1 /*
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   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
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   8  * particular file as subject to the "Classpath" exception as provided
   9  * by Oracle in the LICENSE file that accompanied this code.
  10  *
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  12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14  * version 2 for more details (a copy is included in the LICENSE file that
  15  * accompanied this code).
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  25 
  26 package java.util;
  27 
  28 /**
  29  * A Red-Black tree based {@link NavigableMap} implementation.
  30  * The map is sorted according to the {@linkplain Comparable natural
  31  * ordering} of its keys, or by a {@link Comparator} provided at map
  32  * creation time, depending on which constructor is used.
  33  *
  34  * <p>This implementation provides guaranteed log(n) time cost for the
  35  * <tt>containsKey</tt>, <tt>get</tt>, <tt>put</tt> and <tt>remove</tt>
  36  * operations.  Algorithms are adaptations of those in Cormen, Leiserson, and
  37  * Rivest's <I>Introduction to Algorithms</I>.
  38  *
  39  * <p>Note that the ordering maintained by a tree map, like any sorted map, and
  40  * whether or not an explicit comparator is provided, must be <em>consistent
  41  * with {@code equals}</em> if this sorted map is to correctly implement the
  42  * {@code Map} interface.  (See {@code Comparable} or {@code Comparator} for a
  43  * precise definition of <i>consistent with equals</i>.)  This is so because
  44  * the <tt>Map</tt> interface is defined in terms of the {@code equals}
  45  * operation, but a sorted map performs all key comparisons using its {@code
  46  * compareTo} (or {@code compare}) method, so two keys that are deemed equal by
  47  * this method are, from the standpoint of the sorted map, equal.  The behavior
  48  * of a sorted map <em>is</em> well-defined even if its ordering is
  49  * inconsistent with {@code equals}; it just fails to obey the general contract
  50  * of the {@code Map} interface.
  51  *
  52  * <p><strong>Note that this implementation is not synchronized.</strong>
  53  * If multiple threads access a map concurrently, and at least one of the
  54  * threads modifies the map structurally, it <i>must</i> be synchronized
  55  * externally.  (A structural modification is any operation that adds or
  56  * deletes one or more mappings; merely changing the value associated
  57  * with an existing key is not a structural modification.)  This is
  58  * typically accomplished by synchronizing on some object that naturally
  59  * encapsulates the map.
  60  * If no such object exists, the map should be "wrapped" using the
  61  * {@link Collections#synchronizedSortedMap Collections.synchronizedSortedMap}
  62  * method.  This is best done at creation time, to prevent accidental
  63  * unsynchronized access to the map: <pre>
  64  *   SortedMap m = Collections.synchronizedSortedMap(new TreeMap(...));</pre>
  65  *
  66  * <p>The iterators returned by the <tt>iterator</tt> method of the collections
  67  * returned by all of this class's "collection view methods" are
  68  * <i>fail-fast</i>: if the map is structurally modified at any time after the
  69  * iterator is created, in any way except through the iterator's own
  70  * <tt>remove</tt> method, the iterator will throw a {@link
  71  * ConcurrentModificationException}.  Thus, in the face of concurrent
  72  * modification, the iterator fails quickly and cleanly, rather than risking
  73  * arbitrary, non-deterministic behavior at an undetermined time in the future.
  74  *
  75  * <p>Note that the fail-fast behavior of an iterator cannot be guaranteed
  76  * as it is, generally speaking, impossible to make any hard guarantees in the
  77  * presence of unsynchronized concurrent modification.  Fail-fast iterators
  78  * throw <tt>ConcurrentModificationException</tt> on a best-effort basis.
  79  * Therefore, it would be wrong to write a program that depended on this
  80  * exception for its correctness:   <i>the fail-fast behavior of iterators
  81  * should be used only to detect bugs.</i>
  82  *
  83  * <p>All <tt>Map.Entry</tt> pairs returned by methods in this class
  84  * and its views represent snapshots of mappings at the time they were
  85  * produced. They do <em>not</em> support the <tt>Entry.setValue</tt>
  86  * method. (Note however that it is possible to change mappings in the
  87  * associated map using <tt>put</tt>.)
  88  *
  89  * <p>This class is a member of the
  90  * <a href="{@docRoot}/../technotes/guides/collections/index.html">
  91  * Java Collections Framework</a>.
  92  *
  93  * @param <K> the type of keys maintained by this map
  94  * @param <V> the type of mapped values
  95  *
  96  * @author  Josh Bloch and Doug Lea
  97  * @see Map
  98  * @see HashMap
  99  * @see Hashtable
 100  * @see Comparable
 101  * @see Comparator
 102  * @see Collection
 103  * @since 1.2
 104  */
 105 
 106 public class TreeMap<K,V>
 107     extends AbstractMap<K,V>
 108     implements NavigableMap<K,V>, Cloneable, java.io.Serializable
 109 {
 110     /**
 111      * The comparator used to maintain order in this tree map, or
 112      * null if it uses the natural ordering of its keys.
 113      *
 114      * @serial
 115      */
 116     private final Comparator<? super K> comparator;
 117 
 118     private transient Entry<K,V> root = null;
 119 
 120     /**
 121      * The number of entries in the tree
 122      */
 123     private transient int size = 0;
 124 
 125     /**
 126      * The number of structural modifications to the tree.
 127      */
 128     private transient int modCount = 0;
 129 
 130     /**
 131      * Constructs a new, empty tree map, using the natural ordering of its
 132      * keys.  All keys inserted into the map must implement the {@link
 133      * Comparable} interface.  Furthermore, all such keys must be
 134      * <i>mutually comparable</i>: <tt>k1.compareTo(k2)</tt> must not throw
 135      * a <tt>ClassCastException</tt> for any keys <tt>k1</tt> and
 136      * <tt>k2</tt> in the map.  If the user attempts to put a key into the
 137      * map that violates this constraint (for example, the user attempts to
 138      * put a string key into a map whose keys are integers), the
 139      * <tt>put(Object key, Object value)</tt> call will throw a
 140      * <tt>ClassCastException</tt>.
 141      */
 142     public TreeMap() {
 143         comparator = null;
 144     }
 145 
 146     /**
 147      * Constructs a new, empty tree map, ordered according to the given
 148      * comparator.  All keys inserted into the map must be <i>mutually
 149      * comparable</i> by the given comparator: <tt>comparator.compare(k1,
 150      * k2)</tt> must not throw a <tt>ClassCastException</tt> for any keys
 151      * <tt>k1</tt> and <tt>k2</tt> in the map.  If the user attempts to put
 152      * a key into the map that violates this constraint, the <tt>put(Object
 153      * key, Object value)</tt> call will throw a
 154      * <tt>ClassCastException</tt>.
 155      *
 156      * @param comparator the comparator that will be used to order this map.
 157      *        If <tt>null</tt>, the {@linkplain Comparable natural
 158      *        ordering} of the keys will be used.
 159      */
 160     public TreeMap(Comparator<? super K> comparator) {
 161         this.comparator = comparator;
 162     }
 163 
 164     /**
 165      * Constructs a new tree map containing the same mappings as the given
 166      * map, ordered according to the <i>natural ordering</i> of its keys.
 167      * All keys inserted into the new map must implement the {@link
 168      * Comparable} interface.  Furthermore, all such keys must be
 169      * <i>mutually comparable</i>: <tt>k1.compareTo(k2)</tt> must not throw
 170      * a <tt>ClassCastException</tt> for any keys <tt>k1</tt> and
 171      * <tt>k2</tt> in the map.  This method runs in n*log(n) time.
 172      *
 173      * @param  m the map whose mappings are to be placed in this map
 174      * @throws ClassCastException if the keys in m are not {@link Comparable},
 175      *         or are not mutually comparable
 176      * @throws NullPointerException if the specified map is null
 177      */
 178     public TreeMap(Map<? extends K, ? extends V> m) {
 179         comparator = null;
 180         putAll(m);
 181     }
 182 
 183     /**
 184      * Constructs a new tree map containing the same mappings and
 185      * using the same ordering as the specified sorted map.  This
 186      * method runs in linear time.
 187      *
 188      * @param  m the sorted map whose mappings are to be placed in this map,
 189      *         and whose comparator is to be used to sort this map
 190      * @throws NullPointerException if the specified map is null
 191      */
 192     public TreeMap(SortedMap<K, ? extends V> m) {
 193         comparator = m.comparator();
 194         try {
 195             buildFromSorted(m.size(), m.entrySet().iterator(), null, null);
 196         } catch (java.io.IOException cannotHappen) {
 197         } catch (ClassNotFoundException cannotHappen) {
 198         }
 199     }
 200 
 201 
 202     // Query Operations
 203 
 204     /**
 205      * Returns the number of key-value mappings in this map.
 206      *
 207      * @return the number of key-value mappings in this map
 208      */
 209     public int size() {
 210         return size;
 211     }
 212 
 213     /**
 214      * Returns <tt>true</tt> if this map contains a mapping for the specified
 215      * key.
 216      *
 217      * @param key key whose presence in this map is to be tested
 218      * @return <tt>true</tt> if this map contains a mapping for the
 219      *         specified key
 220      * @throws ClassCastException if the specified key cannot be compared
 221      *         with the keys currently in the map
 222      * @throws NullPointerException if the specified key is null
 223      *         and this map uses natural ordering, or its comparator
 224      *         does not permit null keys
 225      */
 226     public boolean containsKey(Object key) {
 227         return getEntry(key) != null;
 228     }
 229 
 230     /**
 231      * Returns <tt>true</tt> if this map maps one or more keys to the
 232      * specified value.  More formally, returns <tt>true</tt> if and only if
 233      * this map contains at least one mapping to a value <tt>v</tt> such
 234      * that <tt>(value==null ? v==null : value.equals(v))</tt>.  This
 235      * operation will probably require time linear in the map size for
 236      * most implementations.
 237      *
 238      * @param value value whose presence in this map is to be tested
 239      * @return <tt>true</tt> if a mapping to <tt>value</tt> exists;
 240      *         <tt>false</tt> otherwise
 241      * @since 1.2
 242      */
 243     public boolean containsValue(Object value) {
 244         for (Entry<K,V> e = getFirstEntry(); e != null; e = successor(e))
 245             if (valEquals(value, e.value))
 246                 return true;
 247         return false;
 248     }
 249 
 250     /**
 251      * Returns the value to which the specified key is mapped,
 252      * or {@code null} if this map contains no mapping for the key.
 253      *
 254      * <p>More formally, if this map contains a mapping from a key
 255      * {@code k} to a value {@code v} such that {@code key} compares
 256      * equal to {@code k} according to the map's ordering, then this
 257      * method returns {@code v}; otherwise it returns {@code null}.
 258      * (There can be at most one such mapping.)
 259      *
 260      * <p>A return value of {@code null} does not <i>necessarily</i>
 261      * indicate that the map contains no mapping for the key; it's also
 262      * possible that the map explicitly maps the key to {@code null}.
 263      * The {@link #containsKey containsKey} operation may be used to
 264      * distinguish these two cases.
