1 /*
   2  * Copyright (c) 1997, 2014, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.  Oracle designates this
   8  * particular file as subject to the "Classpath" exception as provided
   9  * by Oracle in the LICENSE file that accompanied this code.
  10  *
  11  * This code is distributed in the hope that it will be useful, but WITHOUT
  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).
  16  *
  17  * You should have received a copy of the GNU General Public License version
  18  * 2 along with this work; if not, write to the Free Software Foundation,
  19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  20  *
  21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  22  * or visit www.oracle.com if you need additional information or have any
  23  * questions.
  24  */
  25 
  26 package java.util;
  27 
  28 import java.io.Serializable;
  29 import java.util.function.BiConsumer;
  30 import java.util.function.BiFunction;
  31 import java.util.function.Consumer;
  32 import java.util.function.Function;
  33 
  34 /**
  35  * A Red-Black tree based {@link NavigableMap} implementation.
  36  * The map is sorted according to the {@linkplain Comparable natural
  37  * ordering} of its keys, or by a {@link Comparator} provided at map
  38  * creation time, depending on which constructor is used.
  39  *
  40  * <p>This implementation provides guaranteed log(n) time cost for the
  41  * {@code containsKey}, {@code get}, {@code put} and {@code remove}
  42  * operations.  Algorithms are adaptations of those in Cormen, Leiserson, and
  43  * Rivest's <em>Introduction to Algorithms</em>.
  44  *
  45  * <p>Note that the ordering maintained by a tree map, like any sorted map, and
  46  * whether or not an explicit comparator is provided, must be <em>consistent
  47  * with {@code equals}</em> if this sorted map is to correctly implement the
  48  * {@code Map} interface.  (See {@code Comparable} or {@code Comparator} for a
  49  * precise definition of <em>consistent with equals</em>.)  This is so because
  50  * the {@code Map} interface is defined in terms of the {@code equals}
  51  * operation, but a sorted map performs all key comparisons using its {@code
  52  * compareTo} (or {@code compare}) method, so two keys that are deemed equal by
  53  * this method are, from the standpoint of the sorted map, equal.  The behavior
  54  * of a sorted map <em>is</em> well-defined even if its ordering is
  55  * inconsistent with {@code equals}; it just fails to obey the general contract
  56  * of the {@code Map} interface.
  57  *
  58  * <p><strong>Note that this implementation is not synchronized.</strong>
  59  * If multiple threads access a map concurrently, and at least one of the
  60  * threads modifies the map structurally, it <em>must</em> be synchronized
  61  * externally.  (A structural modification is any operation that adds or
  62  * deletes one or more mappings; merely changing the value associated
  63  * with an existing key is not a structural modification.)  This is
  64  * typically accomplished by synchronizing on some object that naturally
  65  * encapsulates the map.
  66  * If no such object exists, the map should be "wrapped" using the
  67  * {@link Collections#synchronizedSortedMap Collections.synchronizedSortedMap}
  68  * method.  This is best done at creation time, to prevent accidental
  69  * unsynchronized access to the map: <pre>
  70  *   SortedMap m = Collections.synchronizedSortedMap(new TreeMap(...));</pre>
  71  *
  72  * <p>The iterators returned by the {@code iterator} method of the collections
  73  * returned by all of this class's "collection view methods" are
  74  * <em>fail-fast</em>: if the map is structurally modified at any time after
  75  * the iterator is created, in any way except through the iterator's own
  76  * {@code remove} method, the iterator will throw a {@link
  77  * ConcurrentModificationException}.  Thus, in the face of concurrent
  78  * modification, the iterator fails quickly and cleanly, rather than risking
  79  * arbitrary, non-deterministic behavior at an undetermined time in the future.
  80  *
  81  * <p>Note that the fail-fast behavior of an iterator cannot be guaranteed
  82  * as it is, generally speaking, impossible to make any hard guarantees in the
  83  * presence of unsynchronized concurrent modification.  Fail-fast iterators
  84  * throw {@code ConcurrentModificationException} on a best-effort basis.
  85  * Therefore, it would be wrong to write a program that depended on this
  86  * exception for its correctness:   <em>the fail-fast behavior of iterators
  87  * should be used only to detect bugs.</em>
  88  *
  89  * <p>All {@code Map.Entry} pairs returned by methods in this class
  90  * and its views represent snapshots of mappings at the time they were
  91  * produced. They do <strong>not</strong> support the {@code Entry.setValue}
  92  * method. (Note however that it is possible to change mappings in the
  93  * associated map using {@code put}.)
  94  *
  95  * <p>This class is a member of the
  96  * <a href="{@docRoot}/../technotes/guides/collections/index.html">
  97  * Java Collections Framework</a>.
  98  *
  99  * @param <K> the type of keys maintained by this map
 100  * @param <V> the type of mapped values
 101  *
 102  * @author  Josh Bloch and Doug Lea
 103  * @see Map
 104  * @see HashMap
 105  * @see Hashtable
 106  * @see Comparable
 107  * @see Comparator
 108  * @see Collection
 109  * @since 1.2
 110  */
 111 
 112 public class TreeMap<K,V>
 113     extends AbstractMap<K,V>
 114     implements NavigableMap<K,V>, Cloneable, java.io.Serializable
 115 {
 116     /**
 117      * The comparator used to maintain order in this tree map, or
 118      * null if it uses the natural ordering of its keys.
 119      *
 120      * @serial
 121      */
 122     private final Comparator<? super K> comparator;
 123 
 124     private transient Entry<K,V> root;
 125 
 126     /**
 127      * The number of entries in the tree
 128      */
 129     private transient int size = 0;
 130 
 131     /**
 132      * The number of structural modifications to the tree.
 133      */
 134     private transient int modCount = 0;
 135 
 136     /**
 137      * Constructs a new, empty tree map, using the natural ordering of its
 138      * keys.  All keys inserted into the map must implement the {@link
 139      * Comparable} interface.  Furthermore, all such keys must be
 140      * <em>mutually comparable</em>: {@code k1.compareTo(k2)} must not throw
 141      * a {@code ClassCastException} for any keys {@code k1} and
 142      * {@code k2} in the map.  If the user attempts to put a key into the
 143      * map that violates this constraint (for example, the user attempts to
 144      * put a string key into a map whose keys are integers), the
 145      * {@code put(Object key, Object value)} call will throw a
 146      * {@code ClassCastException}.
 147      */
 148     public TreeMap() {
 149         comparator = null;
 150     }
 151 
 152     /**
 153      * Constructs a new, empty tree map, ordered according to the given
 154      * comparator.  All keys inserted into the map must be <em>mutually
 155      * comparable</em> by the given comparator: {@code comparator.compare(k1,
 156      * k2)} must not throw a {@code ClassCastException} for any keys
 157      * {@code k1} and {@code k2} in the map.  If the user attempts to put
 158      * a key into the map that violates this constraint, the {@code put(Object
 159      * key, Object value)} call will throw a
 160      * {@code ClassCastException}.
 161      *
 162      * @param comparator the comparator that will be used to order this map.
 163      *        If {@code null}, the {@linkplain Comparable natural
 164      *        ordering} of the keys will be used.
 165      */
 166     public TreeMap(Comparator<? super K> comparator) {
 167         this.comparator = comparator;
 168     }
 169 
 170     /**
 171      * Constructs a new tree map containing the same mappings as the given
 172      * map, ordered according to the <em>natural ordering</em> of its keys.
 173      * All keys inserted into the new map must implement the {@link
 174      * Comparable} interface.  Furthermore, all such keys must be
 175      * <em>mutually comparable</em>: {@code k1.compareTo(k2)} must not throw
 176      * a {@code ClassCastException} for any keys {@code k1} and
 177      * {@code k2} in the map.  This method runs in n*log(n) time.
 178      *
 179      * @param  m the map whose mappings are to be placed in this map
 180      * @throws ClassCastException if the keys in m are not {@link Comparable},
 181      *         or are not mutually comparable
 182      * @throws NullPointerException if the specified map is null
 183      */
 184     public TreeMap(Map<? extends K, ? extends V> m) {
 185         comparator = null;
 186         putAll(m);
 187     }
 188 
 189     /**
 190      * Constructs a new tree map containing the same mappings and
 191      * using the same ordering as the specified sorted map.  This
 192      * method runs in linear time.
