contains a mapping for the
             *         specified key
             * @throws ClassCastException if the specified key cannot be compared
             *         with the keys currently in the map
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             */
            public boolean containsKey(Object key) {
                return getEntry(key) != null;
            }

            /**
             * Returns <tt>true</tt> if this map maps one or more keys to the
             * specified value.  More formally, returns <tt>true</tt> if and only if
             * this map contains at least one mapping to a value <tt>v</tt> such
             * that <tt>(value==null ? v==null : value.equals(v))</tt>.  This
             * operation will probably require time linear in the map size for
             * most implementations.
             *
             * @param value value whose presence in this map is to be tested
             * @return <tt>true</tt> if a mapping to <tt>value</tt> exists;
             *	       <tt>false</tt> otherwise
             * @since 1.2
             */
            public boolean containsValue(Object value) {
                for (Entry<K, V> e = getFirstEntry(); e != null; e = successor(e))
                    if (valEquals(value, e.value))
                        return true;
                return false;
            }

            /**
             * Returns the value to which the specified key is mapped,
             * or {@code null} if this map contains no mapping for the key.
             *
             * <p>More formally, if this map contains a mapping from a key
             * {@code k} to a value {@code v} such that {@code key} compares
             * equal to {@code k} according to the map's ordering, then this
             * method returns {@code v}; otherwise it returns {@code null}.
             * (There can be at most one such mapping.)
             *
             * <p>A return value of {@code null} does not <i>necessarily</i>
             * indicate that the map contains no mapping for the key; it's also
             * possible that the map explicitly maps the key to {@code null}.
             * The {@link #containsKey containsKey} operation may be used to
             * distinguish these two cases.
             *
             * @throws ClassCastException if the specified key cannot be compared
             *         with the keys currently in the map
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             */
            public V get(Object key) {
                Entry<K, V> p = getEntry(key);
                return (p == null ? null : p.value);
            }

            public Comparator<? super  K> comparator() {
                return comparator;
            }

            /**
             * @throws NoSuchElementException {@inheritDoc}
             */
            public K firstKey() {
                return key(getFirstEntry());
            }

            /**
             * @throws NoSuchElementException {@inheritDoc}
             */
            public K lastKey() {
                return key(getLastEntry());
            }

            /**
             * Copies all of the mappings from the specified map to this map.
             * These mappings replace any mappings that this map had for any
             * of the keys currently in the specified map.
             *
             * @param  map mappings to be stored in this map
             * @throws ClassCastException if the class of a key or value in
             *         the specified map prevents it from being stored in this map
             * @throws NullPointerException if the specified map is null or
             *         the specified map contains a null key and this map does not
             *         permit null keys
             */
            public void putAll(Map<? extends K, ? extends V> map) {
                int mapSize = map.size();
                if (size == 0 && mapSize != 0 && map instanceof  SortedMap) {
                    Comparator c = ((SortedMap) map).comparator();
                    if (c == comparator || (c != null && c.equals(comparator))) {
                        ++modCount;
                        try {
                            buildFromSorted(mapSize, map.entrySet().iterator(),
                                    null, null);
                        } catch (java.io.IOException cannotHappen) {
                        } catch (ClassNotFoundException cannotHappen) {
                        }
                        return;
                    }
                }
                super .putAll(map);
            }

            /**
             * Returns this map's entry for the given key, or <tt>null</tt> if the map
             * does not contain an entry for the key.
             *
             * @return this map's entry for the given key, or <tt>null</tt> if the map
             *         does not contain an entry for the key
             * @throws ClassCastException if the specified key cannot be compared
             *         with the keys currently in the map
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             */
            final Entry<K, V> getEntry(Object key) {
                // Offload comparator-based version for sake of performance
                if (comparator != null)
                    return getEntryUsingComparator(key);
                if (key == null)
                    throw new NullPointerException();
                Comparable<? super  K> k = (Comparable<? super  K>) key;
                Entry<K, V> p = root;
                while (p != null) {
                    int cmp = k.compareTo(p.key);
                    if (cmp < 0)
                        p = p.left;
                    else if (cmp > 0)
                        p = p.right;
                    else
                        return p;
                }
                return null;
            }

            /**
             * Version of getEntry using comparator. Split off from getEntry
             * for performance. (This is not worth doing for most methods,
             * that are less dependent on comparator performance, but is
             * worthwhile here.)
             */
            final Entry<K, V> getEntryUsingComparator(Object key) {
                K k = (K) key;
                Comparator<? super  K> cpr = comparator;
                if (cpr != null) {
                    Entry<K, V> p = root;
                    while (p != null) {
                        int cmp = cpr.compare(k, p.key);
                        if (cmp < 0)
                            p = p.left;
                        else if (cmp > 0)
                            p = p.right;
                        else
                            return p;
                    }
                }
                return null;
            }

            /**
             * Gets the entry corresponding to the specified key; if no such entry
             * exists, returns the entry for the least key greater than the specified
             * key; if no such entry exists (i.e., the greatest key in the Tree is less
             * than the specified key), returns <tt>null</tt>.
             */
            final Entry<K, V> getCeilingEntry(K key) {
                Entry<K, V> p = root;
                while (p != null) {
                    int cmp = compare(key, p.key);
                    if (cmp < 0) {
                        if (p.left != null)
                            p = p.left;
                        else
                            return p;
                    } else if (cmp > 0) {
                        if (p.right != null) {
                            p = p.right;
                        } else {
                            Entry<K, V> parent = p.parent;
                            Entry<K, V> ch = p;
                            while (parent != null && ch == parent.right) {
                                ch = parent;
                                parent = parent.parent;
                            }
                            return parent;
                        }
                    } else
                        return p;
                }
                return null;
            }

            /**
             * Gets the entry corresponding to the specified key; if no such entry
             * exists, returns the entry for the greatest key less than the specified
             * key; if no such entry exists, returns <tt>null</tt>.
             */
            final Entry<K, V> getFloorEntry(K key) {
                Entry<K, V> p = root;
                while (p != null) {
                    int cmp = compare(key, p.key);
                    if (cmp > 0) {
                        if (p.right != null)
                            p = p.right;
                        else
                            return p;
                    } else if (cmp < 0) {
                        if (p.left != null) {
                            p = p.left;
                        } else {
                            Entry<K, V> parent = p.parent;
                            Entry<K, V> ch = p;
                            while (parent != null && ch == parent.left) {
                                ch = parent;
                                parent = parent.parent;
                            }
                            return parent;
                        }
                    } else
                        return p;

                }
                return null;
            }

            /**
             * Gets the entry for the least key greater than the specified
             * key; if no such entry exists, returns the entry for the least
             * key greater than the specified key; if no such entry exists
             * returns <tt>null</tt>.
             */
            final Entry<K, V> getHigherEntry(K key) {
                Entry<K, V> p = root;
                while (p != null) {
                    int cmp = compare(key, p.key);
                    if (cmp < 0) {
                        if (p.left != null)
                            p = p.left;
                        else
                            return p;
                    } else {
                        if (p.right != null) {
                            p = p.right;
                        } else {
                            Entry<K, V> parent = p.parent;
                            Entry<K, V> ch = p;
                            while (parent != null && ch == parent.right) {
                                ch = parent;
                                parent = parent.parent;
                            }
                            return parent;
                        }
                    }
                }
                return null;
            }

            /**
             * Returns the entry for the greatest key less than the specified key; if
             * no such entry exists (i.e., the least key in the Tree is greater than
             * the specified key), returns <tt>null</tt>.
             */
            final Entry<K, V> getLowerEntry(K key) {
                Entry<K, V> p = root;
                while (p != null) {
                    int cmp = compare(key, p.key);
                    if (cmp > 0) {
                        if (p.right != null)
                            p = p.right;
                        else
                            return p;
                    } else {
                        if (p.left != null) {
                            p = p.left;
                        } else {
                            Entry<K, V> parent = p.parent;
                            Entry<K, V> ch = p;
                            while (parent != null && ch == parent.left) {
                                ch = parent;
                                parent = parent.parent;
                            }
                            return parent;
                        }
                    }
                }
                return null;
            }