 265      *
 266      * @throws ClassCastException if the specified key cannot be compared
 267      *         with the keys currently in the map
 268      * @throws NullPointerException if the specified key is null
 269      *         and this map uses natural ordering, or its comparator
 270      *         does not permit null keys
 271      */
 272     public V get(Object key) {
 273         Entry<K,V> p = getEntry(key);
 274         return (p==null ? null : p.value);
 275     }
 276 
 277     public Comparator<? super K> comparator() {
 278         return comparator;
 279     }
 280 
 281     /**
 282      * @throws NoSuchElementException {@inheritDoc}
 283      */
 284     public K firstKey() {
 285         return key(getFirstEntry());
 286     }
 287 
 288     /**
 289      * @throws NoSuchElementException {@inheritDoc}
 290      */
 291     public K lastKey() {
 292         return key(getLastEntry());
 293     }
 294 
 295     /**
 296      * Copies all of the mappings from the specified map to this map.
 297      * These mappings replace any mappings that this map had for any
 298      * of the keys currently in the specified map.
 299      *
 300      * @param  map mappings to be stored in this map
 301      * @throws ClassCastException if the class of a key or value in
 302      *         the specified map prevents it from being stored in this map
 303      * @throws NullPointerException if the specified map is null or
 304      *         the specified map contains a null key and this map does not
 305      *         permit null keys
 306      */
 307     public void putAll(Map<? extends K, ? extends V> map) {
 308         int mapSize = map.size();
 309         if (size==0 && mapSize!=0 && map instanceof SortedMap) {
 310             Comparator c = ((SortedMap)map).comparator();
 311             if (c == comparator || (c != null && c.equals(comparator))) {
 312                 ++modCount;
 313                 try {
 314                     buildFromSorted(mapSize, map.entrySet().iterator(),
 315                                     null, null);
 316                 } catch (java.io.IOException cannotHappen) {
 317                 } catch (ClassNotFoundException cannotHappen) {
 318                 }
 319                 return;
 320             }
 321         }
 322         super.putAll(map);
 323     }
 324 
 325     /**
 326      * Returns this map's entry for the given key, or <tt>null</tt> if the map
 327      * does not contain an entry for the key.
 328      *
 329      * @return this map's entry for the given key, or <tt>null</tt> if the map
 330      *         does not contain an entry for the key
 331      * @throws ClassCastException if the specified key cannot be compared
 332      *         with the keys currently in the map
 333      * @throws NullPointerException if the specified key is null
 334      *         and this map uses natural ordering, or its comparator
 335      *         does not permit null keys
 336      */
 337     final Entry<K,V> getEntry(Object key) {
 338         // Offload comparator-based version for sake of performance
 339         if (comparator != null)
 340             return getEntryUsingComparator(key);
 341         if (key == null)
 342             throw new NullPointerException();
 343         Comparable<? super K> k = (Comparable<? super K>) key;
 344         Entry<K,V> p = root;
 345         while (p != null) {
 346             int cmp = k.compareTo(p.key);
 347             if (cmp < 0)
 348                 p = p.left;
 349             else if (cmp > 0)
 350                 p = p.right;
 351             else
 352                 return p;
 353         }
 354         return null;
 355     }
 356 
 357     /**
 358      * Version of getEntry using comparator. Split off from getEntry
 359      * for performance. (This is not worth doing for most methods,
 360      * that are less dependent on comparator performance, but is
 361      * worthwhile here.)
 362      */
 363     final Entry<K,V> getEntryUsingComparator(Object key) {
 364         K k = (K) key;
 365         Comparator<? super K> cpr = comparator;
 366         if (cpr != null) {
 367             Entry<K,V> p = root;
 368             while (p != null) {
 369                 int cmp = cpr.compare(k, p.key);
 370                 if (cmp < 0)
 371                     p = p.left;
 372                 else if (cmp > 0)
 373                     p = p.right;
 374                 else
 375                     return p;
 376             }
 377         }
 378         return null;
 379     }
 380 
 381     /**
 382      * Gets the entry corresponding to the specified key; if no such entry
 383      * exists, returns the entry for the least key greater than the specified
 384      * key; if no such entry exists (i.e., the greatest key in the Tree is less
 385      * than the specified key), returns <tt>null</tt>.
 386      */
 387     final Entry<K,V> getCeilingEntry(K key) {
 388         Entry<K,V> p = root;
 389         while (p != null) {
 390             int cmp = compare(key, p.key);
 391             if (cmp < 0) {
 392                 if (p.left != null)
 393                     p = p.left;
 394                 else
 395                     return p;
 396             } else if (cmp > 0) {
 397                 if (p.right != null) {
 398                     p = p.right;
 399                 } else {
 400                     Entry<K,V> parent = p.parent;
 401                     Entry<K,V> ch = p;
 402                     while (parent != null && ch == parent.right) {
 403                         ch = parent;
 404                         parent = parent.parent;
 405                     }
 406                     return parent;
 407                 }
 408             } else
 409                 return p;
 410         }
 411         return null;
 412     }
 413 
 414     /**
 415      * Gets the entry corresponding to the specified key; if no such entry
 416      * exists, returns the entry for the greatest key less than the specified
 417      * key; if no such entry exists, returns <tt>null</tt>.
 418      */
 419     final Entry<K,V> getFloorEntry(K key) {
 420         Entry<K,V> p = root;
 421         while (p != null) {
 422             int cmp = compare(key, p.key);
 423             if (cmp > 0) {
 424                 if (p.right != null)
 425                     p = p.right;
 426                 else
 427                     return p;
 428             } else if (cmp < 0) {
 429                 if (p.left != null) {
 430                     p = p.left;
 431                 } else {
 432                     Entry<K,V> parent = p.parent;
 433                     Entry<K,V> ch = p;
 434                     while (parent != null && ch == parent.left) {
 435                         ch = parent;
 436                         parent = parent.parent;
 437                     }
 438                     return parent;
 439                 }
 440             } else
 441                 return p;
 442 
 443         }
 444         return null;
 445     }
 446 
 447     /**
 448      * Gets the entry for the least key greater than the specified
 449      * key; if no such entry exists, returns the entry for the least
 450      * key greater than the specified key; if no such entry exists
 451      * returns <tt>null</tt>.
 452      */
 453     final Entry<K,V> getHigherEntry(K key) {
 454         Entry<K,V> p = root;
 455         while (p != null) {
 456             int cmp = compare(key, p.key);
 457             if (cmp < 0) {
 458                 if (p.left != null)
 459                     p = p.left;
 460                 else
 461                     return p;
 462             } else {
 463                 if (p.right != null) {
 464                     p = p.right;
 465                 } else {
 466                     Entry<K,V> parent = p.parent;
 467                     Entry<K,V> ch = p;
 468                     while (parent != null && ch == parent.right) {
 469                         ch = parent;
 470                         parent = parent.parent;
 471                     }
 472                     return parent;
 473                 }
 474             }
 475         }
 476         return null;
 477     }
 478 
 479     /**
 480      * Returns the entry for the greatest key less than the specified key; if
 481      * no such entry exists (i.e., the least key in the Tree is greater than
 482      * the specified key), returns <tt>null</tt>.
 483      */
 484     final Entry<K,V> getLowerEntry(K key) {
 485         Entry<K,V> p = root;
 486         while (p != null) {
 487             int cmp = compare(key, p.key);
 488             if (cmp > 0) {
 489                 if (p.right != null)
 490                     p = p.right;
 491                 else
 492                     return p;
 493             } else {
 494                 if (p.left != null) {
 495                     p = p.left;
 496                 } else {
 497                     Entry<K,V> parent = p.parent;
 498                     Entry<K,V> ch = p;
 499                     while (parent != null && ch == parent.left) {
 500                         ch = parent;
 501                         parent = parent.parent;
 502                     }
 503                     return parent;
 504                 }
 505             }
 506         }
 507         return null;
 508     }
 509 
 510     /**
 511      * Associates the specified value with the specified key in this map.
 512      * If the map previously contained a mapping for the key, the old
 513      * value is replaced.
 514      *
 515      * @param key key with which the specified value is to be associated
 516      * @param value value to be associated with the specified key
 517      *
 518      * @return the previous value associated with <tt>key</tt>, or
 519      *         <tt>null</tt> if there was no mapping for <tt>key</tt>.
 520      *         (A <tt>null</tt> return can also indicate that the map
 521      *         previously associated <tt>null</tt> with <tt>key</tt>.)
 522      * @throws ClassCastException if the specified key cannot be compared
 523      *         with the keys currently in the map
 524      * @throws NullPointerException if the specified key is null
 525      *         and this map uses natural ordering, or its comparator
 526      *         does not permit null keys
 527      */
 528     public V put(K key, V value) {
 529         Entry<K,V> t = root;
 530         if (t == null) {
 531             // TBD:
 532             // 5045147: (coll) Adding null to an empty TreeSet should
 533             // throw NullPointerException
 534             //
 535             // compare(key, key); // type check
 536             root = new Entry<K,V>(key, value, null);
 537             size = 1;
 538             modCount++;
 539             return null;
 540         }
 541         int cmp;
 542         Entry<K,V> parent;
 543         // split comparator and comparable paths
 544         Comparator<? super K> cpr = comparator;
 545         if (cpr != null) {
 546             do {
 547                 parent = t;
 548                 cmp = cpr.compare(key, t.key);
 549                 if (cmp < 0)
 550                     t = t.left;
 551                 else if (cmp > 0)
 552                     t = t.right;
 553                 else
 554                     return t.setValue(value);
 555             } while (t != null);
 556         }
 557         else {
 558             if (key == null)
 559                 throw new NullPointerException();
 560             Comparable<? super K> k = (Comparable<? super K>) key;
 561             do {
 562                 parent = t;
 563                 cmp = k.compareTo(t.key);
 564                 if (cmp < 0)
 565                     t = t.left;
 566                 else if (cmp > 0)
 567                     t = t.right;
 568                 else
 569                     return t.setValue(value);
 570             } while (t != null);
 571         }
 572         Entry<K,V> e = new Entry<K,V>(key, value, parent);
 573         if (cmp < 0)
 574             parent.left = e;
 575         else
 576             parent.right = e;
 577         fixAfterInsertion(e);
 578         size++;
 579         modCount++;
 580         return null;
 581     }
 582 
 583     /**
 584      * Removes the mapping for this key from this TreeMap if present.
 585      *
 586      * @param  key key for which mapping should be removed
 587      * @return the previous value associated with <tt>key</tt>, or
 588      *         <tt>null</tt> if there was no mapping for <tt>key</tt>.
 589      *         (A <tt>null</tt> return can also indicate that the map
 590      *         previously associated <tt>null</tt> with <tt>key</tt>.)
 591      * @throws ClassCastException if the specified key cannot be compared
 592      *         with the keys currently in the map
 593      * @throws NullPointerException if the specified key is null
 594      *         and this map uses natural ordering, or its comparator
 595      *         does not permit null keys
 596      */
 597     public V remove(Object key) {
 598         Entry<K,V> p = getEntry(key);
 599         if (p == null)
 600             return null;
 601 
 602         V oldValue = p.value;
 603         deleteEntry(p);
 604         return oldValue;
 605     }
 606 
 607     /**
 608      * Removes all of the mappings from this map.