 193      *
 194      * @param  m the sorted map whose mappings are to be placed in this map,
 195      *         and whose comparator is to be used to sort this map
 196      * @throws NullPointerException if the specified map is null
 197      */
 198     public TreeMap(SortedMap<K, ? extends V> m) {
 199         comparator = m.comparator();
 200         try {
 201             buildFromSorted(m.size(), m.entrySet().iterator(), null, null);
 202         } catch (java.io.IOException | ClassNotFoundException cannotHappen) {
 203         }
 204     }
 205 
 206 
 207     // Query Operations
 208 
 209     /**
 210      * Returns the number of key-value mappings in this map.
 211      *
 212      * @return the number of key-value mappings in this map
 213      */
 214     public int size() {
 215         return size;
 216     }
 217 
 218     /**
 219      * Returns {@code true} if this map contains a mapping for the specified
 220      * key.
 221      *
 222      * @param key key whose presence in this map is to be tested
 223      * @return {@code true} if this map contains a mapping for the
 224      *         specified key
 225      * @throws ClassCastException if the specified key cannot be compared
 226      *         with the keys currently in the map
 227      * @throws NullPointerException if the specified key is null
 228      *         and this map uses natural ordering, or its comparator
 229      *         does not permit null keys
 230      */
 231     public boolean containsKey(Object key) {
 232         return getEntry(key) != null;
 233     }
 234 
 235     /**
 236      * Returns {@code true} if this map maps one or more keys to the
 237      * specified value.  More formally, returns {@code true} if and only if
 238      * this map contains at least one mapping to a value {@code v} such
 239      * that {@code (value==null ? v==null : value.equals(v))}.  This
 240      * operation will probably require time linear in the map size for
 241      * most implementations.
 242      *
 243      * @param value value whose presence in this map is to be tested
 244      * @return {@code true} if a mapping to {@code value} exists;
 245      *         {@code false} otherwise
 246      * @since 1.2
 247      */
 248     public boolean containsValue(Object value) {
 249         for (Entry<K,V> e = getFirstEntry(); e != null; e = successor(e))
 250             if (valEquals(value, e.value))
 251                 return true;
 252         return false;
 253     }
 254 
 255     /**
 256      * Returns the value to which the specified key is mapped,
 257      * or {@code null} if this map contains no mapping for the key.
 258      *
 259      * <p>More formally, if this map contains a mapping from a key
 260      * {@code k} to a value {@code v} such that {@code key} compares
 261      * equal to {@code k} according to the map's ordering, then this
 262      * method returns {@code v}; otherwise it returns {@code null}.
 263      * (There can be at most one such mapping.)
 264      *
 265      * <p>A return value of {@code null} does not <em>necessarily</em>
 266      * indicate that the map contains no mapping for the key; it's also
 267      * possible that the map explicitly maps the key to {@code null}.
 268      * The {@link #containsKey containsKey} operation may be used to
 269      * distinguish these two cases.
 270      *
 271      * @throws ClassCastException if the specified key cannot be compared
 272      *         with the keys currently in the map
 273      * @throws NullPointerException if the specified key is null
 274      *         and this map uses natural ordering, or its comparator
 275      *         does not permit null keys
 276      */
 277     public V get(Object key) {
 278         Entry<K,V> p = getEntry(key);
 279         return (p==null ? null : p.value);
 280     }
 281 
 282     public Comparator<? super K> comparator() {
 283         return comparator;
 284     }
 285 
 286     /**
 287      * @throws NoSuchElementException {@inheritDoc}
 288      */
 289     public K firstKey() {
 290         return key(getFirstEntry());
 291     }
 292 
 293     /**
 294      * @throws NoSuchElementException {@inheritDoc}
 295      */
 296     public K lastKey() {
 297         return key(getLastEntry());
 298     }
 299 
 300     /**
 301      * Copies all of the mappings from the specified map to this map.
 302      * These mappings replace any mappings that this map had for any
 303      * of the keys currently in the specified map.
 304      *
 305      * @param  map mappings to be stored in this map
 306      * @throws ClassCastException if the class of a key or value in
 307      *         the specified map prevents it from being stored in this map
 308      * @throws NullPointerException if the specified map is null or
 309      *         the specified map contains a null key and this map does not
 310      *         permit null keys
 311      */
 312     public void putAll(Map<? extends K, ? extends V> map) {
 313         int mapSize = map.size();
 314         if (size==0 && mapSize!=0 && map instanceof SortedMap) {
 315             Comparator<?> c = ((SortedMap<?,?>)map).comparator();
 316             if (c == comparator || (c != null && c.equals(comparator))) {
 317                 ++modCount;
 318                 try {
 319                     buildFromSorted(mapSize, map.entrySet().iterator(),
 320                                     null, null);
 321                 } catch (java.io.IOException | ClassNotFoundException cannotHappen) {
 322                 }
 323                 return;
 324             }
 325         }
 326         super.putAll(map);
 327     }
 328 
 329     /**
 330      * Returns this map's entry for the given key, or {@code null} if the map
 331      * does not contain an entry for the key.
 332      *
 333      * @return this map's entry for the given key, or {@code null} if the map
 334      *         does not contain an entry for the key
 335      * @throws ClassCastException if the specified key cannot be compared
 336      *         with the keys currently in the map
 337      * @throws NullPointerException if the specified key is null
 338      *         and this map uses natural ordering, or its comparator
 339      *         does not permit null keys
 340      */
 341     final Entry<K,V> getEntry(Object key) {
 342         // Offload comparator-based version for sake of performance
 343         if (comparator != null)
 344             return getEntryUsingComparator(key);
 345         if (key == null)
 346             throw new NullPointerException();
 347         @SuppressWarnings("unchecked")
 348             Comparable<? super K> k = (Comparable<? super K>) key;
 349         Entry<K,V> p = root;
 350         while (p != null) {
 351             int cmp = k.compareTo(p.key);
 352             if (cmp < 0)
 353                 p = p.left;
 354             else if (cmp > 0)
 355                 p = p.right;
 356             else
 357                 return p;
 358         }
 359         return null;
 360     }
 361 
 362     /**
 363      * Version of getEntry using comparator. Split off from getEntry
 364      * for performance. (This is not worth doing for most methods,
 365      * that are less dependent on comparator performance, but is
 366      * worthwhile here.)
 367      */
 368     final Entry<K,V> getEntryUsingComparator(Object key) {
 369         @SuppressWarnings("unchecked")
 370             K k = (K) key;
 371         Comparator<? super K> cpr = comparator;
 372         if (cpr != null) {
 373             Entry<K,V> p = root;
 374             while (p != null) {
 375                 int cmp = cpr.compare(k, p.key);
 376                 if (cmp < 0)
 377                     p = p.left;
 378                 else if (cmp > 0)
 379                     p = p.right;
 380                 else
 381                     return p;
 382             }
 383         }
 384         return null;
 385     }
 386 
 387     /**
 388      * Gets the entry corresponding to the specified key; if no such entry
 389      * exists, returns the entry for the least key greater than the specified
 390      * key; if no such entry exists (i.e., the greatest key in the Tree is less
 391      * than the specified key), returns {@code null}.
 392      */
 393     final Entry<K,V> getCeilingEntry(K key) {
 394         Entry<K,V> p = root;
 395         while (p != null) {
 396             int cmp = compare(key, p.key);
 397             if (cmp < 0) {
 398                 if (p.left != null)
 399                     p = p.left;
 400                 else
 401                     return p;
 402             } else if (cmp > 0) {
 403                 if (p.right != null) {
 404                     p = p.right;
 405                 } else {
 406                     Entry<K,V> parent = p.parent;
 407                     Entry<K,V> ch = p;
 408                     while (parent != null && ch == parent.right) {
 409                         ch = parent;
 410                         parent = parent.parent;
 411                     }
 412                     return parent;
 413                 }
 414             } else
 415                 return p;
 416         }
 417         return null;
 418     }
 419 
 420     /**
 421      * Gets the entry corresponding to the specified key; if no such entry
 422      * exists, returns the entry for the greatest key less than the specified
 423      * key; if no such entry exists, returns {@code null}.
 424      */
 425     final Entry<K,V> getFloorEntry(K key) {
 426         Entry<K,V> p = root;
 427         while (p != null) {
 428             int cmp = compare(key, p.key);
 429             if (cmp > 0) {
 430                 if (p.right != null)
 431                     p = p.right;
 432                 else
 433                     return p;
 434             } else if (cmp < 0) {
 435                 if (p.left != null) {
 436                     p = p.left;
 437                 } else {
 438                     Entry<K,V> parent = p.parent;
 439                     Entry<K,V> ch = p;
 440                     while (parent != null && ch == parent.left) {
 441                         ch = parent;
 442                         parent = parent.parent;
 443                     }
 444                     return parent;
 445                 }
 446             } else
 447                 return p;
 448 
 449         }
 450         return null;
 451     }
 452 
 453     /**
 454      * Gets the entry for the least key greater than the specified
 455      * key; if no such entry exists, returns the entry for the least
 456      * key greater than the specified key; if no such entry exists
 457      * returns {@code null}.