            /**
             * Associates the specified value with the specified key in this map.
             * If the map previously contained a mapping for the key, the old
             * value is replaced.
             *
             * @param key key with which the specified value is to be associated
             * @param value value to be associated with the specified key
             *
             * @return the previous value associated with <tt>key</tt>, or
             *         <tt>null</tt> if there was no mapping for <tt>key</tt>.
             *         (A <tt>null</tt> return can also indicate that the map
             *         previously associated <tt>null</tt> with <tt>key</tt>.)
             * @throws ClassCastException if the specified key cannot be compared
             *         with the keys currently in the map
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             */
            public V put(K key, V value) {
                Entry<K, V> t = root;
                if (t == null) {
                    // TBD:
                    // 5045147: (coll) Adding null to an empty TreeSet should
                    // throw NullPointerException
                    //
                    // compare(key, key); // type check
                    root = new Entry<K, V>(key, value, null);
                    size = 1;
                    modCount++;
                    return null;
                }
                int cmp;
                Entry<K, V> parent;
                // split comparator and comparable paths
                Comparator<? super  K> cpr = comparator;
                if (cpr != null) {
                    do {
                        parent = t;
                        cmp = cpr.compare(key, t.key);
                        if (cmp < 0)
                            t = t.left;
                        else if (cmp > 0)
                            t = t.right;
                        else
                            return t.setValue(value);
                    } while (t != null);
                } else {
                    if (key == null)
                        throw new NullPointerException();
                    Comparable<? super  K> k = (Comparable<? super  K>) key;
                    do {
                        parent = t;
                        cmp = k.compareTo(t.key);
                        if (cmp < 0)
                            t = t.left;
                        else if (cmp > 0)
                            t = t.right;
                        else
                            return t.setValue(value);
                    } while (t != null);
                }
                Entry<K, V> e = new Entry<K, V>(key, value, parent);
                if (cmp < 0)
                    parent.left = e;
                else
                    parent.right = e;
                fixAfterInsertion(e);
                size++;
                modCount++;
                return null;
            }

            /**
             * Removes the mapping for this key from this TreeMap if present.
             *
             * @param  key key for which mapping should be removed
             * @return the previous value associated with <tt>key</tt>, or
             *         <tt>null</tt> if there was no mapping for <tt>key</tt>.
             *         (A <tt>null</tt> return can also indicate that the map
             *         previously associated <tt>null</tt> with <tt>key</tt>.)
             * @throws ClassCastException if the specified key cannot be compared
             *         with the keys currently in the map
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             */
            public V remove(Object key) {
                Entry<K, V> p = getEntry(key);
                if (p == null)
                    return null;

                V oldValue = p.value;
                deleteEntry(p);
                return oldValue;
            }

            /**
             * Removes all of the mappings from this map.
             * The map will be empty after this call returns.
             */
            public void clear() {
                modCount++;
                size = 0;
                root = null;
            }

            /**
             * Returns a shallow copy of this <tt>TreeMap</tt> instance. (The keys and
             * values themselves are not cloned.)
             *
             * @return a shallow copy of this map
             */
            public Object clone() {
                TreeMap<K, V> clone = null;
                try {
                    clone = (TreeMap<K, V>) super .clone();
                } catch (CloneNotSupportedException e) {
                    throw new InternalError();
                }

                // Put clone into "virgin" state (except for comparator)
                clone.root = null;
                clone.size = 0;
                clone.modCount = 0;
                clone.entrySet = null;
                clone.navigableKeySet = null;
                clone.descendingMap = null;

                // Initialize clone with our mappings
                try {
                    clone.buildFromSorted(size, entrySet().iterator(), null,
                            null);
                } catch (java.io.IOException cannotHappen) {
                } catch (ClassNotFoundException cannotHappen) {
                }

                return clone;
            }

            // NavigableMap API methods

            /**
             * @since 1.6
             */
            public Map.Entry<K, V> firstEntry() {
                return exportEntry(getFirstEntry());
            }

            /**
             * @since 1.6
             */
            public Map.Entry<K, V> lastEntry() {
                return exportEntry(getLastEntry());
            }

            /**
             * @since 1.6
             */
            public Map.Entry<K, V> pollFirstEntry() {
                Entry<K, V> p = getFirstEntry();
                Map.Entry<K, V> result = exportEntry(p);
                if (p != null)
                    deleteEntry(p);
                return result;
            }

            /**
             * @since 1.6
             */
            public Map.Entry<K, V> pollLastEntry() {
                Entry<K, V> p = getLastEntry();
                Map.Entry<K, V> result = exportEntry(p);
                if (p != null)
                    deleteEntry(p);
                return result;
            }

            /**
             * @throws ClassCastException {@inheritDoc}
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @since 1.6
             */
            public Map.Entry<K, V> lowerEntry(K key) {
                return exportEntry(getLowerEntry(key));
            }

            /**
             * @throws ClassCastException {@inheritDoc}
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @since 1.6
             */
            public K lowerKey(K key) {
                return keyOrNull(getLowerEntry(key));
            }

            /**
             * @throws ClassCastException {@inheritDoc}
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @since 1.6
             */
            public Map.Entry<K, V> floorEntry(K key) {
                return exportEntry(getFloorEntry(key));
            }

            /**
             * @throws ClassCastException {@inheritDoc}
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @since 1.6
             */
            public K floorKey(K key) {
                return keyOrNull(getFloorEntry(key));
            }

            /**
             * @throws ClassCastException {@inheritDoc}
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @since 1.6
             */
            public Map.Entry<K, V> ceilingEntry(K key) {
                return exportEntry(getCeilingEntry(key));
            }

            /**
             * @throws ClassCastException {@inheritDoc}
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @since 1.6
             */
            public K ceilingKey(K key) {
                return keyOrNull(getCeilingEntry(key));
            }

            /**
             * @throws ClassCastException {@inheritDoc}
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @since 1.6
             */
            public Map.Entry<K, V> higherEntry(K key) {
                return exportEntry(getHigherEntry(key));
            }

            /**
             * @throws ClassCastException {@inheritDoc}
             * @throws NullPointerException if the specified key is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @since 1.6
             */
            public K higherKey(K key) {
                return keyOrNull(getHigherEntry(key));
            }

            // Views

            /**
             * Fields initialized to contain an instance of the entry set view
             * the first time this view is requested.  Views are stateless, so
             * there's no reason to create more than one.
             */
            private transient EntrySet entrySet = null;
            private transient KeySet<K> navigableKeySet = null;
            private transient NavigableMap<K, V> descendingMap = null;

            /**
             * Returns a {@link Set} view of the keys contained in this map.
             * The set's iterator returns the keys in ascending order.
             * The set is backed by the map, so changes to the map are
             * reflected in the set, and vice-versa.  If the map is modified
             * while an iteration over the set is in progress (except through
             * the iterator's own <tt>remove</tt> operation), the results of
             * the iteration are undefined.  The set supports element removal,
             * which removes the corresponding mapping from the map, via the
             * <tt>Iterator.remove</tt>, <tt>Set.remove</tt>,
             * <tt>removeAll</tt>, <tt>retainAll</tt>, and <tt>clear</tt>
             * operations.  It does not support the <tt>add</tt> or <tt>addAll</tt>
             * operations.
             */
            public Set<K> keySet() {
                return navigableKeySet();
            }

            /**
             * @since 1.6
             */
            public NavigableSet<K> navigableKeySet() {
                KeySet<K> nks = navigableKeySet;
                return (nks != null) ? nks
                        : (navigableKeySet = new KeySet(this ));
            }

            /**
             * @since 1.6
             */
            public NavigableSet<K> descendingKeySet() {
                return descendingMap().navigableKeySet();
            }

            /**
             * Returns a {@link Collection} view of the values contained in this map.
             * The collection's iterator returns the values in ascending order
             * of the corresponding keys.
             * The collection is backed by the map, so changes to the map are
             * reflected in the collection, and vice-versa.  If the map is
             * modified while an iteration over the collection is in progress
             * (except through the iterator's own <tt>remove</tt> operation),
             * the results of the iteration are undefined.  The collection
             * supports element removal, which removes the corresponding
             * mapping from the map, via the <tt>Iterator.remove</tt>,
             * <tt>Collection.remove</tt>, <tt>removeAll</tt>,
             * <tt>retainAll</tt> and <tt>clear</tt> operations.  It does not
             * support the <tt>add</tt> or <tt>addAll</tt> operations.
             */
            public Collection<V> values() {
                Collection<V> vs = values;
                return (vs != null) ? vs : (values = new Values());
            }