 609      * The map will be empty after this call returns.
 610      */
 611     public void clear() {
 612         modCount++;
 613         size = 0;
 614         root = null;
 615     }
 616 
 617     /**
 618      * Returns a shallow copy of this <tt>TreeMap</tt> instance. (The keys and
 619      * values themselves are not cloned.)
 620      *
 621      * @return a shallow copy of this map
 622      */
 623     public Object clone() {
 624         TreeMap<K,V> clone = null;
 625         try {
 626             clone = (TreeMap<K,V>) super.clone();
 627         } catch (CloneNotSupportedException e) {
 628             throw new InternalError();
 629         }
 630 
 631         // Put clone into "virgin" state (except for comparator)
 632         clone.root = null;
 633         clone.size = 0;
 634         clone.modCount = 0;
 635         clone.entrySet = null;
 636         clone.navigableKeySet = null;
 637         clone.descendingMap = null;
 638 
 639         // Initialize clone with our mappings
 640         try {
 641             clone.buildFromSorted(size, entrySet().iterator(), null, null);
 642         } catch (java.io.IOException cannotHappen) {
 643         } catch (ClassNotFoundException cannotHappen) {
 644         }
 645 
 646         return clone;
 647     }
 648 
 649     // NavigableMap API methods
 650 
 651     /**
 652      * @since 1.6
 653      */
 654     public Map.Entry<K,V> firstEntry() {
 655         return exportEntry(getFirstEntry());
 656     }
 657 
 658     /**
 659      * @since 1.6
 660      */
 661     public Map.Entry<K,V> lastEntry() {
 662         return exportEntry(getLastEntry());
 663     }
 664 
 665     /**
 666      * @since 1.6
 667      */
 668     public Map.Entry<K,V> pollFirstEntry() {
 669         Entry<K,V> p = getFirstEntry();
 670         Map.Entry<K,V> result = exportEntry(p);
 671         if (p != null)
 672             deleteEntry(p);
 673         return result;
 674     }
 675 
 676     /**
 677      * @since 1.6
 678      */
 679     public Map.Entry<K,V> pollLastEntry() {
 680         Entry<K,V> p = getLastEntry();
 681         Map.Entry<K,V> result = exportEntry(p);
 682         if (p != null)
 683             deleteEntry(p);
 684         return result;
 685     }
 686 
 687     /**
 688      * @throws ClassCastException {@inheritDoc}
 689      * @throws NullPointerException if the specified key is null
 690      *         and this map uses natural ordering, or its comparator
 691      *         does not permit null keys
 692      * @since 1.6
 693      */
 694     public Map.Entry<K,V> lowerEntry(K key) {
 695         return exportEntry(getLowerEntry(key));
 696     }
 697 
 698     /**
 699      * @throws ClassCastException {@inheritDoc}
 700      * @throws NullPointerException if the specified key is null
 701      *         and this map uses natural ordering, or its comparator
 702      *         does not permit null keys
 703      * @since 1.6
 704      */
 705     public K lowerKey(K key) {
 706         return keyOrNull(getLowerEntry(key));
 707     }
 708 
 709     /**
 710      * @throws ClassCastException {@inheritDoc}
 711      * @throws NullPointerException if the specified key is null
 712      *         and this map uses natural ordering, or its comparator
 713      *         does not permit null keys
 714      * @since 1.6
 715      */
 716     public Map.Entry<K,V> floorEntry(K key) {
 717         return exportEntry(getFloorEntry(key));
 718     }
 719 
 720     /**
 721      * @throws ClassCastException {@inheritDoc}
 722      * @throws NullPointerException if the specified key is null
 723      *         and this map uses natural ordering, or its comparator
 724      *         does not permit null keys
 725      * @since 1.6
 726      */
 727     public K floorKey(K key) {
 728         return keyOrNull(getFloorEntry(key));
 729     }
 730 
 731     /**
 732      * @throws ClassCastException {@inheritDoc}
 733      * @throws NullPointerException if the specified key is null
 734      *         and this map uses natural ordering, or its comparator
 735      *         does not permit null keys
 736      * @since 1.6
 737      */
 738     public Map.Entry<K,V> ceilingEntry(K key) {
 739         return exportEntry(getCeilingEntry(key));
 740     }
 741 
 742     /**
 743      * @throws ClassCastException {@inheritDoc}
 744      * @throws NullPointerException if the specified key is null
 745      *         and this map uses natural ordering, or its comparator
 746      *         does not permit null keys
 747      * @since 1.6
 748      */
 749     public K ceilingKey(K key) {
 750         return keyOrNull(getCeilingEntry(key));
 751     }
 752 
 753     /**
 754      * @throws ClassCastException {@inheritDoc}
 755      * @throws NullPointerException if the specified key is null
 756      *         and this map uses natural ordering, or its comparator
 757      *         does not permit null keys
 758      * @since 1.6
 759      */
 760     public Map.Entry<K,V> higherEntry(K key) {
 761         return exportEntry(getHigherEntry(key));
 762     }
 763 
 764     /**
 765      * @throws ClassCastException {@inheritDoc}
 766      * @throws NullPointerException if the specified key is null
 767      *         and this map uses natural ordering, or its comparator
 768      *         does not permit null keys
 769      * @since 1.6
 770      */
 771     public K higherKey(K key) {
 772         return keyOrNull(getHigherEntry(key));
 773     }
 774 
 775     // Views
 776 
 777     /**
 778      * Fields initialized to contain an instance of the entry set view
 779      * the first time this view is requested.  Views are stateless, so
 780      * there's no reason to create more than one.
 781      */
 782     private transient EntrySet entrySet = null;
 783     private transient KeySet<K> navigableKeySet = null;
 784     private transient NavigableMap<K,V> descendingMap = null;
 785 
 786     /**
 787      * Returns a {@link Set} view of the keys contained in this map.
 788      * The set's iterator returns the keys in ascending order.
 789      * The set is backed by the map, so changes to the map are
 790      * reflected in the set, and vice-versa.  If the map is modified
 791      * while an iteration over the set is in progress (except through
 792      * the iterator's own <tt>remove</tt> operation), the results of
 793      * the iteration are undefined.  The set supports element removal,
 794      * which removes the corresponding mapping from the map, via the
 795      * <tt>Iterator.remove</tt>, <tt>Set.remove</tt>,
 796      * <tt>removeAll</tt>, <tt>retainAll</tt>, and <tt>clear</tt>
 797      * operations.  It does not support the <tt>add</tt> or <tt>addAll</tt>
 798      * operations.
 799      */
 800     public Set<K> keySet() {
 801         return navigableKeySet();
 802     }
 803 
 804     /**
 805      * @since 1.6
 806      */
 807     public NavigableSet<K> navigableKeySet() {
 808         KeySet<K> nks = navigableKeySet;
 809         return (nks != null) ? nks : (navigableKeySet = new KeySet(this));
 810     }
 811 
 812     /**
 813      * @since 1.6
 814      */
 815     public NavigableSet<K> descendingKeySet() {
 816         return descendingMap().navigableKeySet();
 817     }
 818 
 819     /**
 820      * Returns a {@link Collection} view of the values contained in this map.
 821      * The collection's iterator returns the values in ascending order
 822      * of the corresponding keys.
 823      * The collection is backed by the map, so changes to the map are
 824      * reflected in the collection, and vice-versa.  If the map is
 825      * modified while an iteration over the collection is in progress
 826      * (except through the iterator's own <tt>remove</tt> operation),
 827      * the results of the iteration are undefined.  The collection
 828      * supports element removal, which removes the corresponding
 829      * mapping from the map, via the <tt>Iterator.remove</tt>,
 830      * <tt>Collection.remove</tt>, <tt>removeAll</tt>,
 831      * <tt>retainAll</tt> and <tt>clear</tt> operations.  It does not
 832      * support the <tt>add</tt> or <tt>addAll</tt> operations.
 833      */
 834     public Collection<V> values() {
 835         Collection<V> vs = values;
 836         return (vs != null) ? vs : (values = new Values());
 837     }
 838 
 839     /**
 840      * Returns a {@link Set} view of the mappings contained in this map.
 841      * The set's iterator returns the entries in ascending key order.
 842      * The set is backed by the map, so changes to the map are
 843      * reflected in the set, and vice-versa.  If the map is modified
 844      * while an iteration over the set is in progress (except through
 845      * the iterator's own <tt>remove</tt> operation, or through the
 846      * <tt>setValue</tt> operation on a map entry returned by the
 847      * iterator) the results of the iteration are undefined.  The set
 848      * supports element removal, which removes the corresponding
 849      * mapping from the map, via the <tt>Iterator.remove</tt>,
 850      * <tt>Set.remove</tt>, <tt>removeAll</tt>, <tt>retainAll</tt> and
 851      * <tt>clear</tt> operations.  It does not support the
 852      * <tt>add</tt> or <tt>addAll</tt> operations.