 458      */
 459     final Entry<K,V> getHigherEntry(K key) {
 460         Entry<K,V> p = root;
 461         while (p != null) {
 462             int cmp = compare(key, p.key);
 463             if (cmp < 0) {
 464                 if (p.left != null)
 465                     p = p.left;
 466                 else
 467                     return p;
 468             } else {
 469                 if (p.right != null) {
 470                     p = p.right;
 471                 } else {
 472                     Entry<K,V> parent = p.parent;
 473                     Entry<K,V> ch = p;
 474                     while (parent != null && ch == parent.right) {
 475                         ch = parent;
 476                         parent = parent.parent;
 477                     }
 478                     return parent;
 479                 }
 480             }
 481         }
 482         return null;
 483     }
 484 
 485     /**
 486      * Returns the entry for the greatest key less than the specified key; if
 487      * no such entry exists (i.e., the least key in the Tree is greater than
 488      * the specified key), returns {@code null}.
 489      */
 490     final Entry<K,V> getLowerEntry(K key) {
 491         Entry<K,V> p = root;
 492         while (p != null) {
 493             int cmp = compare(key, p.key);
 494             if (cmp > 0) {
 495                 if (p.right != null)
 496                     p = p.right;
 497                 else
 498                     return p;
 499             } else {
 500                 if (p.left != null) {
 501                     p = p.left;
 502                 } else {
 503                     Entry<K,V> parent = p.parent;
 504                     Entry<K,V> ch = p;
 505                     while (parent != null && ch == parent.left) {
 506                         ch = parent;
 507                         parent = parent.parent;
 508                     }
 509                     return parent;
 510                 }
 511             }
 512         }
 513         return null;
 514     }
 515 
 516     /**
 517      * Associates the specified value with the specified key in this map.
 518      * If the map previously contained a mapping for the key, the old
 519      * value is replaced.
 520      *
 521      * @param key key with which the specified value is to be associated
 522      * @param value value to be associated with the specified key
 523      *
 524      * @return the previous value associated with {@code key}, or
 525      *         {@code null} if there was no mapping for {@code key}.
 526      *         (A {@code null} return can also indicate that the map
 527      *         previously associated {@code null} with {@code key}.)
 528      * @throws ClassCastException if the specified key cannot be compared
 529      *         with the keys currently in the map
 530      * @throws NullPointerException if the specified key is null
 531      *         and this map uses natural ordering, or its comparator
 532      *         does not permit null keys
 533      */
 534     public V put(K key, V value) {
 535         return put(key, value, true);
 536     }
 537 
 538     private void addEntry(K key, V value, int cmp, Entry<K, V> parent) {
 539         Entry<K, V> e = new Entry<>(key, value, parent);
 540         if (cmp < 0)
 541             parent.left = e;
 542         else
 543             parent.right = e;
 544         fixAfterInsertion(e);
 545         size++;
 546         modCount++;
 547     }
 548 
 549     private void addEntryToEmptyMap(K key, V value) {
 550         compare(key, key); // type (and possibly null) check
 551         root = new Entry<>(key, value, null);
 552         size = 1;
 553         modCount++;
 554     }
 555 
 556     private V put(K key, V value, boolean replaceOld) {
 557         Entry<K, V> t = root;
 558         if (t == null) {
 559             addEntryToEmptyMap(key, value);
 560             return null;
 561         }
 562         int cmp;
 563         Entry<K, V> parent;
 564         // split comparator and comparable paths
 565         Comparator<? super K> cpr = comparator;
 566         if (cpr != null) {
 567             do {
 568                 parent = t;
 569                 cmp = cpr.compare(key, t.key);
 570                 if (cmp < 0)
 571                     t = t.left;
 572                 else if (cmp > 0)
 573                     t = t.right;
 574                 else {
 575                     V oldValue = t.value;
 576                     if (replaceOld) {
 577                         t.value = value;
 578                     }
 579                     return oldValue;
 580                 }
 581             } while (t != null);
 582         } else {
 583             if (key == null)
 584                 throw new NullPointerException();
 585             @SuppressWarnings("unchecked")
 586             Comparable<? super K> k = (Comparable<? super K>) key;
 587             do {
 588                 parent = t;
 589                 cmp = k.compareTo(t.key);
 590                 if (cmp < 0)
 591                     t = t.left;
 592                 else if (cmp > 0)
 593                     t = t.right;
 594                 else {
 595                     V oldValue = t.value;
 596                     if (replaceOld) {
 597                         t.value = value;
 598                     }
 599                     return oldValue;
 600                 }
 601             } while (t != null);
 602         }
 603         addEntry(key, value, cmp, parent);
 604         return null;
 605     }
 606 
 607     @Override
 608     public V putIfAbsent(K key, V value) {
 609         return put(key, value, false);
 610     }
 611 
 612     /**
 613      * {@inheritDoc}
 614      *
 615      * <p>This method will, on a best-effort basis, throw a
 616      * {@link ConcurrentModificationException} if it is detected that the
 617      * remapping function modifies this map during computation.
 618      *
 619      * @throws ConcurrentModificationException if it is detected that the
 620      * remapping function modified this map
 621      */
 622     @Override
 623     public V computeIfAbsent(K key, Function<? super K, ? extends V> mappingFunction) {
 624         Objects.requireNonNull(mappingFunction);
 625         V newValue;
 626         Entry<K, V> t = root;
 627         if (t == null) {
 628             newValue = getNewValueAndCheckModification(key, mappingFunction);
 629             if (newValue != null) {
 630                 addEntryToEmptyMap(key, newValue);
 631                 return newValue;
 632             } else {
 633                 return null;
 634             }
 635         }
 636         int cmp;
 637         Entry<K, V> parent;
 638         // split comparator and comparable paths
 639         Comparator<? super K> cpr = comparator;
 640         if (cpr != null) {
 641             do {
 642                 parent = t;
 643                 cmp = cpr.compare(key, t.key);
 644                 if (cmp < 0)
 645                     t = t.left;
 646                 else if (cmp > 0)
 647                     t = t.right;
 648                 else
 649                     return t.value;
 650             } while (t != null);
 651         } else {
 652             if (key == null)
 653                 throw new NullPointerException();
 654             @SuppressWarnings("unchecked")
 655             Comparable<? super K> k = (Comparable<? super K>) key;
 656             do {
 657                 parent = t;
 658                 cmp = k.compareTo(t.key);
 659                 if (cmp < 0)
 660                     t = t.left;
 661                 else if (cmp > 0)
 662                     t = t.right;
 663                 else
 664                     return t.value;
 665             } while (t != null);
 666         }
 667         newValue = getNewValueAndCheckModification(key, mappingFunction);
 668         if (newValue != null) {
 669             addEntry(key, newValue, cmp, parent);
 670             return newValue;
 671         }
 672         return null;
 673     }
 674 
 675     private V getNewValueAndCheckModification(K key, Function<? super K, ? extends V> mappingFunction) {
 676         V newValue;
 677         int mc = modCount;
 678         newValue = mappingFunction.apply(key);
 679         if (mc != modCount) {
 680             throw new ConcurrentModificationException();
 681         }
 682         return newValue;
 683     }
 684 
 685     /**
 686      * {@inheritDoc}
 687      *
 688      * <p>This method will, on a best-effort basis, throw a
 689      * {@link ConcurrentModificationException} if it is detected that the
 690      * remapping function modifies this map during computation.
 691      *
 692      * @throws ConcurrentModificationException if it is detected that the
 693      * remapping function modified this map
 694      */
 695     @Override
 696     public V computeIfPresent(K key, BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
 697         Objects.requireNonNull(remappingFunction);
 698         Entry<K, V> oldEntry = getEntry(key);
 699         if (oldEntry != null && oldEntry.value != null) {
 700             return remapValue(oldEntry, key, remappingFunction);
 701         } else {
 702             return null;
 703         }
 704     }
 705 
 706     private V remapValue(Entry<K, V> t, K key, BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
 707         V newValue = getNewValueAndCheckModification(key, t.value, remappingFunction);
 708         if (newValue == null) {
 709             deleteEntry(t);
 710             return null;
 711         } else {
 712             // replace old mapping
 713             t.value = newValue;
 714             return newValue;
 715         }
 716     }
 717 
 718     private V getNewValueAndCheckModification(K key, V oldValue, BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
 719         int mc = modCount;
 720         V newValue = remappingFunction.apply(key, oldValue);
 721         if (mc != modCount) {
 722             throw new ConcurrentModificationException();
 723         }
 724         return newValue;
 725     }
 726 
 727     /**
 728      * {@inheritDoc}
 729      *
 730      * <p>This method will, on a best-effort basis, throw a
 731      * {@link ConcurrentModificationException} if it is detected that the
 732      * remapping function modifies this map during computation.