            /**
             * Returns a {@link Set} view of the mappings contained in this map.
             * The set's iterator returns the entries in ascending key order.
             * The set is backed by the map, so changes to the map are
             * reflected in the set, and vice-versa.  If the map is modified
             * while an iteration over the set is in progress (except through
             * the iterator's own <tt>remove</tt> operation, or through the
             * <tt>setValue</tt> operation on a map entry returned by the
             * iterator) the results of the iteration are undefined.  The set
             * supports element removal, which removes the corresponding
             * mapping from the map, via the <tt>Iterator.remove</tt>,
             * <tt>Set.remove</tt>, <tt>removeAll</tt>, <tt>retainAll</tt> and
             * <tt>clear</tt> operations.  It does not support the
             * <tt>add</tt> or <tt>addAll</tt> operations.
             */
            public Set<Map.Entry<K, V>> entrySet() {
                EntrySet es = entrySet;
                return (es != null) ? es : (entrySet = new EntrySet());
            }

            /**
             * @since 1.6
             */
            public NavigableMap<K, V> descendingMap() {
                NavigableMap<K, V> km = descendingMap;
                return (km != null) ? km
                        : (descendingMap = new DescendingSubMap(this , true,
                                null, true, true, null, true));
            }

            /**
             * @throws ClassCastException       {@inheritDoc}
             * @throws NullPointerException if <tt>fromKey</tt> or <tt>toKey</tt> is
             *         null and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @throws IllegalArgumentException {@inheritDoc}
             * @since 1.6
             */
            public NavigableMap<K, V> subMap(K fromKey, boolean fromInclusive,
                    K toKey, boolean toInclusive) {
                return new AscendingSubMap(this , false, fromKey, fromInclusive,
                        false, toKey, toInclusive);
            }

            /**
             * @throws ClassCastException       {@inheritDoc}
             * @throws NullPointerException if <tt>toKey</tt> is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @throws IllegalArgumentException {@inheritDoc}
             * @since 1.6
             */
            public NavigableMap<K, V> headMap(K toKey, boolean inclusive) {
                return new AscendingSubMap(this , true, null, true, false,
                        toKey, inclusive);
            }

            /**
             * @throws ClassCastException       {@inheritDoc}
             * @throws NullPointerException if <tt>fromKey</tt> is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @throws IllegalArgumentException {@inheritDoc}
             * @since 1.6
             */
            public NavigableMap<K, V> tailMap(K fromKey, boolean inclusive) {
                return new AscendingSubMap(this , false, fromKey, inclusive,
                        true, null, true);
            }

            /**
             * @throws ClassCastException       {@inheritDoc}
             * @throws NullPointerException if <tt>fromKey</tt> or <tt>toKey</tt> is
             *         null and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @throws IllegalArgumentException {@inheritDoc}
             */
            public SortedMap<K, V> subMap(K fromKey, K toKey) {
                return subMap(fromKey, true, toKey, false);
            }

            /**
             * @throws ClassCastException       {@inheritDoc}
             * @throws NullPointerException if <tt>toKey</tt> is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @throws IllegalArgumentException {@inheritDoc}
             */
            public SortedMap<K, V> headMap(K toKey) {
                return headMap(toKey, false);
            }

            /**
             * @throws ClassCastException       {@inheritDoc}
             * @throws NullPointerException if <tt>fromKey</tt> is null
             *         and this map uses natural ordering, or its comparator
             *         does not permit null keys
             * @throws IllegalArgumentException {@inheritDoc}
             */
            public SortedMap<K, V> tailMap(K fromKey) {
                return tailMap(fromKey, true);
            }

            // View class support

            class Values extends AbstractCollection<V> {
                public Iterator<V> iterator() {
                    return new ValueIterator(getFirstEntry());
                }

                public int size() {
                    return TreeMap.this .size();
                }

                public boolean contains(Object o) {
                    return TreeMap.this .containsValue(o);
                }

                public boolean remove(Object o) {
                    for (Entry<K, V> e = getFirstEntry(); e != null; e = successor(e)) {
                        if (valEquals(e.getValue(), o)) {
                            deleteEntry(e);
                            return true;
                        }
                    }
                    return false;
                }

                public void clear() {
                    TreeMap.this .clear();
                }
            }

            class EntrySet extends AbstractSet<Map.Entry<K, V>> {
                public Iterator<Map.Entry<K, V>> iterator() {
                    return new EntryIterator(getFirstEntry());
                }

                public boolean contains(Object o) {
                    if (!(o instanceof  Map.Entry))
                        return false;
                    Map.Entry<K, V> entry = (Map.Entry<K, V>) o;
                    V value = entry.getValue();
                    Entry<K, V> p = getEntry(entry.getKey());
                    return p != null && valEquals(p.getValue(), value);
                }

                public boolean remove(Object o) {
                    if (!(o instanceof  Map.Entry))
                        return false;
                    Map.Entry<K, V> entry = (Map.Entry<K, V>) o;
                    V value = entry.getValue();
                    Entry<K, V> p = getEntry(entry.getKey());
                    if (p != null && valEquals(p.getValue(), value)) {
                        deleteEntry(p);
                        return true;
                    }
                    return false;
                }

                public int size() {
                    return TreeMap.this .size();
                }

                public void clear() {
                    TreeMap.this .clear();
                }
            }

            /*
             * Unlike Values and EntrySet, the KeySet class is static,
             * delegating to a NavigableMap to allow use by SubMaps, which
             * outweighs the ugliness of needing type-tests for the following
             * Iterator methods that are defined appropriately in main versus
             * submap classes.
             */

            Iterator<K> keyIterator() {
                return new KeyIterator(getFirstEntry());
            }

            Iterator<K> descendingKeyIterator() {
                return new DescendingKeyIterator(getFirstEntry());
            }

            static final class KeySet<E> extends AbstractSet<E> implements 
                    NavigableSet<E> {
                private final NavigableMap<E, Object> m;

                KeySet(NavigableMap<E, Object> map) {
                    m = map;
                }

                public Iterator<E> iterator() {
                    if (m instanceof  TreeMap)
                        return ((TreeMap<E, Object>) m).keyIterator();
                    else
                        return (Iterator<E>) (((TreeMap.NavigableSubMap) m)
                                .keyIterator());
                }

                public Iterator<E> descendingIterator() {
                    if (m instanceof  TreeMap)
                        return ((TreeMap<E, Object>) m).descendingKeyIterator();
                    else
                        return (Iterator<E>) (((TreeMap.NavigableSubMap) m)
                                .descendingKeyIterator());
                }

                public int size() {
                    return m.size();
                }

                public boolean isEmpty() {
                    return m.isEmpty();
                }

                public boolean contains(Object o) {
                    return m.containsKey(o);
                }

                public void clear() {
                    m.clear();
                }

                public E lower(E e) {
                    return m.lowerKey(e);
                }

                public E floor(E e) {
                    return m.floorKey(e);
                }

                public E ceiling(E e) {
                    return m.ceilingKey(e);
                }

                public E higher(E e) {
                    return m.higherKey(e);
                }

                public E first() {
                    return m.firstKey();
                }

                public E last() {
                    return m.lastKey();
                }

                public Comparator<? super  E> comparator() {
                    return m.comparator();
                }

                public E pollFirst() {
                    Map.Entry<E, Object> e = m.pollFirstEntry();
                    return e == null ? null : e.getKey();
                }

                public E pollLast() {
                    Map.Entry<E, Object> e = m.pollLastEntry();
                    return e == null ? null : e.getKey();
                }

                public boolean remove(Object o) {
                    int oldSize = size();
                    m.remove(o);
                    return size() != oldSize;
                }

                public NavigableSet<E> subSet(E fromElement,
                        boolean fromInclusive, E toElement, boolean toInclusive) {
                    return new TreeSet<E>(m.subMap(fromElement, fromInclusive,
                            toElement, toInclusive));
                }

                public NavigableSet<E> headSet(E toElement, boolean inclusive) {
                    return new TreeSet<E>(m.headMap(toElement, inclusive));
                }

                public NavigableSet<E> tailSet(E fromElement, boolean inclusive) {
                    return new TreeSet<E>(m.tailMap(fromElement, inclusive));
                }

                public SortedSet<E> subSet(E fromElement, E toElement) {
                    return subSet(fromElement, true, toElement, false);
                }

                public SortedSet<E> headSet(E toElement) {
                    return headSet(toElement, false);
                }

                public SortedSet<E> tailSet(E fromElement) {
                    return tailSet(fromElement, true);
                }

                public NavigableSet<E> descendingSet() {
                    return new TreeSet(m.descendingMap());
                }
            }

            /**
             * Base class for TreeMap Iterators
             */
            abstract class PrivateEntryIterator<T> implements  Iterator<T> {
                Entry<K, V> next;
                Entry<K, V> lastReturned;
                int expectedModCount;