 853      */
 854     public Set<Map.Entry<K,V>> entrySet() {
 855         EntrySet es = entrySet;
 856         return (es != null) ? es : (entrySet = new EntrySet());
 857     }
 858 
 859     /**
 860      * @since 1.6
 861      */
 862     public NavigableMap<K, V> descendingMap() {
 863         NavigableMap<K, V> km = descendingMap;
 864         return (km != null) ? km :
 865             (descendingMap = new DescendingSubMap(this,
 866                                                   true, null, true,
 867                                                   true, null, true));
 868     }
 869 
 870     /**
 871      * @throws ClassCastException       {@inheritDoc}
 872      * @throws NullPointerException if <tt>fromKey</tt> or <tt>toKey</tt> is
 873      *         null and this map uses natural ordering, or its comparator
 874      *         does not permit null keys
 875      * @throws IllegalArgumentException {@inheritDoc}
 876      * @since 1.6
 877      */
 878     public NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
 879                                     K toKey,   boolean toInclusive) {
 880         return new AscendingSubMap(this,
 881                                    false, fromKey, fromInclusive,
 882                                    false, toKey,   toInclusive);
 883     }
 884 
 885     /**
 886      * @throws ClassCastException       {@inheritDoc}
 887      * @throws NullPointerException if <tt>toKey</tt> is null
 888      *         and this map uses natural ordering, or its comparator
 889      *         does not permit null keys
 890      * @throws IllegalArgumentException {@inheritDoc}
 891      * @since 1.6
 892      */
 893     public NavigableMap<K,V> headMap(K toKey, boolean inclusive) {
 894         return new AscendingSubMap(this,
 895                                    true,  null,  true,
 896                                    false, toKey, inclusive);
 897     }
 898 
 899     /**
 900      * @throws ClassCastException       {@inheritDoc}
 901      * @throws NullPointerException if <tt>fromKey</tt> is null
 902      *         and this map uses natural ordering, or its comparator
 903      *         does not permit null keys
 904      * @throws IllegalArgumentException {@inheritDoc}
 905      * @since 1.6
 906      */
 907     public NavigableMap<K,V> tailMap(K fromKey, boolean inclusive) {
 908         return new AscendingSubMap(this,
 909                                    false, fromKey, inclusive,
 910                                    true,  null,    true);
 911     }
 912 
 913     /**
 914      * @throws ClassCastException       {@inheritDoc}
 915      * @throws NullPointerException if <tt>fromKey</tt> or <tt>toKey</tt> is
 916      *         null and this map uses natural ordering, or its comparator
 917      *         does not permit null keys
 918      * @throws IllegalArgumentException {@inheritDoc}
 919      */
 920     public SortedMap<K,V> subMap(K fromKey, K toKey) {
 921         return subMap(fromKey, true, toKey, false);
 922     }
 923 
 924     /**
 925      * @throws ClassCastException       {@inheritDoc}
 926      * @throws NullPointerException if <tt>toKey</tt> is null
 927      *         and this map uses natural ordering, or its comparator
 928      *         does not permit null keys
 929      * @throws IllegalArgumentException {@inheritDoc}
 930      */
 931     public SortedMap<K,V> headMap(K toKey) {
 932         return headMap(toKey, false);
 933     }
 934 
 935     /**
 936      * @throws ClassCastException       {@inheritDoc}
 937      * @throws NullPointerException if <tt>fromKey</tt> is null
 938      *         and this map uses natural ordering, or its comparator
 939      *         does not permit null keys
 940      * @throws IllegalArgumentException {@inheritDoc}
 941      */
 942     public SortedMap<K,V> tailMap(K fromKey) {
 943         return tailMap(fromKey, true);
 944     }
 945 
 946     // View class support
 947 
 948     class Values extends AbstractCollection<V> {
 949         public Iterator<V> iterator() {
 950             return new ValueIterator(getFirstEntry());
 951         }
 952 
 953         public int size() {
 954             return TreeMap.this.size();
 955         }
 956 
 957         public boolean contains(Object o) {
 958             return TreeMap.this.containsValue(o);
 959         }
 960 
 961         public boolean remove(Object o) {
 962             for (Entry<K,V> e = getFirstEntry(); e != null; e = successor(e)) {
 963                 if (valEquals(e.getValue(), o)) {
 964                     deleteEntry(e);
 965                     return true;
 966                 }
 967             }
 968             return false;
 969         }
 970 
 971         public void clear() {
 972             TreeMap.this.clear();
 973         }
 974     }
 975 
 976     class EntrySet extends AbstractSet<Map.Entry<K,V>> {
 977         public Iterator<Map.Entry<K,V>> iterator() {
 978             return new EntryIterator(getFirstEntry());
 979         }
 980 
 981         public boolean contains(Object o) {
 982             if (!(o instanceof Map.Entry))
 983                 return false;
 984             Map.Entry<K,V> entry = (Map.Entry<K,V>) o;
 985             V value = entry.getValue();
 986             Entry<K,V> p = getEntry(entry.getKey());
 987             return p != null && valEquals(p.getValue(), value);
 988         }
 989 
 990         public boolean remove(Object o) {
 991             if (!(o instanceof Map.Entry))
 992                 return false;
 993             Map.Entry<K,V> entry = (Map.Entry<K,V>) o;
 994             V value = entry.getValue();
 995             Entry<K,V> p = getEntry(entry.getKey());
 996             if (p != null && valEquals(p.getValue(), value)) {
 997                 deleteEntry(p);
 998                 return true;
 999             }
1000             return false;
1001         }
1002 
1003         public int size() {
1004             return TreeMap.this.size();
1005         }
1006 
1007         public void clear() {
1008             TreeMap.this.clear();
1009         }
1010     }
1011 
1012     /*
1013      * Unlike Values and EntrySet, the KeySet class is static,
1014      * delegating to a NavigableMap to allow use by SubMaps, which
1015      * outweighs the ugliness of needing type-tests for the following
1016      * Iterator methods that are defined appropriately in main versus
1017      * submap classes.
1018      */
1019 
1020     Iterator<K> keyIterator() {
1021         return new KeyIterator(getFirstEntry());
1022     }
1023 
1024     Iterator<K> descendingKeyIterator() {
1025         return new DescendingKeyIterator(getLastEntry());
1026     }
1027 
1028     static final class KeySet<E> extends AbstractSet<E> implements NavigableSet<E> {
1029         private final NavigableMap<E, Object> m;
1030         KeySet(NavigableMap<E,Object> map) { m = map; }
1031 
1032         public Iterator<E> iterator() {
1033             if (m instanceof TreeMap)
1034                 return ((TreeMap<E,Object>)m).keyIterator();
1035             else
1036                 return (Iterator<E>)(((TreeMap.NavigableSubMap)m).keyIterator());
1037         }
1038 
1039         public Iterator<E> descendingIterator() {
1040             if (m instanceof TreeMap)
1041                 return ((TreeMap<E,Object>)m).descendingKeyIterator();
1042             else
1043                 return (Iterator<E>)(((TreeMap.NavigableSubMap)m).descendingKeyIterator());
1044         }
1045 
1046         public int size() { return m.size(); }
1047         public boolean isEmpty() { return m.isEmpty(); }
1048         public boolean contains(Object o) { return m.containsKey(o); }
1049         public void clear() { m.clear(); }
1050         public E lower(E e) { return m.lowerKey(e); }
1051         public E floor(E e) { return m.floorKey(e); }
1052         public E ceiling(E e) { return m.ceilingKey(e); }
1053         public E higher(E e) { return m.higherKey(e); }
1054         public E first() { return m.firstKey(); }
1055         public E last() { return m.lastKey(); }
1056         public Comparator<? super E> comparator() { return m.comparator(); }
1057         public E pollFirst() {
1058             Map.Entry<E,Object> e = m.pollFirstEntry();
1059             return e == null? null : e.getKey();
1060         }
1061         public E pollLast() {
1062             Map.Entry<E,Object> e = m.pollLastEntry();
1063             return e == null? null : e.getKey();
1064         }
1065         public boolean remove(Object o) {
1066             int oldSize = size();
1067             m.remove(o);
1068             return size() != oldSize;
1069         }
1070         public NavigableSet<E> subSet(E fromElement, boolean fromInclusive,
1071                                       E toElement,   boolean toInclusive) {
1072             return new KeySet<E>(m.subMap(fromElement, fromInclusive,
1073                                           toElement,   toInclusive));
1074         }
1075         public NavigableSet<E> headSet(E toElement, boolean inclusive) {
1076             return new KeySet<E>(m.headMap(toElement, inclusive));
1077         }
1078         public NavigableSet<E> tailSet(E fromElement, boolean inclusive) {
1079             return new KeySet<E>(m.tailMap(fromElement, inclusive));
1080         }
1081         public SortedSet<E> subSet(E fromElement, E toElement) {
1082             return subSet(fromElement, true, toElement, false);
1083         }
1084         public SortedSet<E> headSet(E toElement) {
1085             return headSet(toElement, false);
1086         }
1087         public SortedSet<E> tailSet(E fromElement) {
1088             return tailSet(fromElement, true);
1089         }
1090         public NavigableSet<E> descendingSet() {
1091             return new KeySet(m.descendingMap());
1092         }
1093     }
1094 
1095     /**
1096      * Base class for TreeMap Iterators
1097      */
1098     abstract class PrivateEntryIterator<T> implements Iterator<T> {
1099         Entry<K,V> next;
1100         Entry<K,V> lastReturned;
1101         int expectedModCount;
1102 
1103         PrivateEntryIterator(Entry<K,V> first) {
1104             expectedModCount = modCount;
1105             lastReturned = null;
1106             next = first;
1107         }
1108 
1109         public final boolean hasNext() {
1110             return next != null;
1111         }
1112 
1113         final Entry<K,V> nextEntry() {
1114             Entry<K,V> e = next;
1115             if (e == null)
1116                 throw new NoSuchElementException();
1117             if (modCount != expectedModCount)
1118                 throw new ConcurrentModificationException();
1119             next = successor(e);
1120             lastReturned = e;
1121             return e;
1122         }
1123 
1124         final Entry<K,V> prevEntry() {
1125             Entry<K,V> e = next;
1126             if (e == null)
1127                 throw new NoSuchElementException();
1128             if (modCount != expectedModCount)
1129                 throw new ConcurrentModificationException();
1130             next = predecessor(e);
1131             lastReturned = e;
1132             return e;
1133         }
1134 
1135         public void remove() {
1136             if (lastReturned == null)
1137                 throw new IllegalStateException();
1138             if (modCount != expectedModCount)
1139                 throw new ConcurrentModificationException();
1140             // deleted entries are replaced by their successors
1141             if (lastReturned.left != null && lastReturned.right != null)
1142                 next = lastReturned;
1143             deleteEntry(lastReturned);
1144             expectedModCount = modCount;
1145             lastReturned = null;
1146         }
1147     }
1148 
1149     final class EntryIterator extends PrivateEntryIterator<Map.Entry<K,V>> {
1150         EntryIterator(Entry<K,V> first) {
1151             super(first);
1152         }
1153         public Map.Entry<K,V> next() {
1154             return nextEntry();
1155         }
1156     }
1157 
1158     final class ValueIterator extends PrivateEntryIterator<V> {
1159         ValueIterator(Entry<K,V> first) {
1160             super(first);
1161         }
1162         public V next() {
1163             return nextEntry().value;
1164         }
1165     }
1166 
1167     final class KeyIterator extends PrivateEntryIterator<K> {
1168         KeyIterator(Entry<K,V> first) {
1169             super(first);
1170         }
1171         public K next() {
1172             return nextEntry().key;
1173         }
1174     }
1175 
1176     final class DescendingKeyIterator extends PrivateEntryIterator<K> {
1177         DescendingKeyIterator(Entry<K,V> first) {
1178             super(first);
1179         }
1180         public K next() {
1181             return prevEntry().key;
1182         }
1183     }
1184 
1185     // Little utilities
1186 
1187     /**
1188      * Compares two keys using the correct comparison method for this TreeMap.
1189      */
1190     final int compare(Object k1, Object k2) {
1191         return comparator==null ? ((Comparable<? super K>)k1).compareTo((K)k2)
1192             : comparator.compare((K)k1, (K)k2);
1193     }
1194 
1195     /**
1196      * Test two values for equality.  Differs from o1.equals(o2) only in
1197      * that it copes with <tt>null</tt> o1 properly.
1198      */
1199     final static boolean valEquals(Object o1, Object o2) {
1200         return (o1==null ? o2==null : o1.equals(o2));
1201     }
1202 
1203     /**
1204      * Return SimpleImmutableEntry for entry, or null if null
1205      */
1206     static <K,V> Map.Entry<K,V> exportEntry(TreeMap.Entry<K,V> e) {
1207         return e == null? null :
1208             new AbstractMap.SimpleImmutableEntry<K,V>(e);
1209     }
1210 
1211     /**
1212      * Return key for entry, or null if null
1213      */
1214     static <K,V> K keyOrNull(TreeMap.Entry<K,V> e) {
1215         return e == null? null : e.key;
1216     }
1217 
1218     /**
1219      * Returns the key corresponding to the specified Entry.