 733      *
 734      * @throws ConcurrentModificationException if it is detected that the
 735      * remapping function modified this map
 736      */
 737     @Override
 738     public V compute(K key, BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
 739         Objects.requireNonNull(remappingFunction);
 740         V newValue;
 741         Entry<K, V> t = root;
 742         if (t == null) {
 743             newValue = getNewValueAndCheckModification(key, null, remappingFunction);
 744             if (newValue != null) {
 745                 addEntryToEmptyMap(key, newValue);
 746                 return newValue;
 747             } else {
 748                 return null;
 749             }
 750         }
 751         int cmp;
 752         Entry<K, V> parent;
 753         // split comparator and comparable paths
 754         Comparator<? super K> cpr = comparator;
 755         if (cpr != null) {
 756             do {
 757                 parent = t;
 758                 cmp = cpr.compare(key, t.key);
 759                 if (cmp < 0)
 760                     t = t.left;
 761                 else if (cmp > 0)
 762                     t = t.right;
 763                 else
 764                     return remapValue(t, key, remappingFunction);
 765             } while (t != null);
 766         } else {
 767             if (key == null)
 768                 throw new NullPointerException();
 769             @SuppressWarnings("unchecked")
 770             Comparable<? super K> k = (Comparable<? super K>) key;
 771             do {
 772                 parent = t;
 773                 cmp = k.compareTo(t.key);
 774                 if (cmp < 0)
 775                     t = t.left;
 776                 else if (cmp > 0)
 777                     t = t.right;
 778                 else
 779                     return remapValue(t, key, remappingFunction);
 780             } while (t != null);
 781         }
 782         newValue = getNewValueAndCheckModification(key, null, remappingFunction);
 783         if (newValue != null) {
 784             addEntry(key, newValue, cmp, parent);
 785             return newValue;
 786         }
 787         return null;
 788     }
 789 
 790     /**
 791      * Removes the mapping for this key from this TreeMap if present.
 792      *
 793      * @param  key key for which mapping should be removed
 794      * @return the previous value associated with {@code key}, or
 795      *         {@code null} if there was no mapping for {@code key}.
 796      *         (A {@code null} return can also indicate that the map
 797      *         previously associated {@code null} with {@code key}.)
 798      * @throws ClassCastException if the specified key cannot be compared
 799      *         with the keys currently in the map
 800      * @throws NullPointerException if the specified key is null
 801      *         and this map uses natural ordering, or its comparator
 802      *         does not permit null keys
 803      */
 804     public V remove(Object key) {
 805         Entry<K,V> p = getEntry(key);
 806         if (p == null)
 807             return null;
 808 
 809         V oldValue = p.value;
 810         deleteEntry(p);
 811         return oldValue;
 812     }
 813 
 814     /**
 815      * Removes all of the mappings from this map.
 816      * The map will be empty after this call returns.
 817      */
 818     public void clear() {
 819         modCount++;
 820         size = 0;
 821         root = null;
 822     }
 823 
 824     /**
 825      * Returns a shallow copy of this {@code TreeMap} instance. (The keys and
 826      * values themselves are not cloned.)
 827      *
 828      * @return a shallow copy of this map
 829      */
 830     public Object clone() {
 831         TreeMap<?,?> clone;
 832         try {
 833             clone = (TreeMap<?,?>) super.clone();
 834         } catch (CloneNotSupportedException e) {
 835             throw new InternalError(e);
 836         }
 837 
 838         // Put clone into "virgin" state (except for comparator)
 839         clone.root = null;
 840         clone.size = 0;
 841         clone.modCount = 0;
 842         clone.entrySet = null;
 843         clone.navigableKeySet = null;
 844         clone.descendingMap = null;
 845 
 846         // Initialize clone with our mappings
 847         try {
 848             clone.buildFromSorted(size, entrySet().iterator(), null, null);
 849         } catch (java.io.IOException | ClassNotFoundException cannotHappen) {
 850         }
 851 
 852         return clone;
 853     }
 854 
 855     // NavigableMap API methods
 856 
 857     /**
 858      * @since 1.6
 859      */
 860     public Map.Entry<K,V> firstEntry() {
 861         return exportEntry(getFirstEntry());
 862     }
 863 
 864     /**
 865      * @since 1.6
 866      */
 867     public Map.Entry<K,V> lastEntry() {
 868         return exportEntry(getLastEntry());
 869     }
 870 
 871     /**
 872      * @since 1.6
 873      */
 874     public Map.Entry<K,V> pollFirstEntry() {
 875         Entry<K,V> p = getFirstEntry();
 876         Map.Entry<K,V> result = exportEntry(p);
 877         if (p != null)
 878             deleteEntry(p);
 879         return result;
 880     }
 881 
 882     /**
 883      * @since 1.6
 884      */
 885     public Map.Entry<K,V> pollLastEntry() {
 886         Entry<K,V> p = getLastEntry();
 887         Map.Entry<K,V> result = exportEntry(p);
 888         if (p != null)
 889             deleteEntry(p);
 890         return result;
 891     }
 892 
 893     /**
 894      * @throws ClassCastException {@inheritDoc}
 895      * @throws NullPointerException if the specified key is null
 896      *         and this map uses natural ordering, or its comparator
 897      *         does not permit null keys
 898      * @since 1.6
 899      */
 900     public Map.Entry<K,V> lowerEntry(K key) {
 901         return exportEntry(getLowerEntry(key));
 902     }
 903 
 904     /**
 905      * @throws ClassCastException {@inheritDoc}
 906      * @throws NullPointerException if the specified key is null
 907      *         and this map uses natural ordering, or its comparator
 908      *         does not permit null keys
 909      * @since 1.6
 910      */
 911     public K lowerKey(K key) {
 912         return keyOrNull(getLowerEntry(key));
 913     }
 914 
 915     /**
 916      * @throws ClassCastException {@inheritDoc}
 917      * @throws NullPointerException if the specified key is null
 918      *         and this map uses natural ordering, or its comparator
 919      *         does not permit null keys
 920      * @since 1.6
 921      */
 922     public Map.Entry<K,V> floorEntry(K key) {
 923         return exportEntry(getFloorEntry(key));
 924     }
 925 
 926     /**
 927      * @throws ClassCastException {@inheritDoc}
 928      * @throws NullPointerException if the specified key is null
 929      *         and this map uses natural ordering, or its comparator
 930      *         does not permit null keys
 931      * @since 1.6
 932      */
 933     public K floorKey(K key) {
 934         return keyOrNull(getFloorEntry(key));
 935     }
 936 
 937     /**
 938      * @throws ClassCastException {@inheritDoc}
 939      * @throws NullPointerException if the specified key is null
 940      *         and this map uses natural ordering, or its comparator
 941      *         does not permit null keys
 942      * @since 1.6
 943      */
 944     public Map.Entry<K,V> ceilingEntry(K key) {
 945         return exportEntry(getCeilingEntry(key));
 946     }
 947 
 948     /**
 949      * @throws ClassCastException {@inheritDoc}
 950      * @throws NullPointerException if the specified key is null
 951      *         and this map uses natural ordering, or its comparator
 952      *         does not permit null keys
 953      * @since 1.6
 954      */
 955     public K ceilingKey(K key) {
 956         return keyOrNull(getCeilingEntry(key));
 957     }
 958 
 959     /**
 960      * @throws ClassCastException {@inheritDoc}
 961      * @throws NullPointerException if the specified key is null
 962      *         and this map uses natural ordering, or its comparator
 963      *         does not permit null keys
 964      * @since 1.6
 965      */
 966     public Map.Entry<K,V> higherEntry(K key) {
 967         return exportEntry(getHigherEntry(key));
 968     }
 969 
 970     /**
 971      * @throws ClassCastException {@inheritDoc}
 972      * @throws NullPointerException if the specified key is null
 973      *         and this map uses natural ordering, or its comparator
 974      *         does not permit null keys
 975      * @since 1.6
 976      */
 977     public K higherKey(K key) {
 978         return keyOrNull(getHigherEntry(key));
 979     }
 980 
 981     // Views
 982 
 983     /**
 984      * Fields initialized to contain an instance of the entry set view
 985      * the first time this view is requested.  Views are stateless, so
 986      * there's no reason to create more than one.