                PrivateEntryIterator(Entry<K, V> first) {
                    expectedModCount = modCount;
                    lastReturned = null;
                    next = first;
                }

                public final boolean hasNext() {
                    return next != null;
                }

                final Entry<K, V> nextEntry() {
                    Entry<K, V> e = next;
                    if (e == null)
                        throw new NoSuchElementException();
                    if (modCount != expectedModCount)
                        throw new ConcurrentModificationException();
                    next = successor(e);
                    lastReturned = e;
                    return e;
                }

                final Entry<K, V> prevEntry() {
                    Entry<K, V> e = next;
                    if (e == null)
                        throw new NoSuchElementException();
                    if (modCount != expectedModCount)
                        throw new ConcurrentModificationException();
                    next = predecessor(e);
                    lastReturned = e;
                    return e;
                }

                public void remove() {
                    if (lastReturned == null)
                        throw new IllegalStateException();
                    if (modCount != expectedModCount)
                        throw new ConcurrentModificationException();
                    // deleted entries are replaced by their successors
                    if (lastReturned.left != null && lastReturned.right != null)
                        next = lastReturned;
                    deleteEntry(lastReturned);
                    expectedModCount = modCount;
                    lastReturned = null;
                }
            }

            final class EntryIterator extends
                    PrivateEntryIterator<Map.Entry<K, V>> {
                EntryIterator(Entry<K, V> first) {
                    super (first);
                }

                public Map.Entry<K, V> next() {
                    return nextEntry();
                }
            }

            final class ValueIterator extends PrivateEntryIterator<V> {
                ValueIterator(Entry<K, V> first) {
                    super (first);
                }

                public V next() {
                    return nextEntry().value;
                }
            }

            final class KeyIterator extends PrivateEntryIterator<K> {
                KeyIterator(Entry<K, V> first) {
                    super (first);
                }

                public K next() {
                    return nextEntry().key;
                }
            }

            final class DescendingKeyIterator extends PrivateEntryIterator<K> {
                DescendingKeyIterator(Entry<K, V> first) {
                    super (first);
                }

                public K next() {
                    return prevEntry().key;
                }
            }

            // Little utilities

            /**
             * Compares two keys using the correct comparison method for this TreeMap.
             */
            final int compare(Object k1, Object k2) {
                return comparator == null ? ((Comparable<? super  K>) k1)
                        .compareTo((K) k2) : comparator.compare((K) k1, (K) k2);
            }

            /**
             * Test two values for equality.  Differs from o1.equals(o2) only in
             * that it copes with <tt>null</tt> o1 properly.
             */
            final static boolean valEquals(Object o1, Object o2) {
                return (o1 == null ? o2 == null : o1.equals(o2));
            }

            /**
             * Return SimpleImmutableEntry for entry, or null if null
             */
            static <K, V> Map.Entry<K, V> exportEntry(TreeMap.Entry<K, V> e) {
                return e == null ? null
                        : new AbstractMap.SimpleImmutableEntry<K, V>(e);
            }

            /**
             * Return key for entry, or null if null
             */
            static <K, V> K keyOrNull(TreeMap.Entry<K, V> e) {
                return e == null ? null : e.key;
            }

            /**
             * Returns the key corresponding to the specified Entry.
             * @throws NoSuchElementException if the Entry is null
             */
            static <K> K key(Entry<K, ?> e) {
                if (e == null)
                    throw new NoSuchElementException();
                return e.key;
            }

            // SubMaps

            /**
             * Dummy value serving as unmatchable fence key for unbounded
             * SubMapIterators
             */
            private static final Object UNBOUNDED = new Object();

            /**
             * @serial include
             */
            static abstract class NavigableSubMap<K, V> extends
                    AbstractMap<K, V> implements  NavigableMap<K, V>,
                    java.io.Serializable {
                /**
                 * The backing map.
                 */
                final TreeMap<K, V> m;

                /**
                 * Endpoints are represented as triples (fromStart, lo,
                 * loInclusive) and (toEnd, hi, hiInclusive). If fromStart is
                 * true, then the low (absolute) bound is the start of the
                 * backing map, and the other values are ignored. Otherwise,
                 * if loInclusive is true, lo is the inclusive bound, else lo
                 * is the exclusive bound. Similarly for the upper bound.
                 */
                final K lo, hi;
                final boolean fromStart, toEnd;
                final boolean loInclusive, hiInclusive;

                NavigableSubMap(TreeMap<K, V> m, boolean fromStart, K lo,
                        boolean loInclusive, boolean toEnd, K hi,
                        boolean hiInclusive) {
                    if (!fromStart && !toEnd) {
                        if (m.compare(lo, hi) > 0)
                            throw new IllegalArgumentException(
                                    "fromKey > toKey");
                    } else {
                        if (!fromStart) // type check
                            m.compare(lo, lo);
                        if (!toEnd)
                            m.compare(hi, hi);
                    }

                    this .m = m;
                    this .fromStart = fromStart;
                    this .lo = lo;
                    this .loInclusive = loInclusive;
                    this .toEnd = toEnd;
                    this .hi = hi;
                    this .hiInclusive = hiInclusive;
                }

                // internal utilities

                final boolean tooLow(Object key) {
                    if (!fromStart) {
                        int c = m.compare(key, lo);
                        if (c < 0 || (c == 0 && !loInclusive))
                            return true;
                    }
                    return false;
                }

                final boolean tooHigh(Object key) {
                    if (!toEnd) {
                        int c = m.compare(key, hi);
                        if (c > 0 || (c == 0 && !hiInclusive))
                            return true;
                    }
                    return false;
                }

                final boolean inRange(Object key) {
                    return !tooLow(key) && !tooHigh(key);
                }

                final boolean inClosedRange(Object key) {
                    return (fromStart || m.compare(key, lo) >= 0)
                            && (toEnd || m.compare(hi, key) >= 0);
                }

                final boolean inRange(Object key, boolean inclusive) {
                    return inclusive ? inRange(key) : inClosedRange(key);
                }

                /*
                 * Absolute versions of relation operations.
                 * Subclasses map to these using like-named "sub"
                 * versions that invert senses for descending maps
                 */

                final TreeMap.Entry<K, V> absLowest() {
                    TreeMap.Entry<K, V> e = (fromStart ? m.getFirstEntry()
                            : (loInclusive ? m.getCeilingEntry(lo) : m
                                    .getHigherEntry(lo)));
                    return (e == null || tooHigh(e.key)) ? null : e;
                }

                final TreeMap.Entry<K, V> absHighest() {
                    TreeMap.Entry<K, V> e = (toEnd ? m.getLastEntry()
                            : (hiInclusive ? m.getFloorEntry(hi) : m
                                    .getLowerEntry(hi)));
                    return (e == null || tooLow(e.key)) ? null : e;
                }

                final TreeMap.Entry<K, V> absCeiling(K key) {
                    if (tooLow(key))
                        return absLowest();
                    TreeMap.Entry<K, V> e = m.getCeilingEntry(key);
                    return (e == null || tooHigh(e.key)) ? null : e;
                }

                final TreeMap.Entry<K, V> absHigher(K key) {
                    if (tooLow(key))
                        return absLowest();
                    TreeMap.Entry<K, V> e = m.getHigherEntry(key);
                    return (e == null || tooHigh(e.key)) ? null : e;
                }

                final TreeMap.Entry<K, V> absFloor(K key) {
                    if (tooHigh(key))
                        return absHighest();
                    TreeMap.Entry<K, V> e = m.getFloorEntry(key);
                    return (e == null || tooLow(e.key)) ? null : e;
                }

                final TreeMap.Entry<K, V> absLower(K key) {
                    if (tooHigh(key))
                        return absHighest();
                    TreeMap.Entry<K, V> e = m.getLowerEntry(key);
                    return (e == null || tooLow(e.key)) ? null : e;
                }

                /** Returns the absolute high fence for ascending traversal */
                final TreeMap.Entry<K, V> absHighFence() {
                    return (toEnd ? null : (hiInclusive ? m.getHigherEntry(hi)
                            : m.getCeilingEntry(hi)));
                }

                /** Return the absolute low fence for descending traversal  */
                final TreeMap.Entry<K, V> absLowFence() {
                    return (fromStart ? null : (loInclusive ? m
                            .getLowerEntry(lo) : m.getFloorEntry(lo)));
                }