1220      * @throws NoSuchElementException if the Entry is null
1221      */
1222     static <K> K key(Entry<K,?> e) {
1223         if (e==null)
1224             throw new NoSuchElementException();
1225         return e.key;
1226     }
1227 
1228 
1229     // SubMaps
1230 
1231     /**
1232      * Dummy value serving as unmatchable fence key for unbounded
1233      * SubMapIterators
1234      */
1235     private static final Object UNBOUNDED = new Object();
1236 
1237     /**
1238      * @serial include
1239      */
1240     static abstract class NavigableSubMap<K,V> extends AbstractMap<K,V>
1241         implements NavigableMap<K,V>, java.io.Serializable {
1242         /**
1243          * The backing map.
1244          */
1245         final TreeMap<K,V> m;
1246 
1247         /**
1248          * Endpoints are represented as triples (fromStart, lo,
1249          * loInclusive) and (toEnd, hi, hiInclusive). If fromStart is
1250          * true, then the low (absolute) bound is the start of the
1251          * backing map, and the other values are ignored. Otherwise,
1252          * if loInclusive is true, lo is the inclusive bound, else lo
1253          * is the exclusive bound. Similarly for the upper bound.
1254          */
1255         final K lo, hi;
1256         final boolean fromStart, toEnd;
1257         final boolean loInclusive, hiInclusive;
1258 
1259         NavigableSubMap(TreeMap<K,V> m,
1260                         boolean fromStart, K lo, boolean loInclusive,
1261                         boolean toEnd,     K hi, boolean hiInclusive) {
1262             if (!fromStart && !toEnd) {
1263                 if (m.compare(lo, hi) > 0)
1264                     throw new IllegalArgumentException("fromKey > toKey");
1265             } else {
1266                 if (!fromStart) // type check
1267                     m.compare(lo, lo);
1268                 if (!toEnd)
1269                     m.compare(hi, hi);
1270             }
1271 
1272             this.m = m;
1273             this.fromStart = fromStart;
1274             this.lo = lo;
1275             this.loInclusive = loInclusive;
1276             this.toEnd = toEnd;
1277             this.hi = hi;
1278             this.hiInclusive = hiInclusive;
1279         }
1280 
1281         // internal utilities
1282 
1283         final boolean tooLow(Object key) {
1284             if (!fromStart) {
1285                 int c = m.compare(key, lo);
1286                 if (c < 0 || (c == 0 && !loInclusive))
1287                     return true;
1288             }
1289             return false;
1290         }
1291 
1292         final boolean tooHigh(Object key) {
1293             if (!toEnd) {
1294                 int c = m.compare(key, hi);
1295                 if (c > 0 || (c == 0 && !hiInclusive))
1296                     return true;
1297             }
1298             return false;
1299         }
1300 
1301         final boolean inRange(Object key) {
1302             return !tooLow(key) && !tooHigh(key);
1303         }
1304 
1305         final boolean inClosedRange(Object key) {
1306             return (fromStart || m.compare(key, lo) >= 0)
1307                 && (toEnd || m.compare(hi, key) >= 0);
1308         }
1309 
1310         final boolean inRange(Object key, boolean inclusive) {
1311             return inclusive ? inRange(key) : inClosedRange(key);
1312         }
1313 
1314         /*
1315          * Absolute versions of relation operations.
1316          * Subclasses map to these using like-named "sub"
1317          * versions that invert senses for descending maps
1318          */
1319 
1320         final TreeMap.Entry<K,V> absLowest() {
1321             TreeMap.Entry<K,V> e =
1322                 (fromStart ?  m.getFirstEntry() :
1323                  (loInclusive ? m.getCeilingEntry(lo) :
1324                                 m.getHigherEntry(lo)));
1325             return (e == null || tooHigh(e.key)) ? null : e;
1326         }
1327 
1328         final TreeMap.Entry<K,V> absHighest() {
1329             TreeMap.Entry<K,V> e =
1330                 (toEnd ?  m.getLastEntry() :
1331                  (hiInclusive ?  m.getFloorEntry(hi) :
1332                                  m.getLowerEntry(hi)));
1333             return (e == null || tooLow(e.key)) ? null : e;
1334         }
1335 
1336         final TreeMap.Entry<K,V> absCeiling(K key) {
1337             if (tooLow(key))
1338                 return absLowest();
1339             TreeMap.Entry<K,V> e = m.getCeilingEntry(key);
1340             return (e == null || tooHigh(e.key)) ? null : e;
1341         }
1342 
1343         final TreeMap.Entry<K,V> absHigher(K key) {
1344             if (tooLow(key))
1345                 return absLowest();
1346             TreeMap.Entry<K,V> e = m.getHigherEntry(key);
1347             return (e == null || tooHigh(e.key)) ? null : e;
1348         }
1349 
1350         final TreeMap.Entry<K,V> absFloor(K key) {
1351             if (tooHigh(key))
1352                 return absHighest();
1353             TreeMap.Entry<K,V> e = m.getFloorEntry(key);
1354             return (e == null || tooLow(e.key)) ? null : e;
1355         }
1356 
1357         final TreeMap.Entry<K,V> absLower(K key) {
1358             if (tooHigh(key))
1359                 return absHighest();
1360             TreeMap.Entry<K,V> e = m.getLowerEntry(key);
1361             return (e == null || tooLow(e.key)) ? null : e;
1362         }
1363 
1364         /** Returns the absolute high fence for ascending traversal */
1365         final TreeMap.Entry<K,V> absHighFence() {
1366             return (toEnd ? null : (hiInclusive ?
1367                                     m.getHigherEntry(hi) :
1368                                     m.getCeilingEntry(hi)));
1369         }
1370 
1371         /** Return the absolute low fence for descending traversal  */
1372         final TreeMap.Entry<K,V> absLowFence() {
1373             return (fromStart ? null : (loInclusive ?
1374                                         m.getLowerEntry(lo) :
1375                                         m.getFloorEntry(lo)));
1376         }
1377 
1378         // Abstract methods defined in ascending vs descending classes
1379         // These relay to the appropriate absolute versions
1380 
1381         abstract TreeMap.Entry<K,V> subLowest();
1382         abstract TreeMap.Entry<K,V> subHighest();
1383         abstract TreeMap.Entry<K,V> subCeiling(K key);
1384         abstract TreeMap.Entry<K,V> subHigher(K key);
1385         abstract TreeMap.Entry<K,V> subFloor(K key);
1386         abstract TreeMap.Entry<K,V> subLower(K key);
1387 
1388         /** Returns ascending iterator from the perspective of this submap */
1389         abstract Iterator<K> keyIterator();
1390 
1391         /** Returns descending iterator from the perspective of this submap */
1392         abstract Iterator<K> descendingKeyIterator();
1393 
1394         // public methods
1395 
1396         public boolean isEmpty() {
1397             return (fromStart && toEnd) ? m.isEmpty() : entrySet().isEmpty();
1398         }
1399 
1400         public int size() {
1401             return (fromStart && toEnd) ? m.size() : entrySet().size();
1402         }
1403 
1404         public final boolean containsKey(Object key) {
1405             return inRange(key) && m.containsKey(key);
1406         }
1407 
1408         public final V put(K key, V value) {
1409             if (!inRange(key))
1410                 throw new IllegalArgumentException("key out of range");
1411             return m.put(key, value);
1412         }
1413 
1414         public final V get(Object key) {
1415             return !inRange(key)? null :  m.get(key);
1416         }
1417 
1418         public final V remove(Object key) {
1419             return !inRange(key)? null  : m.remove(key);
1420         }
1421 
1422         public final Map.Entry<K,V> ceilingEntry(K key) {
1423             return exportEntry(subCeiling(key));
1424         }
1425 
1426         public final K ceilingKey(K key) {
1427             return keyOrNull(subCeiling(key));
1428         }
1429 
1430         public final Map.Entry<K,V> higherEntry(K key) {
1431             return exportEntry(subHigher(key));
1432         }
1433 
1434         public final K higherKey(K key) {
1435             return keyOrNull(subHigher(key));
1436         }
1437 
1438         public final Map.Entry<K,V> floorEntry(K key) {
1439             return exportEntry(subFloor(key));
1440         }
1441 
1442         public final K floorKey(K key) {
1443             return keyOrNull(subFloor(key));
1444         }
1445 
1446         public final Map.Entry<K,V> lowerEntry(K key) {
1447             return exportEntry(subLower(key));
1448         }
1449 
1450         public final K lowerKey(K key) {
1451             return keyOrNull(subLower(key));
1452         }
1453 
1454         public final K firstKey() {
1455             return key(subLowest());
1456         }
1457 
1458         public final K lastKey() {
1459             return key(subHighest());
1460         }
1461 
1462         public final Map.Entry<K,V> firstEntry() {
1463             return exportEntry(subLowest());
1464         }
1465 
1466         public final Map.Entry<K,V> lastEntry() {
1467             return exportEntry(subHighest());
1468         }
1469 
1470         public final Map.Entry<K,V> pollFirstEntry() {
1471             TreeMap.Entry<K,V> e = subLowest();
1472             Map.Entry<K,V> result = exportEntry(e);
1473             if (e != null)
1474                 m.deleteEntry(e);
1475             return result;
1476         }
1477 
1478         public final Map.Entry<K,V> pollLastEntry() {
1479             TreeMap.Entry<K,V> e = subHighest();
1480             Map.Entry<K,V> result = exportEntry(e);
1481             if (e != null)
1482                 m.deleteEntry(e);
1483             return result;
1484         }
1485 
1486         // Views
1487         transient NavigableMap<K,V> descendingMapView = null;
1488         transient EntrySetView entrySetView = null;
1489         transient KeySet<K> navigableKeySetView = null;
1490 
1491         public final NavigableSet<K> navigableKeySet() {
1492             KeySet<K> nksv = navigableKeySetView;
1493             return (nksv != null) ? nksv :
1494                 (navigableKeySetView = new TreeMap.KeySet(this));
1495         }
1496 
1497         public final Set<K> keySet() {
1498             return navigableKeySet();
1499         }
1500 
1501         public NavigableSet<K> descendingKeySet() {
1502             return descendingMap().navigableKeySet();
1503         }
1504 
1505         public final SortedMap<K,V> subMap(K fromKey, K toKey) {
1506             return subMap(fromKey, true, toKey, false);
1507         }
1508 
1509         public final SortedMap<K,V> headMap(K toKey) {
1510             return headMap(toKey, false);
1511         }
1512 
1513         public final SortedMap<K,V> tailMap(K fromKey) {
1514             return tailMap(fromKey, true);
1515         }
1516 
1517         // View classes
1518 
1519         abstract class EntrySetView extends AbstractSet<Map.Entry<K,V>> {
1520             private transient int size = -1, sizeModCount;
1521 
1522             public int size() {
1523                 if (fromStart && toEnd)
1524                     return m.size();
1525                 if (size == -1 || sizeModCount != m.modCount) {
1526                     sizeModCount = m.modCount;
1527                     size = 0;
1528                     Iterator i = iterator();
1529                     while (i.hasNext()) {
1530                         size++;
1531                         i.next();
1532                     }
1533                 }
1534                 return size;
1535             }
1536 
1537             public boolean isEmpty() {
1538                 TreeMap.Entry<K,V> n = absLowest();
1539                 return n == null || tooHigh(n.key);
1540             }
1541 
1542             public boolean contains(Object o) {
1543                 if (!(o instanceof Map.Entry))
1544                     return false;
1545                 Map.Entry<K,V> entry = (Map.Entry<K,V>) o;
1546                 K key = entry.getKey();
1547                 if (!inRange(key))
1548                     return false;
1549                 TreeMap.Entry node = m.getEntry(key);
1550                 return node != null &&
1551                     valEquals(node.getValue(), entry.getValue());
1552             }
1553 
1554             public boolean remove(Object o) {
1555                 if (!(o instanceof Map.Entry))
1556                     return false;
1557                 Map.Entry<K,V> entry = (Map.Entry<K,V>) o;
1558                 K key = entry.getKey();
1559                 if (!inRange(key))
1560                     return false;
1561                 TreeMap.Entry<K,V> node = m.getEntry(key);
1562                 if (node!=null && valEquals(node.getValue(),entry.getValue())){
1563                     m.deleteEntry(node);