 987      */
 988     private transient EntrySet entrySet;
 989     private transient KeySet<K> navigableKeySet;
 990     private transient NavigableMap<K,V> descendingMap;
 991 
 992     /**
 993      * Returns a {@link Set} view of the keys contained in this map.
 994      *
 995      * <p>The set's iterator returns the keys in ascending order.
 996      * The set's spliterator is
 997      * <em><a href="Spliterator.html#binding">late-binding</a></em>,
 998      * <em>fail-fast</em>, and additionally reports {@link Spliterator#SORTED}
 999      * and {@link Spliterator#ORDERED} with an encounter order that is ascending
1000      * key order.  The spliterator's comparator (see
1001      * {@link java.util.Spliterator#getComparator()}) is {@code null} if
1002      * the tree map's comparator (see {@link #comparator()}) is {@code null}.
1003      * Otherwise, the spliterator's comparator is the same as or imposes the
1004      * same total ordering as the tree map's comparator.
1005      *
1006      * <p>The set is backed by the map, so changes to the map are
1007      * reflected in the set, and vice-versa.  If the map is modified
1008      * while an iteration over the set is in progress (except through
1009      * the iterator's own {@code remove} operation), the results of
1010      * the iteration are undefined.  The set supports element removal,
1011      * which removes the corresponding mapping from the map, via the
1012      * {@code Iterator.remove}, {@code Set.remove},
1013      * {@code removeAll}, {@code retainAll}, and {@code clear}
1014      * operations.  It does not support the {@code add} or {@code addAll}
1015      * operations.
1016      */
1017     public Set<K> keySet() {
1018         return navigableKeySet();
1019     }
1020 
1021     /**
1022      * @since 1.6
1023      */
1024     public NavigableSet<K> navigableKeySet() {
1025         KeySet<K> nks = navigableKeySet;
1026         return (nks != null) ? nks : (navigableKeySet = new KeySet<>(this));
1027     }
1028 
1029     /**
1030      * @since 1.6
1031      */
1032     public NavigableSet<K> descendingKeySet() {
1033         return descendingMap().navigableKeySet();
1034     }
1035 
1036     /**
1037      * Returns a {@link Collection} view of the values contained in this map.
1038      *
1039      * <p>The collection's iterator returns the values in ascending order
1040      * of the corresponding keys. The collection's spliterator is
1041      * <em><a href="Spliterator.html#binding">late-binding</a></em>,
1042      * <em>fail-fast</em>, and additionally reports {@link Spliterator#ORDERED}
1043      * with an encounter order that is ascending order of the corresponding
1044      * keys.
1045      *
1046      * <p>The collection is backed by the map, so changes to the map are
1047      * reflected in the collection, and vice-versa.  If the map is
1048      * modified while an iteration over the collection is in progress
1049      * (except through the iterator's own {@code remove} operation),
1050      * the results of the iteration are undefined.  The collection
1051      * supports element removal, which removes the corresponding
1052      * mapping from the map, via the {@code Iterator.remove},
1053      * {@code Collection.remove}, {@code removeAll},
1054      * {@code retainAll} and {@code clear} operations.  It does not
1055      * support the {@code add} or {@code addAll} operations.
1056      */
1057     public Collection<V> values() {
1058         Collection<V> vs = values;
1059         if (vs == null) {
1060             vs = new Values();
1061             values = vs;
1062         }
1063         return vs;
1064     }
1065 
1066     /**
1067      * Returns a {@link Set} view of the mappings contained in this map.
1068      *
1069      * <p>The set's iterator returns the entries in ascending key order. The
1070      * set's spliterator is
1071      * <em><a href="Spliterator.html#binding">late-binding</a></em>,
1072      * <em>fail-fast</em>, and additionally reports {@link Spliterator#SORTED} and
1073      * {@link Spliterator#ORDERED} with an encounter order that is ascending key
1074      * order.
1075      *
1076      * <p>The set is backed by the map, so changes to the map are
1077      * reflected in the set, and vice-versa.  If the map is modified
1078      * while an iteration over the set is in progress (except through
1079      * the iterator's own {@code remove} operation, or through the
1080      * {@code setValue} operation on a map entry returned by the
1081      * iterator) the results of the iteration are undefined.  The set
1082      * supports element removal, which removes the corresponding
1083      * mapping from the map, via the {@code Iterator.remove},
1084      * {@code Set.remove}, {@code removeAll}, {@code retainAll} and
1085      * {@code clear} operations.  It does not support the
1086      * {@code add} or {@code addAll} operations.
1087      */
1088     public Set<Map.Entry<K,V>> entrySet() {
1089         EntrySet es = entrySet;
1090         return (es != null) ? es : (entrySet = new EntrySet());
1091     }
1092 
1093     /**
1094      * @since 1.6
1095      */
1096     public NavigableMap<K, V> descendingMap() {
1097         NavigableMap<K, V> km = descendingMap;
1098         return (km != null) ? km :
1099             (descendingMap = new DescendingSubMap<>(this,
1100                                                     true, null, true,
1101                                                     true, null, true));
1102     }
1103 
1104     /**
1105      * @throws ClassCastException       {@inheritDoc}
1106      * @throws NullPointerException if {@code fromKey} or {@code toKey} is
1107      *         null and this map uses natural ordering, or its comparator
1108      *         does not permit null keys
1109      * @throws IllegalArgumentException {@inheritDoc}
1110      * @since 1.6
1111      */
1112     public NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
1113                                     K toKey,   boolean toInclusive) {
1114         return new AscendingSubMap<>(this,
1115                                      false, fromKey, fromInclusive,
1116                                      false, toKey,   toInclusive);
1117     }
1118 
1119     /**
1120      * @throws ClassCastException       {@inheritDoc}
1121      * @throws NullPointerException if {@code toKey} is null
1122      *         and this map uses natural ordering, or its comparator
1123      *         does not permit null keys
1124      * @throws IllegalArgumentException {@inheritDoc}
1125      * @since 1.6
1126      */
1127     public NavigableMap<K,V> headMap(K toKey, boolean inclusive) {
1128         return new AscendingSubMap<>(this,
1129                                      true,  null,  true,
1130                                      false, toKey, inclusive);
1131     }
1132 
1133     /**
1134      * @throws ClassCastException       {@inheritDoc}
1135      * @throws NullPointerException if {@code fromKey} is null
1136      *         and this map uses natural ordering, or its comparator
1137      *         does not permit null keys
1138      * @throws IllegalArgumentException {@inheritDoc}
1139      * @since 1.6
1140      */
1141     public NavigableMap<K,V> tailMap(K fromKey, boolean inclusive) {
1142         return new AscendingSubMap<>(this,
1143                                      false, fromKey, inclusive,
1144                                      true,  null,    true);
1145     }
1146 
1147     /**
1148      * @throws ClassCastException       {@inheritDoc}
1149      * @throws NullPointerException if {@code fromKey} or {@code toKey} is
1150      *         null and this map uses natural ordering, or its comparator
1151      *         does not permit null keys
1152      * @throws IllegalArgumentException {@inheritDoc}
1153      */
1154     public SortedMap<K,V> subMap(K fromKey, K toKey) {
1155         return subMap(fromKey, true, toKey, false);
1156     }
1157 
1158     /**
1159      * @throws ClassCastException       {@inheritDoc}
1160      * @throws NullPointerException if {@code toKey} is null
1161      *         and this map uses natural ordering, or its comparator
1162      *         does not permit null keys
1163      * @throws IllegalArgumentException {@inheritDoc}
1164      */
1165     public SortedMap<K,V> headMap(K toKey) {
1166         return headMap(toKey, false);
1167     }
1168 
1169     /**
1170      * @throws ClassCastException       {@inheritDoc}
1171      * @throws NullPointerException if {@code fromKey} is null
1172      *         and this map uses natural ordering, or its comparator
1173      *         does not permit null keys
1174      * @throws IllegalArgumentException {@inheritDoc}
1175      */
1176     public SortedMap<K,V> tailMap(K fromKey) {
1177         return tailMap(fromKey, true);
1178     }
1179 
1180     @Override
1181     public boolean replace(K key, V oldValue, V newValue) {
1182         Entry<K,V> p = getEntry(key);
1183         if (p!=null && Objects.equals(oldValue, p.value)) {
1184             p.value = newValue;
1185             return true;
1186         }
1187         return false;
1188     }
1189 
1190     @Override
1191     public V replace(K key, V value) {
1192         Entry<K,V> p = getEntry(key);
1193         if (p!=null) {
1194             V oldValue = p.value;
1195             p.value = value;
1196             return oldValue;
1197         }
1198         return null;
1199     }
1200 
1201     @Override
1202     public void forEach(BiConsumer<? super K, ? super V> action) {
1203         Objects.requireNonNull(action);
1204         int expectedModCount = modCount;
1205         for (Entry<K, V> e = getFirstEntry(); e != null; e = successor(e)) {
1206             action.accept(e.key, e.value);
1207 
1208             if (expectedModCount != modCount) {
1209                 throw new ConcurrentModificationException();
1210             }
1211         }
1212     }
1213 
1214     @Override
1215     public void replaceAll(BiFunction<? super K, ? super V, ? extends V> function) {
1216         Objects.requireNonNull(function);
1217         int expectedModCount = modCount;
1218 
1219         for (Entry<K, V> e = getFirstEntry(); e != null; e = successor(e)) {