                // Abstract methods defined in ascending vs descending classes
                // These relay to the appropriate absolute versions

                abstract TreeMap.Entry<K, V> subLowest();

                abstract TreeMap.Entry<K, V> subHighest();

                abstract TreeMap.Entry<K, V> subCeiling(K key);

                abstract TreeMap.Entry<K, V> subHigher(K key);

                abstract TreeMap.Entry<K, V> subFloor(K key);

                abstract TreeMap.Entry<K, V> subLower(K key);

                /** Returns ascending iterator from the perspective of this submap */
                abstract Iterator<K> keyIterator();

                /** Returns descending iterator from the perspective of this submap */
                abstract Iterator<K> descendingKeyIterator();

                // public methods

                public boolean isEmpty() {
                    return (fromStart && toEnd) ? m.isEmpty() : entrySet()
                            .isEmpty();
                }

                public int size() {
                    return (fromStart && toEnd) ? m.size() : entrySet().size();
                }

                public final boolean containsKey(Object key) {
                    return inRange(key) && m.containsKey(key);
                }

                public final V put(K key, V value) {
                    if (!inRange(key))
                        throw new IllegalArgumentException("key out of range");
                    return m.put(key, value);
                }

                public final V get(Object key) {
                    return !inRange(key) ? null : m.get(key);
                }

                public final V remove(Object key) {
                    return !inRange(key) ? null : m.remove(key);
                }

                public final Map.Entry<K, V> ceilingEntry(K key) {
                    return exportEntry(subCeiling(key));
                }

                public final K ceilingKey(K key) {
                    return keyOrNull(subCeiling(key));
                }

                public final Map.Entry<K, V> higherEntry(K key) {
                    return exportEntry(subHigher(key));
                }

                public final K higherKey(K key) {
                    return keyOrNull(subHigher(key));
                }

                public final Map.Entry<K, V> floorEntry(K key) {
                    return exportEntry(subFloor(key));
                }

                public final K floorKey(K key) {
                    return keyOrNull(subFloor(key));
                }

                public final Map.Entry<K, V> lowerEntry(K key) {
                    return exportEntry(subLower(key));
                }

                public final K lowerKey(K key) {
                    return keyOrNull(subLower(key));
                }

                public final K firstKey() {
                    return key(subLowest());
                }

                public final K lastKey() {
                    return key(subHighest());
                }

                public final Map.Entry<K, V> firstEntry() {
                    return exportEntry(subLowest());
                }

                public final Map.Entry<K, V> lastEntry() {
                    return exportEntry(subHighest());
                }

                public final Map.Entry<K, V> pollFirstEntry() {
                    TreeMap.Entry<K, V> e = subLowest();
                    Map.Entry<K, V> result = exportEntry(e);
                    if (e != null)
                        m.deleteEntry(e);
                    return result;
                }

                public final Map.Entry<K, V> pollLastEntry() {
                    TreeMap.Entry<K, V> e = subHighest();
                    Map.Entry<K, V> result = exportEntry(e);
                    if (e != null)
                        m.deleteEntry(e);
                    return result;
                }

                // Views
                transient NavigableMap<K, V> descendingMapView = null;
                transient EntrySetView entrySetView = null;
                transient KeySet<K> navigableKeySetView = null;

                public final NavigableSet<K> navigableKeySet() {
                    KeySet<K> nksv = navigableKeySetView;
                    return (nksv != null) ? nksv
                            : (navigableKeySetView = new TreeMap.KeySet(this ));
                }

                public final Set<K> keySet() {
                    return navigableKeySet();
                }

                public NavigableSet<K> descendingKeySet() {
                    return descendingMap().navigableKeySet();
                }

                public final SortedMap<K, V> subMap(K fromKey, K toKey) {
                    return subMap(fromKey, true, toKey, false);
                }

                public final SortedMap<K, V> headMap(K toKey) {
                    return headMap(toKey, false);
                }

                public final SortedMap<K, V> tailMap(K fromKey) {
                    return tailMap(fromKey, true);
                }

                // View classes

                abstract class EntrySetView extends
                        AbstractSet<Map.Entry<K, V>> {
                    private transient int size = -1, sizeModCount;

                    public int size() {
                        if (fromStart && toEnd)
                            return m.size();
                        if (size == -1 || sizeModCount != m.modCount) {
                            sizeModCount = m.modCount;
                            size = 0;
                            Iterator i = iterator();
                            while (i.hasNext()) {
                                size++;
                                i.next();
                            }
                        }
                        return size;
                    }

                    public boolean isEmpty() {
                        TreeMap.Entry<K, V> n = absLowest();
                        return n == null || tooHigh(n.key);
                    }

                    public boolean contains(Object o) {
                        if (!(o instanceof  Map.Entry))
                            return false;
                        Map.Entry<K, V> entry = (Map.Entry<K, V>) o;
                        K key = entry.getKey();
                        if (!inRange(key))
                            return false;
                        TreeMap.Entry node = m.getEntry(key);
                        return node != null
                                && valEquals(node.getValue(), entry.getValue());
                    }

                    public boolean remove(Object o) {
                        if (!(o instanceof  Map.Entry))
                            return false;
                        Map.Entry<K, V> entry = (Map.Entry<K, V>) o;
                        K key = entry.getKey();
                        if (!inRange(key))
                            return false;
                        TreeMap.Entry<K, V> node = m.getEntry(key);
                        if (node != null
                                && valEquals(node.getValue(), entry.getValue())) {
                            m.deleteEntry(node);
                            return true;
                        }
                        return false;
                    }
                }

                /**
                 * Iterators for SubMaps
                 */
                abstract class SubMapIterator<T> implements  Iterator<T> {
                    TreeMap.Entry<K, V> lastReturned;
                    TreeMap.Entry<K, V> next;
                    final Object fenceKey;
                    int expectedModCount;

                    SubMapIterator(TreeMap.Entry<K, V> first,
                            TreeMap.Entry<K, V> fence) {
                        expectedModCount = m.modCount;
                        lastReturned = null;
                        next = first;
                        fenceKey = fence == null ? UNBOUNDED : fence.key;
                    }

                    public final boolean hasNext() {
                        return next != null && next.key != fenceKey;
                    }

                    final TreeMap.Entry<K, V> nextEntry() {
                        TreeMap.Entry<K, V> e = next;
                        if (e == null || e.key == fenceKey)
                            throw new NoSuchElementException();
                        if (m.modCount != expectedModCount)
                            throw new ConcurrentModificationException();
                        next = successor(e);
                        lastReturned = e;
                        return e;
                    }

                    final TreeMap.Entry<K, V> prevEntry() {
                        TreeMap.Entry<K, V> e = next;
                        if (e == null || e.key == fenceKey)
                            throw new NoSuchElementException();
                        if (m.modCount != expectedModCount)
                            throw new ConcurrentModificationException();
                        next = predecessor(e);
                        lastReturned = e;
                        return e;
                    }

                    final void removeAscending() {
                        if (lastReturned == null)
                            throw new IllegalStateException();
                        if (m.modCount != expectedModCount)
                            throw new ConcurrentModificationException();
                        // deleted entries are replaced by their successors
                        if (lastReturned.left != null
                                && lastReturned.right != null)
                            next = lastReturned;
                        m.deleteEntry(lastReturned);
                        lastReturned = null;
                        expectedModCount = m.modCount;
                    }

                    final void removeDescending() {
                        if (lastReturned == null)
                            throw new IllegalStateException();
                        if (m.modCount != expectedModCount)
                            throw new ConcurrentModificationException();
                        m.deleteEntry(lastReturned);
                        lastReturned = null;
                        expectedModCount = m.modCount;
                    }

                }

                final class SubMapEntryIterator extends
                        SubMapIterator<Map.Entry<K, V>> {
                    SubMapEntryIterator(TreeMap.Entry<K, V> first,
                            TreeMap.Entry<K, V> fence) {
                        super (first, fence);
                    }

                    public Map.Entry<K, V> next() {
                        return nextEntry();
                    }

                    public void remove() {
                        removeAscending();
                    }
                }

                final class SubMapKeyIterator extends SubMapIterator<K> {
                    SubMapKeyIterator(TreeMap.Entry<K, V> first,
                            TreeMap.Entry<K, V> fence) {
                        super (first, fence);
                    }

                    public K next() {
                        return nextEntry().key;
                    }

                    public void remove() {
                        removeAscending();
                    }
                }

                final class DescendingSubMapEntryIterator extends
                        SubMapIterator<Map.Entry<K, V>> {
                    DescendingSubMapEntryIterator(TreeMap.Entry<K, V> last,
                            TreeMap.Entry<K, V> fence) {
                        super (last, fence);
                    }

                    public Map.Entry<K, V> next() {
                        return prevEntry();
                    }

                    public void remove() {
                        removeDescending();
                    }
                }

                final class DescendingSubMapKeyIterator extends
                        SubMapIterator<K> {
                    DescendingSubMapKeyIterator(TreeMap.Entry<K, V> last,
                            TreeMap.Entry<K, V> fence) {
                        super (last, fence);
                    }

                    public K next() {
                        return prevEntry().key;
                    }

                    public void remove() {
                        removeDescending();
                    }
                }
            }