1564                     return true;
1565                 }
1566                 return false;
1567             }
1568         }
1569 
1570         /**
1571          * Iterators for SubMaps
1572          */
1573         abstract class SubMapIterator<T> implements Iterator<T> {
1574             TreeMap.Entry<K,V> lastReturned;
1575             TreeMap.Entry<K,V> next;
1576             final Object fenceKey;
1577             int expectedModCount;
1578 
1579             SubMapIterator(TreeMap.Entry<K,V> first,
1580                            TreeMap.Entry<K,V> fence) {
1581                 expectedModCount = m.modCount;
1582                 lastReturned = null;
1583                 next = first;
1584                 fenceKey = fence == null ? UNBOUNDED : fence.key;
1585             }
1586 
1587             public final boolean hasNext() {
1588                 return next != null && next.key != fenceKey;
1589             }
1590 
1591             final TreeMap.Entry<K,V> nextEntry() {
1592                 TreeMap.Entry<K,V> e = next;
1593                 if (e == null || e.key == fenceKey)
1594                     throw new NoSuchElementException();
1595                 if (m.modCount != expectedModCount)
1596                     throw new ConcurrentModificationException();
1597                 next = successor(e);
1598                 lastReturned = e;
1599                 return e;
1600             }
1601 
1602             final TreeMap.Entry<K,V> prevEntry() {
1603                 TreeMap.Entry<K,V> e = next;
1604                 if (e == null || e.key == fenceKey)
1605                     throw new NoSuchElementException();
1606                 if (m.modCount != expectedModCount)
1607                     throw new ConcurrentModificationException();
1608                 next = predecessor(e);
1609                 lastReturned = e;
1610                 return e;
1611             }
1612 
1613             final void removeAscending() {
1614                 if (lastReturned == null)
1615                     throw new IllegalStateException();
1616                 if (m.modCount != expectedModCount)
1617                     throw new ConcurrentModificationException();
1618                 // deleted entries are replaced by their successors
1619                 if (lastReturned.left != null && lastReturned.right != null)
1620                     next = lastReturned;
1621                 m.deleteEntry(lastReturned);
1622                 lastReturned = null;
1623                 expectedModCount = m.modCount;
1624             }
1625 
1626             final void removeDescending() {
1627                 if (lastReturned == null)
1628                     throw new IllegalStateException();
1629                 if (m.modCount != expectedModCount)
1630                     throw new ConcurrentModificationException();
1631                 m.deleteEntry(lastReturned);
1632                 lastReturned = null;
1633                 expectedModCount = m.modCount;
1634             }
1635 
1636         }
1637 
1638         final class SubMapEntryIterator extends SubMapIterator<Map.Entry<K,V>> {
1639             SubMapEntryIterator(TreeMap.Entry<K,V> first,
1640                                 TreeMap.Entry<K,V> fence) {
1641                 super(first, fence);
1642             }
1643             public Map.Entry<K,V> next() {
1644                 return nextEntry();
1645             }
1646             public void remove() {
1647                 removeAscending();
1648             }
1649         }
1650 
1651         final class SubMapKeyIterator extends SubMapIterator<K> {
1652             SubMapKeyIterator(TreeMap.Entry<K,V> first,
1653                               TreeMap.Entry<K,V> fence) {
1654                 super(first, fence);
1655             }
1656             public K next() {
1657                 return nextEntry().key;
1658             }
1659             public void remove() {
1660                 removeAscending();
1661             }
1662         }
1663 
1664         final class DescendingSubMapEntryIterator extends SubMapIterator<Map.Entry<K,V>> {
1665             DescendingSubMapEntryIterator(TreeMap.Entry<K,V> last,
1666                                           TreeMap.Entry<K,V> fence) {
1667                 super(last, fence);
1668             }
1669 
1670             public Map.Entry<K,V> next() {
1671                 return prevEntry();
1672             }
1673             public void remove() {
1674                 removeDescending();
1675             }
1676         }
1677 
1678         final class DescendingSubMapKeyIterator extends SubMapIterator<K> {
1679             DescendingSubMapKeyIterator(TreeMap.Entry<K,V> last,
1680                                         TreeMap.Entry<K,V> fence) {
1681                 super(last, fence);
1682             }
1683             public K next() {
1684                 return prevEntry().key;
1685             }
1686             public void remove() {
1687                 removeDescending();
1688             }
1689         }
1690     }
1691 
1692     /**
1693      * @serial include
1694      */
1695     static final class AscendingSubMap<K,V> extends NavigableSubMap<K,V> {
1696         private static final long serialVersionUID = 912986545866124060L;
1697 
1698         AscendingSubMap(TreeMap<K,V> m,
1699                         boolean fromStart, K lo, boolean loInclusive,
1700                         boolean toEnd,     K hi, boolean hiInclusive) {
1701             super(m, fromStart, lo, loInclusive, toEnd, hi, hiInclusive);
1702         }
1703 
1704         public Comparator<? super K> comparator() {
1705             return m.comparator();
1706         }
1707 
1708         public NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
1709                                         K toKey,   boolean toInclusive) {
1710             if (!inRange(fromKey, fromInclusive))
1711                 throw new IllegalArgumentException("fromKey out of range");
1712             if (!inRange(toKey, toInclusive))
1713                 throw new IllegalArgumentException("toKey out of range");
1714             return new AscendingSubMap(m,
1715                                        false, fromKey, fromInclusive,
1716                                        false, toKey,   toInclusive);
1717         }
1718 
1719         public NavigableMap<K,V> headMap(K toKey, boolean inclusive) {
1720             if (!inRange(toKey, inclusive))
1721                 throw new IllegalArgumentException("toKey out of range");
1722             return new AscendingSubMap(m,
1723                                        fromStart, lo,    loInclusive,
1724                                        false,     toKey, inclusive);
1725         }
1726 
1727         public NavigableMap<K,V> tailMap(K fromKey, boolean inclusive){
1728             if (!inRange(fromKey, inclusive))
1729                 throw new IllegalArgumentException("fromKey out of range");
1730             return new AscendingSubMap(m,
1731                                        false, fromKey, inclusive,
1732                                        toEnd, hi,      hiInclusive);
1733         }
1734 
1735         public NavigableMap<K,V> descendingMap() {
1736             NavigableMap<K,V> mv = descendingMapView;
1737             return (mv != null) ? mv :
1738                 (descendingMapView =
1739                  new DescendingSubMap(m,
1740                                       fromStart, lo, loInclusive,
1741                                       toEnd,     hi, hiInclusive));
1742         }
1743 
1744         Iterator<K> keyIterator() {
1745             return new SubMapKeyIterator(absLowest(), absHighFence());
1746         }
1747 
1748         Iterator<K> descendingKeyIterator() {
1749             return new DescendingSubMapKeyIterator(absHighest(), absLowFence());
1750         }
1751 
1752         final class AscendingEntrySetView extends EntrySetView {
1753             public Iterator<Map.Entry<K,V>> iterator() {
1754                 return new SubMapEntryIterator(absLowest(), absHighFence());
1755             }
1756         }
1757 
1758         public Set<Map.Entry<K,V>> entrySet() {
1759             EntrySetView es = entrySetView;
1760             return (es != null) ? es : new AscendingEntrySetView();
1761         }
1762 
1763         TreeMap.Entry<K,V> subLowest()       { return absLowest(); }
1764         TreeMap.Entry<K,V> subHighest()      { return absHighest(); }
1765         TreeMap.Entry<K,V> subCeiling(K key) { return absCeiling(key); }
1766         TreeMap.Entry<K,V> subHigher(K key)  { return absHigher(key); }
1767         TreeMap.Entry<K,V> subFloor(K key)   { return absFloor(key); }
1768         TreeMap.Entry<K,V> subLower(K key)   { return absLower(key); }
1769     }
1770 
1771     /**
1772      * @serial include
1773      */
1774     static final class DescendingSubMap<K,V>  extends NavigableSubMap<K,V> {
1775         private static final long serialVersionUID = 912986545866120460L;
1776         DescendingSubMap(TreeMap<K,V> m,
1777                         boolean fromStart, K lo, boolean loInclusive,
1778                         boolean toEnd,     K hi, boolean hiInclusive) {
1779             super(m, fromStart, lo, loInclusive, toEnd, hi, hiInclusive);
1780         }
1781 
1782         private final Comparator<? super K> reverseComparator =
1783             Collections.reverseOrder(m.comparator);
1784 
1785         public Comparator<? super K> comparator() {
1786             return reverseComparator;
1787         }
1788 
1789         public NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
1790                                         K toKey,   boolean toInclusive) {
1791             if (!inRange(fromKey, fromInclusive))
1792                 throw new IllegalArgumentException("fromKey out of range");
1793             if (!inRange(toKey, toInclusive))
1794                 throw new IllegalArgumentException("toKey out of range");
1795             return new DescendingSubMap(m,
1796                                         false, toKey,   toInclusive,
1797                                         false, fromKey, fromInclusive);
1798         }
1799 
1800         public NavigableMap<K,V> headMap(K toKey, boolean inclusive) {
1801             if (!inRange(toKey, inclusive))
1802                 throw new IllegalArgumentException("toKey out of range");
1803             return new DescendingSubMap(m,
1804                                         false, toKey, inclusive,
1805                                         toEnd, hi,    hiInclusive);
1806         }
1807 
1808         public NavigableMap<K,V> tailMap(K fromKey, boolean inclusive){
1809             if (!inRange(fromKey, inclusive))
1810                 throw new IllegalArgumentException("fromKey out of range");
1811             return new DescendingSubMap(m,
1812                                         fromStart, lo, loInclusive,
1813                                         false, fromKey, inclusive);
1814         }
1815 
1816         public NavigableMap<K,V> descendingMap() {
1817             NavigableMap<K,V> mv = descendingMapView;
1818             return (mv != null) ? mv :
1819                 (descendingMapView =
1820                  new AscendingSubMap(m,
1821                                      fromStart, lo, loInclusive,
1822                                      toEnd,     hi, hiInclusive));
1823         }
1824 
1825         Iterator<K> keyIterator() {
1826             return new DescendingSubMapKeyIterator(absHighest(), absLowFence());
1827         }
1828 
1829         Iterator<K> descendingKeyIterator() {
1830             return new SubMapKeyIterator(absLowest(), absHighFence());
1831         }
1832 
1833         final class DescendingEntrySetView extends EntrySetView {
1834             public Iterator<Map.Entry<K,V>> iterator() {
1835                 return new DescendingSubMapEntryIterator(absHighest(), absLowFence());
1836             }
1837         }
1838 
1839         public Set<Map.Entry<K,V>> entrySet() {
1840             EntrySetView es = entrySetView;
1841             return (es != null) ? es : new DescendingEntrySetView();
1842         }
1843 
1844         TreeMap.Entry<K,V> subLowest()       { return absHighest(); }
1845         TreeMap.Entry<K,V> subHighest()      { return absLowest(); }
1846         TreeMap.Entry<K,V> subCeiling(K key) { return absFloor(key); }
1847         TreeMap.Entry<K,V> subHigher(K key)  { return absLower(key); }
1848         TreeMap.Entry<K,V> subFloor(K key)   { return absCeiling(key); }
1849         TreeMap.Entry<K,V> subLower(K key)   { return absHigher(key); }
1850     }
1851 
1852     /**
1853      * This class exists solely for the sake of serialization
1854      * compatibility with previous releases of TreeMap that did not
1855      * support NavigableMap.  It translates an old-version SubMap into
1856      * a new-version AscendingSubMap. This class is never otherwise
1857      * used.