1220             e.value = function.apply(e.key, e.value);
1221 
1222             if (expectedModCount != modCount) {
1223                 throw new ConcurrentModificationException();
1224             }
1225         }
1226     }
1227 
1228     // View class support
1229 
1230     class Values extends AbstractCollection<V> {
1231         public Iterator<V> iterator() {
1232             return new ValueIterator(getFirstEntry());
1233         }
1234 
1235         public int size() {
1236             return TreeMap.this.size();
1237         }
1238 
1239         public boolean contains(Object o) {
1240             return TreeMap.this.containsValue(o);
1241         }
1242 
1243         public boolean remove(Object o) {
1244             for (Entry<K,V> e = getFirstEntry(); e != null; e = successor(e)) {
1245                 if (valEquals(e.getValue(), o)) {
1246                     deleteEntry(e);
1247                     return true;
1248                 }
1249             }
1250             return false;
1251         }
1252 
1253         public void clear() {
1254             TreeMap.this.clear();
1255         }
1256 
1257         public Spliterator<V> spliterator() {
1258             return new ValueSpliterator<>(TreeMap.this, null, null, 0, -1, 0);
1259         }
1260     }
1261 
1262     class EntrySet extends AbstractSet<Map.Entry<K,V>> {
1263         public Iterator<Map.Entry<K,V>> iterator() {
1264             return new EntryIterator(getFirstEntry());
1265         }
1266 
1267         public boolean contains(Object o) {
1268             if (!(o instanceof Map.Entry))
1269                 return false;
1270             Map.Entry<?,?> entry = (Map.Entry<?,?>) o;
1271             Object value = entry.getValue();
1272             Entry<K,V> p = getEntry(entry.getKey());
1273             return p != null && valEquals(p.getValue(), value);
1274         }
1275 
1276         public boolean remove(Object o) {
1277             if (!(o instanceof Map.Entry))
1278                 return false;
1279             Map.Entry<?,?> entry = (Map.Entry<?,?>) o;
1280             Object value = entry.getValue();
1281             Entry<K,V> p = getEntry(entry.getKey());
1282             if (p != null && valEquals(p.getValue(), value)) {
1283                 deleteEntry(p);
1284                 return true;
1285             }
1286             return false;
1287         }
1288 
1289         public int size() {
1290             return TreeMap.this.size();
1291         }
1292 
1293         public void clear() {
1294             TreeMap.this.clear();
1295         }
1296 
1297         public Spliterator<Map.Entry<K,V>> spliterator() {
1298             return new EntrySpliterator<>(TreeMap.this, null, null, 0, -1, 0);
1299         }
1300     }
1301 
1302     /*
1303      * Unlike Values and EntrySet, the KeySet class is static,
1304      * delegating to a NavigableMap to allow use by SubMaps, which
1305      * outweighs the ugliness of needing type-tests for the following
1306      * Iterator methods that are defined appropriately in main versus
1307      * submap classes.
1308      */
1309 
1310     Iterator<K> keyIterator() {
1311         return new KeyIterator(getFirstEntry());
1312     }
1313 
1314     Iterator<K> descendingKeyIterator() {
1315         return new DescendingKeyIterator(getLastEntry());
1316     }
1317 
1318     static final class KeySet<E> extends AbstractSet<E> implements NavigableSet<E> {
1319         private final NavigableMap<E, ?> m;
1320         KeySet(NavigableMap<E,?> map) { m = map; }
1321 
1322         public Iterator<E> iterator() {
1323             if (m instanceof TreeMap)
1324                 return ((TreeMap<E,?>)m).keyIterator();
1325             else
1326                 return ((TreeMap.NavigableSubMap<E,?>)m).keyIterator();
1327         }
1328 
1329         public Iterator<E> descendingIterator() {
1330             if (m instanceof TreeMap)
1331                 return ((TreeMap<E,?>)m).descendingKeyIterator();
1332             else
1333                 return ((TreeMap.NavigableSubMap<E,?>)m).descendingKeyIterator();
1334         }
1335 
1336         public int size() { return m.size(); }
1337         public boolean isEmpty() { return m.isEmpty(); }
1338         public boolean contains(Object o) { return m.containsKey(o); }
1339         public void clear() { m.clear(); }
1340         public E lower(E e) { return m.lowerKey(e); }
1341         public E floor(E e) { return m.floorKey(e); }
1342         public E ceiling(E e) { return m.ceilingKey(e); }
1343         public E higher(E e) { return m.higherKey(e); }
1344         public E first() { return m.firstKey(); }
1345         public E last() { return m.lastKey(); }
1346         public Comparator<? super E> comparator() { return m.comparator(); }
1347         public E pollFirst() {
1348             Map.Entry<E,?> e = m.pollFirstEntry();
1349             return (e == null) ? null : e.getKey();
1350         }
1351         public E pollLast() {
1352             Map.Entry<E,?> e = m.pollLastEntry();
1353             return (e == null) ? null : e.getKey();
1354         }
1355         public boolean remove(Object o) {
1356             int oldSize = size();
1357             m.remove(o);
1358             return size() != oldSize;
1359         }
1360         public NavigableSet<E> subSet(E fromElement, boolean fromInclusive,
1361                                       E toElement,   boolean toInclusive) {
1362             return new KeySet<>(m.subMap(fromElement, fromInclusive,
1363                                           toElement,   toInclusive));
1364         }
1365         public NavigableSet<E> headSet(E toElement, boolean inclusive) {
1366             return new KeySet<>(m.headMap(toElement, inclusive));
1367         }
1368         public NavigableSet<E> tailSet(E fromElement, boolean inclusive) {
1369             return new KeySet<>(m.tailMap(fromElement, inclusive));
1370         }
1371         public SortedSet<E> subSet(E fromElement, E toElement) {
1372             return subSet(fromElement, true, toElement, false);
1373         }
1374         public SortedSet<E> headSet(E toElement) {
1375             return headSet(toElement, false);
1376         }
1377         public SortedSet<E> tailSet(E fromElement) {
1378             return tailSet(fromElement, true);
1379         }
1380         public NavigableSet<E> descendingSet() {
1381             return new KeySet<>(m.descendingMap());
1382         }
1383 
1384         public Spliterator<E> spliterator() {
1385             return keySpliteratorFor(m);
1386         }
1387     }
1388 
1389     /**
1390      * Base class for TreeMap Iterators
1391      */
1392     abstract class PrivateEntryIterator<T> implements Iterator<T> {
1393         Entry<K,V> next;
1394         Entry<K,V> lastReturned;
1395         int expectedModCount;
1396 
1397         PrivateEntryIterator(Entry<K,V> first) {
1398             expectedModCount = modCount;
1399             lastReturned = null;
1400             next = first;
1401         }
1402 
1403         public final boolean hasNext() {
1404             return next != null;
1405         }
1406 
1407         final Entry<K,V> nextEntry() {
1408             Entry<K,V> e = next;
1409             if (e == null)
1410                 throw new NoSuchElementException();
1411             if (modCount != expectedModCount)
1412                 throw new ConcurrentModificationException();
1413             next = successor(e);
1414             lastReturned = e;
1415             return e;
1416         }
1417 
1418         final Entry<K,V> prevEntry() {
1419             Entry<K,V> e = next;
1420             if (e == null)
1421                 throw new NoSuchElementException();
1422             if (modCount != expectedModCount)
1423                 throw new ConcurrentModificationException();
1424             next = predecessor(e);
1425             lastReturned = e;
1426             return e;
1427         }
1428 
1429         public void remove() {
1430             if (lastReturned == null)
1431                 throw new IllegalStateException();
1432             if (modCount != expectedModCount)
1433                 throw new ConcurrentModificationException();
1434             // deleted entries are replaced by their successors
1435             if (lastReturned.left != null && lastReturned.right != null)
1436                 next = lastReturned;
1437             deleteEntry(lastReturned);
1438             expectedModCount = modCount;
1439             lastReturned = null;
1440         }
1441     }
1442 
1443     final class EntryIterator extends PrivateEntryIterator<Map.Entry<K,V>> {
1444         EntryIterator(Entry<K,V> first) {
1445             super(first);
1446         }
1447         public Map.Entry<K,V> next() {
1448             return nextEntry();
1449         }
1450     }
1451 
1452     final class ValueIterator extends PrivateEntryIterator<V> {
1453         ValueIterator(Entry<K,V> first) {
1454             super(first);
1455         }
1456         public V next() {
1457             return nextEntry().value;
1458         }
1459     }
1460 
1461     final class KeyIterator extends PrivateEntryIterator<K> {
1462         KeyIterator(Entry<K,V> first) {
1463             super(first);
1464         }
1465         public K next() {
1466             return nextEntry().key;
1467         }
1468     }
1469 
1470     final class DescendingKeyIterator extends PrivateEntryIterator<K> {
1471         DescendingKeyIterator(Entry<K,V> first) {
1472             super(first);
1473         }
1474         public K next() {
1475             return prevEntry().key;
1476         }
1477         public void remove() {
1478             if (lastReturned == null)
1479                 throw new IllegalStateException();
1480             if (modCount != expectedModCount)
1481                 throw new ConcurrentModificationException();
1482             deleteEntry(lastReturned);
1483             lastReturned = null;
1484             expectedModCount = modCount;
1485         }
1486     }
1487 
1488     // Little utilities
1489 
1490     /**
1491      * Compares two keys using the correct comparison method for this TreeMap.