            /**
             * @serial include
             */
            static final class AscendingSubMap<K, V> extends
                    NavigableSubMap<K, V> {
                private static final long serialVersionUID = 912986545866124060L;

                AscendingSubMap(TreeMap<K, V> m, boolean fromStart, K lo,
                        boolean loInclusive, boolean toEnd, K hi,
                        boolean hiInclusive) {
                    super (m, fromStart, lo, loInclusive, toEnd, hi, hiInclusive);
                }

                public Comparator<? super  K> comparator() {
                    return m.comparator();
                }

                public NavigableMap<K, V> subMap(K fromKey,
                        boolean fromInclusive, K toKey, boolean toInclusive) {
                    if (!inRange(fromKey, fromInclusive))
                        throw new IllegalArgumentException(
                                "fromKey out of range");
                    if (!inRange(toKey, toInclusive))
                        throw new IllegalArgumentException("toKey out of range");
                    return new AscendingSubMap(m, false, fromKey,
                            fromInclusive, false, toKey, toInclusive);
                }

                public NavigableMap<K, V> headMap(K toKey, boolean inclusive) {
                    if (!inRange(toKey, inclusive))
                        throw new IllegalArgumentException("toKey out of range");
                    return new AscendingSubMap(m, fromStart, lo, loInclusive,
                            false, toKey, inclusive);
                }

                public NavigableMap<K, V> tailMap(K fromKey, boolean inclusive) {
                    if (!inRange(fromKey, inclusive))
                        throw new IllegalArgumentException(
                                "fromKey out of range");
                    return new AscendingSubMap(m, false, fromKey, inclusive,
                            toEnd, hi, hiInclusive);
                }

                public NavigableMap<K, V> descendingMap() {
                    NavigableMap<K, V> mv = descendingMapView;
                    return (mv != null) ? mv
                            : (descendingMapView = new DescendingSubMap(m,
                                    fromStart, lo, loInclusive, toEnd, hi,
                                    hiInclusive));
                }

                Iterator<K> keyIterator() {
                    return new SubMapKeyIterator(absLowest(), absHighFence());
                }

                Iterator<K> descendingKeyIterator() {
                    return new DescendingSubMapKeyIterator(absHighest(),
                            absLowFence());
                }

                final class AscendingEntrySetView extends EntrySetView {
                    public Iterator<Map.Entry<K, V>> iterator() {
                        return new SubMapEntryIterator(absLowest(),
                                absHighFence());
                    }
                }

                public Set<Map.Entry<K, V>> entrySet() {
                    EntrySetView es = entrySetView;
                    return (es != null) ? es : new AscendingEntrySetView();
                }

                TreeMap.Entry<K, V> subLowest() {
                    return absLowest();
                }

                TreeMap.Entry<K, V> subHighest() {
                    return absHighest();
                }

                TreeMap.Entry<K, V> subCeiling(K key) {
                    return absCeiling(key);
                }

                TreeMap.Entry<K, V> subHigher(K key) {
                    return absHigher(key);
                }

                TreeMap.Entry<K, V> subFloor(K key) {
                    return absFloor(key);
                }

                TreeMap.Entry<K, V> subLower(K key) {
                    return absLower(key);
                }
            }

            /**
             * @serial include
             */
            static final class DescendingSubMap<K, V> extends
                    NavigableSubMap<K, V> {
                private static final long serialVersionUID = 912986545866120460L;

                DescendingSubMap(TreeMap<K, V> m, boolean fromStart, K lo,
                        boolean loInclusive, boolean toEnd, K hi,
                        boolean hiInclusive) {
                    super (m, fromStart, lo, loInclusive, toEnd, hi, hiInclusive);
                }

                private final Comparator<? super  K> reverseComparator = Collections
                        .reverseOrder(m.comparator);

                public Comparator<? super  K> comparator() {
                    return reverseComparator;
                }

                public NavigableMap<K, V> subMap(K fromKey,
                        boolean fromInclusive, K toKey, boolean toInclusive) {
                    if (!inRange(fromKey, fromInclusive))
                        throw new IllegalArgumentException(
                                "fromKey out of range");
                    if (!inRange(toKey, toInclusive))
                        throw new IllegalArgumentException("toKey out of range");
                    return new DescendingSubMap(m, false, toKey, toInclusive,
                            false, fromKey, fromInclusive);
                }

                public NavigableMap<K, V> headMap(K toKey, boolean inclusive) {
                    if (!inRange(toKey, inclusive))
                        throw new IllegalArgumentException("toKey out of range");
                    return new DescendingSubMap(m, false, toKey, inclusive,
                            toEnd, hi, hiInclusive);
                }

                public NavigableMap<K, V> tailMap(K fromKey, boolean inclusive) {
                    if (!inRange(fromKey, inclusive))
                        throw new IllegalArgumentException(
                                "fromKey out of range");
                    return new DescendingSubMap(m, fromStart, lo, loInclusive,
                            false, fromKey, inclusive);
                }

                public NavigableMap<K, V> descendingMap() {
                    NavigableMap<K, V> mv = descendingMapView;
                    return (mv != null) ? mv
                            : (descendingMapView = new AscendingSubMap(m,
                                    fromStart, lo, loInclusive, toEnd, hi,
                                    hiInclusive));
                }

                Iterator<K> keyIterator() {
                    return new DescendingSubMapKeyIterator(absHighest(),
                            absLowFence());
                }

                Iterator<K> descendingKeyIterator() {
                    return new SubMapKeyIterator(absLowest(), absHighFence());
                }

                final class DescendingEntrySetView extends EntrySetView {
                    public Iterator<Map.Entry<K, V>> iterator() {
                        return new DescendingSubMapEntryIterator(absHighest(),
                                absLowFence());
                    }
                }

                public Set<Map.Entry<K, V>> entrySet() {
                    EntrySetView es = entrySetView;
                    return (es != null) ? es : new DescendingEntrySetView();
                }

                TreeMap.Entry<K, V> subLowest() {
                    return absHighest();
                }

                TreeMap.Entry<K, V> subHighest() {
                    return absLowest();
                }

                TreeMap.Entry<K, V> subCeiling(K key) {
                    return absFloor(key);
                }

                TreeMap.Entry<K, V> subHigher(K key) {
                    return absLower(key);
                }

                TreeMap.Entry<K, V> subFloor(K key) {
                    return absCeiling(key);
                }

                TreeMap.Entry<K, V> subLower(K key) {
                    return absHigher(key);
                }
            }

            /**
             * This class exists solely for the sake of serialization
             * compatibility with previous releases of TreeMap that did not
             * support NavigableMap.  It translates an old-version SubMap into
             * a new-version AscendingSubMap. This class is never otherwise
             * used.
             *
             * @serial include
             */
            private class SubMap extends AbstractMap<K, V> implements 
                    SortedMap<K, V>, java.io.Serializable {
                private static final long serialVersionUID = -6520786458950516097L;
                private boolean fromStart = false, toEnd = false;
                private K fromKey, toKey;

                private Object readResolve() {
                    return new AscendingSubMap(TreeMap.this , fromStart,
                            fromKey, true, toEnd, toKey, false);
                }

                public Set<Map.Entry<K, V>> entrySet() {
                    throw new InternalError();
                }

                public K lastKey() {
                    throw new InternalError();
                }

                public K firstKey() {
                    throw new InternalError();
                }

                public SortedMap<K, V> subMap(K fromKey, K toKey) {
                    throw new InternalError();
                }

                public SortedMap<K, V> headMap(K toKey) {
                    throw new InternalError();
                }

                public SortedMap<K, V> tailMap(K fromKey) {
                    throw new InternalError();
                }

                public Comparator<? super  K> comparator() {
                    throw new InternalError();
                }
            }

            // Red-black mechanics

            private static final boolean RED = false;
            private static final boolean BLACK = true;

            /**
             * Node in the Tree.  Doubles as a means to pass key-value pairs back to
             * user (see Map.Entry).
             */

            static final class Entry<K, V> implements  Map.Entry<K, V> {
                K key;
                V value;
                Entry<K, V> left = null;
                Entry<K, V> right = null;
                Entry<K, V> parent;
                boolean color = BLACK;