1858      *
1859      * @serial include
1860      */
1861     private class SubMap extends AbstractMap<K,V>
1862         implements SortedMap<K,V>, java.io.Serializable {
1863         private static final long serialVersionUID = -6520786458950516097L;
1864         private boolean fromStart = false, toEnd = false;
1865         private K fromKey, toKey;
1866         private Object readResolve() {
1867             return new AscendingSubMap(TreeMap.this,
1868                                        fromStart, fromKey, true,
1869                                        toEnd, toKey, false);
1870         }
1871         public Set<Map.Entry<K,V>> entrySet() { throw new InternalError(); }
1872         public K lastKey() { throw new InternalError(); }
1873         public K firstKey() { throw new InternalError(); }
1874         public SortedMap<K,V> subMap(K fromKey, K toKey) { throw new InternalError(); }
1875         public SortedMap<K,V> headMap(K toKey) { throw new InternalError(); }
1876         public SortedMap<K,V> tailMap(K fromKey) { throw new InternalError(); }
1877         public Comparator<? super K> comparator() { throw new InternalError(); }
1878     }
1879 
1880 
1881     // Red-black mechanics
1882 
1883     private static final boolean RED   = false;
1884     private static final boolean BLACK = true;
1885 
1886     /**
1887      * Node in the Tree.  Doubles as a means to pass key-value pairs back to
1888      * user (see Map.Entry).
1889      */
1890 
1891     static final class Entry<K,V> implements Map.Entry<K,V> {
1892         K key;
1893         V value;
1894         Entry<K,V> left = null;
1895         Entry<K,V> right = null;
1896         Entry<K,V> parent;
1897         boolean color = BLACK;
1898 
1899         /**
1900          * Make a new cell with given key, value, and parent, and with
1901          * <tt>null</tt> child links, and BLACK color.
1902          */
1903         Entry(K key, V value, Entry<K,V> parent) {
1904             this.key = key;
1905             this.value = value;
1906             this.parent = parent;
1907         }
1908 
1909         /**
1910          * Returns the key.
1911          *
1912          * @return the key
1913          */
1914         public K getKey() {
1915             return key;
1916         }
1917 
1918         /**
1919          * Returns the value associated with the key.
1920          *
1921          * @return the value associated with the key
1922          */
1923         public V getValue() {
1924             return value;
1925         }
1926 
1927         /**
1928          * Replaces the value currently associated with the key with the given
1929          * value.
1930          *
1931          * @return the value associated with the key before this method was
1932          *         called
1933          */
1934         public V setValue(V value) {
1935             V oldValue = this.value;
1936             this.value = value;
1937             return oldValue;
1938         }
1939 
1940         public boolean equals(Object o) {
1941             if (!(o instanceof Map.Entry))
1942                 return false;
1943             Map.Entry<?,?> e = (Map.Entry<?,?>)o;
1944 
1945             return valEquals(key,e.getKey()) && valEquals(value,e.getValue());
1946         }
1947 
1948         public int hashCode() {
1949             int keyHash = (key==null ? 0 : key.hashCode());
1950             int valueHash = (value==null ? 0 : value.hashCode());
1951             return keyHash ^ valueHash;
1952         }
1953 
1954         public String toString() {
1955             return key + "=" + value;
1956         }
1957     }
1958 
1959     /**
1960      * Returns the first Entry in the TreeMap (according to the TreeMap's
1961      * key-sort function).  Returns null if the TreeMap is empty.
1962      */
1963     final Entry<K,V> getFirstEntry() {
1964         Entry<K,V> p = root;
1965         if (p != null)
1966             while (p.left != null)
1967                 p = p.left;
1968         return p;
1969     }
1970 
1971     /**
1972      * Returns the last Entry in the TreeMap (according to the TreeMap's
1973      * key-sort function).  Returns null if the TreeMap is empty.
1974      */
1975     final Entry<K,V> getLastEntry() {
1976         Entry<K,V> p = root;
1977         if (p != null)
1978             while (p.right != null)
1979                 p = p.right;
1980         return p;
1981     }
1982 
1983     /**
1984      * Returns the successor of the specified Entry, or null if no such.
1985      */
1986     static <K,V> TreeMap.Entry<K,V> successor(Entry<K,V> t) {
1987         if (t == null)
1988             return null;
1989         else if (t.right != null) {
1990             Entry<K,V> p = t.right;
1991             while (p.left != null)
1992                 p = p.left;
1993             return p;
1994         } else {
1995             Entry<K,V> p = t.parent;
1996             Entry<K,V> ch = t;
1997             while (p != null && ch == p.right) {
1998                 ch = p;
1999                 p = p.parent;
2000             }
2001             return p;
2002         }
2003     }
2004 
2005     /**
2006      * Returns the predecessor of the specified Entry, or null if no such.
2007      */
2008     static <K,V> Entry<K,V> predecessor(Entry<K,V> t) {
2009         if (t == null)
2010             return null;
2011         else if (t.left != null) {
2012             Entry<K,V> p = t.left;
2013             while (p.right != null)
2014                 p = p.right;
2015             return p;
2016         } else {
2017             Entry<K,V> p = t.parent;
2018             Entry<K,V> ch = t;
2019             while (p != null && ch == p.left) {
2020                 ch = p;
2021                 p = p.parent;
2022             }
2023             return p;
2024         }
2025     }
2026 
2027     /**
2028      * Balancing operations.
2029      *
2030      * Implementations of rebalancings during insertion and deletion are
2031      * slightly different than the CLR version.  Rather than using dummy
2032      * nilnodes, we use a set of accessors that deal properly with null.  They
2033      * are used to avoid messiness surrounding nullness checks in the main
2034      * algorithms.
2035      */
2036 
2037     private static <K,V> boolean colorOf(Entry<K,V> p) {
2038         return (p == null ? BLACK : p.color);
2039     }
2040 
2041     private static <K,V> Entry<K,V> parentOf(Entry<K,V> p) {
2042         return (p == null ? null: p.parent);
2043     }
2044 
2045     private static <K,V> void setColor(Entry<K,V> p, boolean c) {
2046         if (p != null)
2047             p.color = c;
2048     }
2049 
2050     private static <K,V> Entry<K,V> leftOf(Entry<K,V> p) {
2051         return (p == null) ? null: p.left;
2052     }
2053 
2054     private static <K,V> Entry<K,V> rightOf(Entry<K,V> p) {
2055         return (p == null) ? null: p.right;
2056     }
2057 
2058     /** From CLR */
2059     private void rotateLeft(Entry<K,V> p) {
2060         if (p != null) {
2061             Entry<K,V> r = p.right;
2062             p.right = r.left;
2063             if (r.left != null)
2064                 r.left.parent = p;
2065             r.parent = p.parent;
2066             if (p.parent == null)
2067                 root = r;
2068             else if (p.parent.left == p)
2069                 p.parent.left = r;
2070             else
2071                 p.parent.right = r;
2072             r.left = p;
2073             p.parent = r;
2074         }
2075     }
2076 
2077     /** From CLR */
2078     private void rotateRight(Entry<K,V> p) {
2079         if (p != null) {
2080             Entry<K,V> l = p.left;
2081             p.left = l.right;
2082             if (l.right != null) l.right.parent = p;
2083             l.parent = p.parent;
2084             if (p.parent == null)
2085                 root = l;
2086             else if (p.parent.right == p)
2087                 p.parent.right = l;
2088             else p.parent.left = l;
2089             l.right = p;
2090             p.parent = l;
2091         }
2092     }
2093 
2094     /** From CLR */
2095     private void fixAfterInsertion(Entry<K,V> x) {
2096         x.color = RED;
2097 
2098         while (x != null && x != root && x.parent.color == RED) {
2099             if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {
2100                 Entry<K,V> y = rightOf(parentOf(parentOf(x)));
2101                 if (colorOf(y) == RED) {
2102                     setColor(parentOf(x), BLACK);
2103                     setColor(y, BLACK);
2104                     setColor(parentOf(parentOf(x)), RED);
2105                     x = parentOf(parentOf(x));
2106                 } else {
2107                     if (x == rightOf(parentOf(x))) {
2108                         x = parentOf(x);
2109                         rotateLeft(x);
2110                     }
2111                     setColor(parentOf(x), BLACK);
2112                     setColor(parentOf(parentOf(x)), RED);
2113                     rotateRight(parentOf(parentOf(x)));
2114                 }
2115             } else {
2116                 Entry<K,V> y = leftOf(parentOf(parentOf(x)));
2117                 if (colorOf(y) == RED) {
2118                     setColor(parentOf(x), BLACK);
2119                     setColor(y, BLACK);
2120                     setColor(parentOf(parentOf(x)), RED);
2121                     x = parentOf(parentOf(x));
2122                 } else {
2123                     if (x == leftOf(parentOf(x))) {
2124                         x = parentOf(x);
2125                         rotateRight(x);
2126                     }
2127                     setColor(parentOf(x), BLACK);
2128                     setColor(parentOf(parentOf(x)), RED);
2129                     rotateLeft(parentOf(parentOf(x)));
2130                 }
2131             }
2132         }
2133         root.color = BLACK;
2134     }
2135 
2136     /**
2137      * Delete node p, and then rebalance the tree.
2138      */
2139     private void deleteEntry(Entry<K,V> p) {
2140         modCount++;
2141         size--;
2142 
2143         // If strictly internal, copy successor's element to p and then make p
2144         // point to successor.
2145         if (p.left != null && p.right != null) {
2146             Entry<K,V> s = successor (p);
2147             p.key = s.key;
2148             p.value = s.value;
2149             p = s;
2150         } // p has 2 children
2151 
2152         // Start fixup at replacement node, if it exists.
2153         Entry<K,V> replacement = (p.left != null ? p.left : p.right);
2154 
2155         if (replacement != null) {
2156             // Link replacement to parent
2157             replacement.parent = p.parent;
2158             if (p.parent == null)
2159                 root = replacement;
2160             else if (p == p.parent.left)
2161                 p.parent.left  = replacement;
2162             else
2163                 p.parent.right = replacement;
2164 
2165             // Null out links so they are OK to use by fixAfterDeletion.