1492      */
1493     @SuppressWarnings("unchecked")
1494     final int compare(Object k1, Object k2) {
1495         return comparator==null ? ((Comparable<? super K>)k1).compareTo((K)k2)
1496             : comparator.compare((K)k1, (K)k2);
1497     }
1498 
1499     /**
1500      * Test two values for equality.  Differs from o1.equals(o2) only in
1501      * that it copes with {@code null} o1 properly.
1502      */
1503     static final boolean valEquals(Object o1, Object o2) {
1504         return (o1==null ? o2==null : o1.equals(o2));
1505     }
1506 
1507     /**
1508      * Return SimpleImmutableEntry for entry, or null if null
1509      */
1510     static <K,V> Map.Entry<K,V> exportEntry(TreeMap.Entry<K,V> e) {
1511         return (e == null) ? null :
1512             new AbstractMap.SimpleImmutableEntry<>(e);
1513     }
1514 
1515     /**
1516      * Return key for entry, or null if null
1517      */
1518     static <K,V> K keyOrNull(TreeMap.Entry<K,V> e) {
1519         return (e == null) ? null : e.key;
1520     }
1521 
1522     /**
1523      * Returns the key corresponding to the specified Entry.
1524      * @throws NoSuchElementException if the Entry is null
1525      */
1526     static <K> K key(Entry<K,?> e) {
1527         if (e==null)
1528             throw new NoSuchElementException();
1529         return e.key;
1530     }
1531 
1532 
1533     // SubMaps
1534 
1535     /**
1536      * Dummy value serving as unmatchable fence key for unbounded
1537      * SubMapIterators
1538      */
1539     private static final Object UNBOUNDED = new Object();
1540 
1541     /**
1542      * @serial include
1543      */
1544     abstract static class NavigableSubMap<K,V> extends AbstractMap<K,V>
1545         implements NavigableMap<K,V>, java.io.Serializable {
1546         private static final long serialVersionUID = -2102997345730753016L;
1547         /**
1548          * The backing map.
1549          */
1550         final TreeMap<K,V> m;
1551 
1552         /**
1553          * Endpoints are represented as triples (fromStart, lo,
1554          * loInclusive) and (toEnd, hi, hiInclusive). If fromStart is
1555          * true, then the low (absolute) bound is the start of the
1556          * backing map, and the other values are ignored. Otherwise,
1557          * if loInclusive is true, lo is the inclusive bound, else lo
1558          * is the exclusive bound. Similarly for the upper bound.
1559          */
1560         final K lo, hi;
1561         final boolean fromStart, toEnd;
1562         final boolean loInclusive, hiInclusive;
1563 
1564         NavigableSubMap(TreeMap<K,V> m,
1565                         boolean fromStart, K lo, boolean loInclusive,
1566                         boolean toEnd,     K hi, boolean hiInclusive) {
1567             if (!fromStart && !toEnd) {
1568                 if (m.compare(lo, hi) > 0)
1569                     throw new IllegalArgumentException("fromKey > toKey");
1570             } else {
1571                 if (!fromStart) // type check
1572                     m.compare(lo, lo);
1573                 if (!toEnd)
1574                     m.compare(hi, hi);
1575             }
1576 
1577             this.m = m;
1578             this.fromStart = fromStart;
1579             this.lo = lo;
1580             this.loInclusive = loInclusive;
1581             this.toEnd = toEnd;
1582             this.hi = hi;
1583             this.hiInclusive = hiInclusive;
1584         }
1585 
1586         // internal utilities
1587 
1588         final boolean tooLow(Object key) {
1589             if (!fromStart) {
1590                 int c = m.compare(key, lo);
1591                 if (c < 0 || (c == 0 && !loInclusive))
1592                     return true;
1593             }
1594             return false;
1595         }
1596 
1597         final boolean tooHigh(Object key) {
1598             if (!toEnd) {
1599                 int c = m.compare(key, hi);
1600                 if (c > 0 || (c == 0 && !hiInclusive))
1601                     return true;
1602             }
1603             return false;
1604         }
1605 
1606         final boolean inRange(Object key) {
1607             return !tooLow(key) && !tooHigh(key);
1608         }
1609 
1610         final boolean inClosedRange(Object key) {
1611             return (fromStart || m.compare(key, lo) >= 0)
1612                 && (toEnd || m.compare(hi, key) >= 0);
1613         }
1614 
1615         final boolean inRange(Object key, boolean inclusive) {
1616             return inclusive ? inRange(key) : inClosedRange(key);
1617         }
1618 
1619         /*
1620          * Absolute versions of relation operations.
1621          * Subclasses map to these using like-named "sub"
1622          * versions that invert senses for descending maps
1623          */
1624 
1625         final TreeMap.Entry<K,V> absLowest() {
1626             TreeMap.Entry<K,V> e =
1627                 (fromStart ?  m.getFirstEntry() :
1628                  (loInclusive ? m.getCeilingEntry(lo) :
1629                                 m.getHigherEntry(lo)));
1630             return (e == null || tooHigh(e.key)) ? null : e;
1631         }
1632 
1633         final TreeMap.Entry<K,V> absHighest() {
1634             TreeMap.Entry<K,V> e =
1635                 (toEnd ?  m.getLastEntry() :
1636                  (hiInclusive ?  m.getFloorEntry(hi) :
1637                                  m.getLowerEntry(hi)));
1638             return (e == null || tooLow(e.key)) ? null : e;
1639         }
1640 
1641         final TreeMap.Entry<K,V> absCeiling(K key) {
1642             if (tooLow(key))
1643                 return absLowest();
1644             TreeMap.Entry<K,V> e = m.getCeilingEntry(key);
1645             return (e == null || tooHigh(e.key)) ? null : e;
1646         }
1647 
1648         final TreeMap.Entry<K,V> absHigher(K key) {
1649             if (tooLow(key))
1650                 return absLowest();
1651             TreeMap.Entry<K,V> e = m.getHigherEntry(key);
1652             return (e == null || tooHigh(e.key)) ? null : e;
1653         }
1654 
1655         final TreeMap.Entry<K,V> absFloor(K key) {
1656             if (tooHigh(key))
1657                 return absHighest();
1658             TreeMap.Entry<K,V> e = m.getFloorEntry(key);
1659             return (e == null || tooLow(e.key)) ? null : e;
1660         }
1661 
1662         final TreeMap.Entry<K,V> absLower(K key) {
1663             if (tooHigh(key))
1664                 return absHighest();
1665             TreeMap.Entry<K,V> e = m.getLowerEntry(key);
1666             return (e == null || tooLow(e.key)) ? null : e;
1667         }
1668 
1669         /** Returns the absolute high fence for ascending traversal */
1670         final TreeMap.Entry<K,V> absHighFence() {
1671             return (toEnd ? null : (hiInclusive ?