                /**
                 * Make a new cell with given key, value, and parent, and with
                 * <tt>null</tt> child links, and BLACK color.
                 */
                Entry(K key, V value, Entry<K, V> parent) {
                    this .key = key;
                    this .value = value;
                    this .parent = parent;
                }

                /**
                 * Returns the key.
                 *
                 * @return the key
                 */
                public K getKey() {
                    return key;
                }

                /**
                 * Returns the value associated with the key.
                 *
                 * @return the value associated with the key
                 */
                public V getValue() {
                    return value;
                }

                /**
                 * Replaces the value currently associated with the key with the given
                 * value.
                 *
                 * @return the value associated with the key before this method was
                 *         called
                 */
                public V setValue(V value) {
                    V oldValue = this .value;
                    this .value = value;
                    return oldValue;
                }

                public boolean equals(Object o) {
                    if (!(o instanceof  Map.Entry))
                        return false;
                    Map.Entry<?, ?> e = (Map.Entry<?, ?>) o;

                    return valEquals(key, e.getKey())
                            && valEquals(value, e.getValue());
                }

                public int hashCode() {
                    int keyHash = (key == null ? 0 : key.hashCode());
                    int valueHash = (value == null ? 0 : value.hashCode());
                    return keyHash ^ valueHash;
                }

                public String toString() {
                    return key + "=" + value;
                }
            }

            /**
             * Returns the first Entry in the TreeMap (according to the TreeMap's
             * key-sort function).  Returns null if the TreeMap is empty.
             */
            final Entry<K, V> getFirstEntry() {
                Entry<K, V> p = root;
                if (p != null)
                    while (p.left != null)
                        p = p.left;
                return p;
            }

            /**
             * Returns the last Entry in the TreeMap (according to the TreeMap's
             * key-sort function).  Returns null if the TreeMap is empty.
             */
            final Entry<K, V> getLastEntry() {
                Entry<K, V> p = root;
                if (p != null)
                    while (p.right != null)
                        p = p.right;
                return p;
            }

            /**
             * Returns the successor of the specified Entry, or null if no such.
             */
            static <K, V> TreeMap.Entry<K, V> successor(Entry<K, V> t) {
                if (t == null)
                    return null;
                else if (t.right != null) {
                    Entry<K, V> p = t.right;
                    while (p.left != null)
                        p = p.left;
                    return p;
                } else {
                    Entry<K, V> p = t.parent;
                    Entry<K, V> ch = t;
                    while (p != null && ch == p.right) {
                        ch = p;
                        p = p.parent;
                    }
                    return p;
                }
            }

            /**
             * Returns the predecessor of the specified Entry, or null if no such.
             */
            static <K, V> Entry<K, V> predecessor(Entry<K, V> t) {
                if (t == null)
                    return null;
                else if (t.left != null) {
                    Entry<K, V> p = t.left;
                    while (p.right != null)
                        p = p.right;
                    return p;
                } else {
                    Entry<K, V> p = t.parent;
                    Entry<K, V> ch = t;
                    while (p != null && ch == p.left) {
                        ch = p;
                        p = p.parent;
                    }
                    return p;
                }
            }

            /**
             * Balancing operations.
             *
             * Implementations of rebalancings during insertion and deletion are
             * slightly different than the CLR version.  Rather than using dummy
             * nilnodes, we use a set of accessors that deal properly with null.  They
             * are used to avoid messiness surrounding nullness checks in the main
             * algorithms.
             */

            private static <K, V> boolean colorOf(Entry<K, V> p) {
                return (p == null ? BLACK : p.color);
            }

            private static <K, V> Entry<K, V> parentOf(Entry<K, V> p) {
                return (p == null ? null : p.parent);
            }

            private static <K, V> void setColor(Entry<K, V> p, boolean c) {
                if (p != null)
                    p.color = c;
            }

            private static <K, V> Entry<K, V> leftOf(Entry<K, V> p) {
                return (p == null) ? null : p.left;
            }

            private static <K, V> Entry<K, V> rightOf(Entry<K, V> p) {
                return (p == null) ? null : p.right;
            }

            /** From CLR */
            private void rotateLeft(Entry<K, V> p) {
                if (p != null) {
                    Entry<K, V> r = p.right;
                    p.right = r.left;
                    if (r.left != null)
                        r.left.parent = p;
                    r.parent = p.parent;
                    if (p.parent == null)
                        root = r;
                    else if (p.parent.left == p)
                        p.parent.left = r;
                    else
                        p.parent.right = r;
                    r.left = p;
                    p.parent = r;
                }
            }

            /** From CLR */
            private void rotateRight(Entry<K, V> p) {
                if (p != null) {
                    Entry<K, V> l = p.left;
                    p.left = l.right;
                    if (l.right != null)
                        l.right.parent = p;
                    l.parent = p.parent;
                    if (p.parent == null)
                        root = l;
                    else if (p.parent.right == p)
                        p.parent.right = l;
                    else
                        p.parent.left = l;
                    l.right = p;
                    p.parent = l;
                }
            }

            /** From CLR */
            private void fixAfterInsertion(Entry<K, V> x) {
                x.color = RED;

                while (x != null && x != root && x.parent.color == RED) {
                    if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {
                        Entry<K, V> y = rightOf(parentOf(parentOf(x)));
                        if (colorOf(y) == RED) {
                            setColor(parentOf(x), BLACK);
                            setColor(y, BLACK);
                            setColor(parentOf(parentOf(x)), RED);
                            x = parentOf(parentOf(x));
                        } else {
                            if (x == rightOf(parentOf(x))) {
                                x = parentOf(x);
                                rotateLeft(x);
                            }
                            setColor(parentOf(x), BLACK);
                            setColor(parentOf(parentOf(x)), RED);
                            rotateRight(parentOf(parentOf(x)));
                        }
                    } else {
                        Entry<K, V> y = leftOf(parentOf(parentOf(x)));
                        if (colorOf(y) == RED) {
                            setColor(parentOf(x), BLACK);
                            setColor(y, BLACK);
                            setColor(parentOf(parentOf(x)), RED);
                            x = parentOf(parentOf(x));
                        } else {
                            if (x == leftOf(parentOf(x))) {
                                x = parentOf(x);
                                rotateRight(x);
                            }
                            setColor(parentOf(x), BLACK);
                            setColor(parentOf(parentOf(x)), RED);
                            rotateLeft(parentOf(parentOf(x)));
                        }
                    }
                }
                root.color = BLACK;
            }

            /**
             * Delete node p, and then rebalance the tree.
             */
            private void deleteEntry(Entry<K, V> p) {
                modCount++;
                size--;

                // If strictly internal, copy successor's element to p and then make p
                // point to successor.
                if (p.left != null && p.right != null) {
                    Entry<K, V> s = successor(p);
                    p.key = s.key;
                    p.value = s.value;
                    p = s;
                } // p has 2 children

                // Start fixup at replacement node, if it exists.
                Entry<K, V> replacement = (p.left != null ? p.left : p.right);

                if (replacement != null) {
                    // Link replacement to parent
                    replacement.parent = p.parent;
                    if (p.parent == null)
                        root = replacement;
                    else if (p == p.parent.left)
                        p.parent.left = replacement;
                    else
                        p.parent.right = replacement;

                    // Null out links so they are OK to use by fixAfterDeletion.
                    p.left = p.right = p.parent = null;

                    // Fix replacement
                    if (p.color == BLACK)
                        fixAfterDeletion(replacement);
                } else if (p.parent == null) { // return if we are the only node.
                    root = null;
                } else { //  No children. Use self as phantom replacement and unlink.
                    if (p.color == BLACK)
                        fixAfterDeletion(p);

                    if (p.parent != null) {
                        if (p == p.parent.left)
                            p.parent.left = null;
                        else if (p == p.parent.right)
                            p.parent.right = null;
                        p.parent = null;
                    }
                }
            }

            /** From CLR */
            private void fixAfterDeletion(Entry<K, V> x) {
                while (x != root && colorOf(x) == BLACK) {
                    if (x == leftOf(parentOf(x))) {
                        Entry<K, V> sib = rightOf(parentOf(x));

                        if (colorOf(sib) == RED) {
                            setColor(sib, BLACK);
                            setColor(parentOf(x), RED);
                            rotateLeft(parentOf(x));
                            sib = rightOf(parentOf(x));
                        }