2166             p.left = p.right = p.parent = null;
2167 
2168             // Fix replacement
2169             if (p.color == BLACK)
2170                 fixAfterDeletion(replacement);
2171         } else if (p.parent == null) { // return if we are the only node.
2172             root = null;
2173         } else { //  No children. Use self as phantom replacement and unlink.
2174             if (p.color == BLACK)
2175                 fixAfterDeletion(p);
2176 
2177             if (p.parent != null) {
2178                 if (p == p.parent.left)
2179                     p.parent.left = null;
2180                 else if (p == p.parent.right)
2181                     p.parent.right = null;
2182                 p.parent = null;
2183             }
2184         }
2185     }
2186 
2187     /** From CLR */
2188     private void fixAfterDeletion(Entry<K,V> x) {
2189         while (x != root && colorOf(x) == BLACK) {
2190             if (x == leftOf(parentOf(x))) {
2191                 Entry<K,V> sib = rightOf(parentOf(x));
2192 
2193                 if (colorOf(sib) == RED) {
2194                     setColor(sib, BLACK);
2195                     setColor(parentOf(x), RED);
2196                     rotateLeft(parentOf(x));
2197                     sib = rightOf(parentOf(x));
2198                 }
2199 
2200                 if (colorOf(leftOf(sib))  == BLACK &&
2201                     colorOf(rightOf(sib)) == BLACK) {
2202                     setColor(sib, RED);
2203                     x = parentOf(x);
2204                 } else {
2205                     if (colorOf(rightOf(sib)) == BLACK) {
2206                         setColor(leftOf(sib), BLACK);
2207                         setColor(sib, RED);
2208                         rotateRight(sib);
2209                         sib = rightOf(parentOf(x));
2210                     }
2211                     setColor(sib, colorOf(parentOf(x)));
2212                     setColor(parentOf(x), BLACK);
2213                     setColor(rightOf(sib), BLACK);
2214                     rotateLeft(parentOf(x));
2215                     x = root;
2216                 }
2217             } else { // symmetric
2218                 Entry<K,V> sib = leftOf(parentOf(x));
2219 
2220                 if (colorOf(sib) == RED) {
2221                     setColor(sib, BLACK);
2222                     setColor(parentOf(x), RED);
2223                     rotateRight(parentOf(x));
2224                     sib = leftOf(parentOf(x));
2225                 }
2226 
2227                 if (colorOf(rightOf(sib)) == BLACK &&
2228                     colorOf(leftOf(sib)) == BLACK) {
2229                     setColor(sib, RED);
2230                     x = parentOf(x);
2231                 } else {
2232                     if (colorOf(leftOf(sib)) == BLACK) {
2233                         setColor(rightOf(sib), BLACK);
2234                         setColor(sib, RED);
2235                         rotateLeft(sib);
2236                         sib = leftOf(parentOf(x));
2237                     }
2238                     setColor(sib, colorOf(parentOf(x)));
2239                     setColor(parentOf(x), BLACK);
2240                     setColor(leftOf(sib), BLACK);
2241                     rotateRight(parentOf(x));
2242                     x = root;
2243                 }
2244             }
2245         }
2246 
2247         setColor(x, BLACK);
2248     }
2249 
2250     private static final long serialVersionUID = 919286545866124006L;
2251 
2252     /**
2253      * Save the state of the <tt>TreeMap</tt> instance to a stream (i.e.,
2254      * serialize it).
2255      *
2256      * @serialData The <i>size</i> of the TreeMap (the number of key-value
2257      *             mappings) is emitted (int), followed by the key (Object)
2258      *             and value (Object) for each key-value mapping represented
2259      *             by the TreeMap. The key-value mappings are emitted in
2260      *             key-order (as determined by the TreeMap's Comparator,
2261      *             or by the keys' natural ordering if the TreeMap has no
2262      *             Comparator).
2263      */
2264     private void writeObject(java.io.ObjectOutputStream s)
2265         throws java.io.IOException {
2266         // Write out the Comparator and any hidden stuff
2267         s.defaultWriteObject();
2268 
2269         // Write out size (number of Mappings)
2270         s.writeInt(size);
2271 
2272         // Write out keys and values (alternating)
2273         for (Iterator<Map.Entry<K,V>> i = entrySet().iterator(); i.hasNext(); ) {
2274             Map.Entry<K,V> e = i.next();
2275             s.writeObject(e.getKey());
2276             s.writeObject(e.getValue());
2277         }
2278     }
2279 
2280     /**
2281      * Reconstitute the <tt>TreeMap</tt> instance from a stream (i.e.,
2282      * deserialize it).
2283      */
2284     private void readObject(final java.io.ObjectInputStream s)
2285         throws java.io.IOException, ClassNotFoundException {
2286         // Read in the Comparator and any hidden stuff
2287         s.defaultReadObject();
2288 
2289         // Read in size
2290         int size = s.readInt();
2291 
2292         buildFromSorted(size, null, s, null);
2293     }
2294 
2295     /** Intended to be called only from TreeSet.readObject */
2296     void readTreeSet(int size, java.io.ObjectInputStream s, V defaultVal)
2297         throws java.io.IOException, ClassNotFoundException {
2298         buildFromSorted(size, null, s, defaultVal);
2299     }
2300 
2301     /** Intended to be called only from TreeSet.addAll */
2302     void addAllForTreeSet(SortedSet<? extends K> set, V defaultVal) {
2303         try {
2304             buildFromSorted(set.size(), set.iterator(), null, defaultVal);
2305         } catch (java.io.IOException cannotHappen) {
2306         } catch (ClassNotFoundException cannotHappen) {
2307         }
2308     }
2309 
2310 
2311     /**
2312      * Linear time tree building algorithm from sorted data.  Can accept keys
2313      * and/or values from iterator or stream. This leads to too many
2314      * parameters, but seems better than alternatives.  The four formats
2315      * that this method accepts are:
2316      *
2317      *    1) An iterator of Map.Entries.  (it != null, defaultVal == null).
2318      *    2) An iterator of keys.         (it != null, defaultVal != null).
2319      *    3) A stream of alternating serialized keys and values.
2320      *                                   (it == null, defaultVal == null).
2321      *    4) A stream of serialized keys. (it == null, defaultVal != null).
2322      *
2323      * It is assumed that the comparator of the TreeMap is already set prior
2324      * to calling this method.
2325      *
2326      * @param size the number of keys (or key-value pairs) to be read from
2327      *        the iterator or stream
2328      * @param it If non-null, new entries are created from entries
2329      *        or keys read from this iterator.
2330      * @param str If non-null, new entries are created from keys and
2331      *        possibly values read from this stream in serialized form.
2332      *        Exactly one of it and str should be non-null.
2333      * @param defaultVal if non-null, this default value is used for
2334      *        each value in the map.  If null, each value is read from
2335      *        iterator or stream, as described above.
2336      * @throws IOException propagated from stream reads. This cannot
2337      *         occur if str is null.
2338      * @throws ClassNotFoundException propagated from readObject.
2339      *         This cannot occur if str is null.
2340      */
2341     private void buildFromSorted(int size, Iterator it,
2342                                  java.io.ObjectInputStream str,
2343                                  V defaultVal)
2344         throws  java.io.IOException, ClassNotFoundException {
2345         this.size = size;
2346         root = buildFromSorted(0, 0, size-1, computeRedLevel(size),
2347                                it, str, defaultVal);
2348     }
2349 
2350     /**
2351      * Recursive "helper method" that does the real work of the
2352      * previous method.  Identically named parameters have
2353      * identical definitions.  Additional parameters are documented below.
2354      * It is assumed that the comparator and size fields of the TreeMap are
2355      * already set prior to calling this method.  (It ignores both fields.)
2356      *
2357      * @param level the current level of tree. Initial call should be 0.
2358      * @param lo the first element index of this subtree. Initial should be 0.
2359      * @param hi the last element index of this subtree.  Initial should be
2360      *        size-1.
2361      * @param redLevel the level at which nodes should be red.
2362      *        Must be equal to computeRedLevel for tree of this size.
2363      */
2364     private final Entry<K,V> buildFromSorted(int level, int lo, int hi,
2365                                              int redLevel,
2366                                              Iterator it,
2367                                              java.io.ObjectInputStream str,
2368                                              V defaultVal)
2369         throws  java.io.IOException, ClassNotFoundException {
2370         /*
2371          * Strategy: The root is the middlemost element. To get to it, we
2372          * have to first recursively construct the entire left subtree,
2373          * so as to grab all of its elements. We can then proceed with right
2374          * subtree.
2375          *
2376          * The lo and hi arguments are the minimum and maximum
2377          * indices to pull out of the iterator or stream for current subtree.
2378          * They are not actually indexed, we just proceed sequentially,
2379          * ensuring that items are extracted in corresponding order.
2380          */
2381 
2382         if (hi < lo) return null;
2383 
2384         int mid = (lo + hi) >>> 1;
2385 
2386         Entry<K,V> left  = null;
2387         if (lo < mid)
2388             left = buildFromSorted(level+1, lo, mid - 1, redLevel,
2389                                    it, str, defaultVal);
2390 
2391         // extract key and/or value from iterator or stream
2392         K key;
2393         V value;
2394         if (it != null) {
2395             if (defaultVal==null) {
2396                 Map.Entry<K,V> entry = (Map.Entry<K,V>)it.next();
2397                 key = entry.getKey();
2398                 value = entry.getValue();
2399             } else {
2400                 key = (K)it.next();
2401                 value = defaultVal;
2402             }
2403         } else { // use stream
2404             key = (K) str.readObject();
2405             value = (defaultVal != null ? defaultVal : (V) str.readObject());
2406         }
2407 
2408         Entry<K,V> middle =  new Entry<K,V>(key, value, null);
2409 
2410         // color nodes in non-full bottommost level red
2411         if (level == redLevel)
2412             middle.color = RED;
2413 
2414         if (left != null) {
2415             middle.left = left;
2416             left.parent = middle;
2417         }
2418 
2419         if (mid < hi) {
2420             Entry<K,V> right = buildFromSorted(level+1, mid+1, hi, redLevel,
2421                                                it, str, defaultVal);
2422             middle.right = right;
2423             right.parent = middle;
2424         }
2425 
2426         return middle;
2427     }
2428 
2429     /**
2430      * Find the level down to which to assign all nodes BLACK.  This is the
2431      * last `full' level of the complete binary tree produced by
2432      * buildTree. The remaining nodes are colored RED. (This makes a `nice'
2433      * set of color assignments wrt future insertions.) This level number is
2434      * computed by finding the number of splits needed to reach the zeroeth
2435      * node.  (The answer is ~lg(N), but in any case must be computed by same
2436      * quick O(lg(N)) loop.)
2437      */
2438     private static int computeRedLevel(int sz) {
2439         int level = 0;
2440         for (int m = sz - 1; m >= 0; m = m / 2 - 1)
2441             level++;
2442         return level;
2443     }
2444 }