                        if (colorOf(leftOf(sib)) == BLACK
                                && colorOf(rightOf(sib)) == BLACK) {
                            setColor(sib, RED);
                            x = parentOf(x);
                        } else {
                            if (colorOf(rightOf(sib)) == BLACK) {
                                setColor(leftOf(sib), BLACK);
                                setColor(sib, RED);
                                rotateRight(sib);
                                sib = rightOf(parentOf(x));
                            }
                            setColor(sib, colorOf(parentOf(x)));
                            setColor(parentOf(x), BLACK);
                            setColor(rightOf(sib), BLACK);
                            rotateLeft(parentOf(x));
                            x = root;
                        }
                    } else { // symmetric
                        Entry<K, V> sib = leftOf(parentOf(x));

                        if (colorOf(sib) == RED) {
                            setColor(sib, BLACK);
                            setColor(parentOf(x), RED);
                            rotateRight(parentOf(x));
                            sib = leftOf(parentOf(x));
                        }

                        if (colorOf(rightOf(sib)) == BLACK
                                && colorOf(leftOf(sib)) == BLACK) {
                            setColor(sib, RED);
                            x = parentOf(x);
                        } else {
                            if (colorOf(leftOf(sib)) == BLACK) {
                                setColor(rightOf(sib), BLACK);
                                setColor(sib, RED);
                                rotateLeft(sib);
                                sib = leftOf(parentOf(x));
                            }
                            setColor(sib, colorOf(parentOf(x)));
                            setColor(parentOf(x), BLACK);
                            setColor(leftOf(sib), BLACK);
                            rotateRight(parentOf(x));
                            x = root;
                        }
                    }
                }

                setColor(x, BLACK);
            }

            private static final long serialVersionUID = 919286545866124006L;

            /**
             * Save the state of the <tt>TreeMap</tt> instance to a stream (i.e.,
             * serialize it).
             *
             * @serialData The <i>size</i> of the TreeMap (the number of key-value
             *             mappings) is emitted (int), followed by the key (Object)
             *             and value (Object) for each key-value mapping represented
             *             by the TreeMap. The key-value mappings are emitted in
             *             key-order (as determined by the TreeMap's Comparator,
             *             or by the keys' natural ordering if the TreeMap has no
             *             Comparator).
             */
            private void writeObject(java.io.ObjectOutputStream s)
                    throws java.io.IOException {
                // Write out the Comparator and any hidden stuff
                s.defaultWriteObject();

                // Write out size (number of Mappings)
                s.writeInt(size);

                // Write out keys and values (alternating)
                for (Iterator<Map.Entry<K, V>> i = entrySet().iterator(); i
                        .hasNext();) {
                    Map.Entry<K, V> e = i.next();
                    s.writeObject(e.getKey());
                    s.writeObject(e.getValue());
                }
            }

            /**
             * Reconstitute the <tt>TreeMap</tt> instance from a stream (i.e.,
             * deserialize it).
             */
            private void readObject(final java.io.ObjectInputStream s)
                    throws java.io.IOException, ClassNotFoundException {
                // Read in the Comparator and any hidden stuff
                s.defaultReadObject();

                // Read in size
                int size = s.readInt();

                buildFromSorted(size, null, s, null);
            }

            /** Intended to be called only from TreeSet.readObject */
            void readTreeSet(int size, java.io.ObjectInputStream s, V defaultVal)
                    throws java.io.IOException, ClassNotFoundException {
                buildFromSorted(size, null, s, defaultVal);
            }

            /** Intended to be called only from TreeSet.addAll */
            void addAllForTreeSet(SortedSet<? extends K> set, V defaultVal) {
                try {
                    buildFromSorted(set.size(), set.iterator(), null,
                            defaultVal);
                } catch (java.io.IOException cannotHappen) {
                } catch (ClassNotFoundException cannotHappen) {
                }
            }

            /**
             * Linear time tree building algorithm from sorted data.  Can accept keys
             * and/or values from iterator or stream. This leads to too many
             * parameters, but seems better than alternatives.  The four formats
             * that this method accepts are:
             *
             *    1) An iterator of Map.Entries.  (it != null, defaultVal == null).
             *    2) An iterator of keys.         (it != null, defaultVal != null).
             *    3) A stream of alternating serialized keys and values.
             *                                   (it == null, defaultVal == null).
             *    4) A stream of serialized keys. (it == null, defaultVal != null).
             *
             * It is assumed that the comparator of the TreeMap is already set prior
             * to calling this method.
             *
             * @param size the number of keys (or key-value pairs) to be read from
             *        the iterator or stream
             * @param it If non-null, new entries are created from entries
             *        or keys read from this iterator.
             * @param str If non-null, new entries are created from keys and
             *        possibly values read from this stream in serialized form.
             *        Exactly one of it and str should be non-null.
             * @param defaultVal if non-null, this default value is used for
             *        each value in the map.  If null, each value is read from
             *        iterator or stream, as described above.
             * @throws IOException propagated from stream reads. This cannot
             *         occur if str is null.
             * @throws ClassNotFoundException propagated from readObject.
             *         This cannot occur if str is null.
             */
            private void buildFromSorted(int size, Iterator it,
                    java.io.ObjectInputStream str, V defaultVal)
                    throws java.io.IOException, ClassNotFoundException {
                this .size = size;
                root = buildFromSorted(0, 0, size - 1, computeRedLevel(size),
                        it, str, defaultVal);
            }

            /**
             * Recursive "helper method" that does the real work of the
             * previous method.  Identically named parameters have
             * identical definitions.  Additional parameters are documented below.
             * It is assumed that the comparator and size fields of the TreeMap are
             * already set prior to calling this method.  (It ignores both fields.)
             *
             * @param level the current level of tree. Initial call should be 0.
             * @param lo the first element index of this subtree. Initial should be 0.
             * @param hi the last element index of this subtree.  Initial should be
             *        size-1.
             * @param redLevel the level at which nodes should be red.
             *        Must be equal to computeRedLevel for tree of this size.
             */
            private final Entry<K, V> buildFromSorted(int level, int lo,
                    int hi, int redLevel, Iterator it,
                    java.io.ObjectInputStream str, V defaultVal)
                    throws java.io.IOException, ClassNotFoundException {
                /*
                 * Strategy: The root is the middlemost element. To get to it, we
                 * have to first recursively construct the entire left subtree,
                 * so as to grab all of its elements. We can then proceed with right
                 * subtree.
                 *
                 * The lo and hi arguments are the minimum and maximum
                 * indices to pull out of the iterator or stream for current subtree.
                 * They are not actually indexed, we just proceed sequentially,
                 * ensuring that items are extracted in corresponding order.
                 */

                if (hi < lo)
                    return null;

                int mid = (lo + hi) >>> 1;

                Entry<K, V> left = null;
                if (lo < mid)
                    left = buildFromSorted(level + 1, lo, mid - 1, redLevel,
                            it, str, defaultVal);

                // extract key and/or value from iterator or stream
                K key;
                V value;
                if (it != null) {
                    if (defaultVal == null) {
                        Map.Entry<K, V> entry = (Map.Entry<K, V>) it.next();
                        key = entry.getKey();
                        value = entry.getValue();
                    } else {
                        key = (K) it.next();
                        value = defaultVal;
                    }
                } else { // use stream
                    key = (K) str.readObject();
                    value = (defaultVal != null ? defaultVal : (V) str
                            .readObject());
                }

                Entry<K, V> middle = new Entry<K, V>(key, value, null);

                // color nodes in non-full bottommost level red
                if (level == redLevel)
                    middle.color = RED;

                if (left != null) {
                    middle.left = left;
                    left.parent = middle;
                }

                if (mid < hi) {
                    Entry<K, V> right = buildFromSorted(level + 1, mid + 1, hi,
                            redLevel, it, str, defaultVal);
                    middle.right = right;
                    right.parent = middle;
                }

                return middle;
            }

            /**
             * Find the level down to which to assign all nodes BLACK.  This is the
             * last `full' level of the complete binary tree produced by
             * buildTree. The remaining nodes are colored RED. (This makes a `nice'
             * set of color assignments wrt future insertions.) This level number is
             * computed by finding the number of splits needed to reach the zeroeth
             * node.  (The answer is ~lg(N), but in any case must be computed by same
             * quick O(lg(N)) loop.)
             */
            private static int computeRedLevel(int sz) {
                int level = 0;
                for (int m = sz - 1; m >= 0; m = m / 2 - 1)
                    level++;
                return level;
            }
        }
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