1672                                     m.getHigherEntry(hi) :
1673                                     m.getCeilingEntry(hi)));
1674         }
1675 
1676         /** Return the absolute low fence for descending traversal  */
1677         final TreeMap.Entry<K,V> absLowFence() {
1678             return (fromStart ? null : (loInclusive ?
1679                                         m.getLowerEntry(lo) :
1680                                         m.getFloorEntry(lo)));
1681         }
1682 
1683         // Abstract methods defined in ascending vs descending classes
1684         // These relay to the appropriate absolute versions
1685 
1686         abstract TreeMap.Entry<K,V> subLowest();
1687         abstract TreeMap.Entry<K,V> subHighest();
1688         abstract TreeMap.Entry<K,V> subCeiling(K key);
1689         abstract TreeMap.Entry<K,V> subHigher(K key);
1690         abstract TreeMap.Entry<K,V> subFloor(K key);
1691         abstract TreeMap.Entry<K,V> subLower(K key);
1692 
1693         /** Returns ascending iterator from the perspective of this submap */
1694         abstract Iterator<K> keyIterator();
1695 
1696         abstract Spliterator<K> keySpliterator();
1697 
1698         /** Returns descending iterator from the perspective of this submap */
1699         abstract Iterator<K> descendingKeyIterator();
1700 
1701         // public methods
1702 
1703         public boolean isEmpty() {
1704             return (fromStart && toEnd) ? m.isEmpty() : entrySet().isEmpty();
1705         }
1706 
1707         public int size() {
1708             return (fromStart && toEnd) ? m.size() : entrySet().size();
1709         }
1710 
1711         public final boolean containsKey(Object key) {
1712             return inRange(key) && m.containsKey(key);
1713         }
1714 
1715         public final V put(K key, V value) {
1716             if (!inRange(key))
1717                 throw new IllegalArgumentException("key out of range");
1718             return m.put(key, value);
1719         }
1720 
1721         public final V get(Object key) {
1722             return !inRange(key) ? null :  m.get(key);
1723         }
1724 
1725         public final V remove(Object key) {
1726             return !inRange(key) ? null : m.remove(key);
1727         }
1728 
1729         public final Map.Entry<K,V> ceilingEntry(K key) {
1730             return exportEntry(subCeiling(key));
1731         }
1732 
1733         public final K ceilingKey(K key) {
1734             return keyOrNull(subCeiling(key));
1735         }
1736 
1737         public final Map.Entry<K,V> higherEntry(K key) {
1738             return exportEntry(subHigher(key));
1739         }
1740 
1741         public final K higherKey(K key) {
1742             return keyOrNull(subHigher(key));
1743         }
1744 
1745         public final Map.Entry<K,V> floorEntry(K key) {
1746             return exportEntry(subFloor(key));
1747         }
1748 
1749         public final K floorKey(K key) {
1750             return keyOrNull(subFloor(key));
1751         }
1752 
1753         public final Map.Entry<K,V> lowerEntry(K key) {
1754             return exportEntry(subLower(key));
1755         }
1756 
1757         public final K lowerKey(K key) {
1758             return keyOrNull(subLower(key));
1759         }
1760 
1761         public final K firstKey() {
1762             return key(subLowest());
1763         }
1764 
1765         public final K lastKey() {
1766             return key(subHighest());
1767         }
1768 
1769         public final Map.Entry<K,V> firstEntry() {
1770             return exportEntry(subLowest());
1771         }
1772 
1773         public final Map.Entry<K,V> lastEntry() {
1774             return exportEntry(subHighest());
1775         }
1776 
1777         public final Map.Entry<K,V> pollFirstEntry() {
1778             TreeMap.Entry<K,V> e = subLowest();
1779             Map.Entry<K,V> result = exportEntry(e);
1780             if (e != null)
1781                 m.deleteEntry(e);
1782             return result;
1783         }
1784 
1785         public final Map.Entry<K,V> pollLastEntry() {
1786             TreeMap.Entry<K,V> e = subHighest();
1787             Map.Entry<K,V> result = exportEntry(e);
1788             if (e != null)
1789                 m.deleteEntry(e);
1790             return result;
1791         }
1792 
1793         // Views
1794         transient NavigableMap<K,V> descendingMapView;
1795         transient EntrySetView entrySetView;
1796         transient KeySet<K> navigableKeySetView;
1797 
1798         public final NavigableSet<K> navigableKeySet() {
1799             KeySet<K> nksv = navigableKeySetView;
1800             return (nksv != null) ? nksv :
1801                 (navigableKeySetView = new TreeMap.KeySet<>(this));
1802         }
1803 
1804         public final Set<K> keySet() {
1805             return navigableKeySet();
1806         }
1807 
1808         public NavigableSet<K> descendingKeySet() {
1809             return descendingMap().navigableKeySet();
1810         }
1811 
1812         public final SortedMap<K,V> subMap(K fromKey, K toKey) {
1813             return subMap(fromKey, true, toKey, false);
1814         }
1815 
1816         public final SortedMap<K,V> headMap(K toKey) {
1817             return headMap(toKey, false);
1818         }
1819 
1820         public final SortedMap<K,V> tailMap(K fromKey) {
1821             return tailMap(fromKey, true);
1822         }
1823 
1824         // View classes
1825 
1826         abstract class EntrySetView extends AbstractSet<Map.Entry<K,V>> {
1827             private transient int size = -1, sizeModCount;
1828 
1829             public int size() {
1830                 if (fromStart && toEnd)
1831                     return m.size();
1832                 if (size == -1 || sizeModCount != m.modCount) {
1833                     sizeModCount = m.modCount;
1834                     size = 0;
1835                     Iterator<?> i = iterator();
1836                     while (i.hasNext()) {
1837                         size++;
1838                         i.next();
1839                     }
1840                 }
1841                 return size;
1842             }
1843 
1844             public boolean isEmpty() {
1845                 TreeMap.Entry<K,V> n = absLowest();
1846                 return n == null || tooHigh(n.key);
1847             }
1848 
1849             public boolean contains(Object o) {
1850                 if (!(o instanceof Map.Entry))
1851                     return false;
1852                 Map.Entry<?,?> entry = (Map.Entry<?,?>) o;
1853                 Object key = entry.getKey();
1854                 if (!inRange(key))
1855                     return false;
1856                 TreeMap.Entry<?,?> node = m.getEntry(key);
1857                 return node != null &&
1858                     valEquals(node.getValue(), entry.getValue());
1859             }
1860 
1861             public boolean remove(Object o) {
1862                 if (!(o instanceof Map.Entry))
1863                     return false;
1864                 Map.Entry<?,?> entry = (Map.Entry<?,?>) o;
1865                 Object key = entry.getKey();
1866                 if (!inRange(key))
1867                     return false;
1868                 TreeMap.Entry<K,V> node = m.getEntry(key);
1869                 if (node!=null && valEquals(node.getValue(),
1870                                             entry.getValue())) {
1871                     m.deleteEntry(node);
1872                     return true;
1873                 }
1874                 return false;
1875             }
1876         }
1877 
1878         /**
1879          * Iterators for SubMaps
1880          */
1881         abstract class SubMapIterator<T> implements Iterator<T> {
1882             TreeMap.Entry<K,V> lastReturned;
1883             TreeMap.Entry<K,V> next;
1884             final Object fenceKey;
1885             int expectedModCount;
1886 
1887             SubMapIterator(TreeMap.Entry<K,V> first,
1888                            TreeMap.Entry<K,V> fence) {
1889                 expectedModCount = m.modCount;
1890                 lastReturned = null;
1891                 next = first;
1892                 fenceKey = fence == null ? UNBOUNDED : fence.key;
1893             }
1894 
1895             public final boolean hasNext() {
1896                 return next != null && next.key != fenceKey;
1897             }
1898 
1899             final TreeMap.Entry<K,V> nextEntry() {
1900                 TreeMap.Entry<K,V> e = next;
1901                 if (e == null || e.key == fenceKey)
1902                     throw new NoSuchElementException();
1903                 if (m.modCount != expectedModCount)
1904                     throw new ConcurrentModificationException();
1905                 next = successor(e);
1906                 lastReturned = e;
1907                 return e;
1908             }
1909 
1910             final TreeMap.Entry<K,V> prevEntry() {
1911                 TreeMap.Entry<K,V> e = next;
1912                 if (e == null || e.key == fenceKey)
1913                     throw new NoSuchElementException();
1914                 if (m.modCount != expectedModCount)
1915                     throw new ConcurrentModificationException();
1916                 next = predecessor(e);
1917                 lastReturned = e;
1918                 return e;
1919             }
1920 
1921             final void removeAscending() {
1922                 if (lastReturned == null)
1923                     throw new IllegalStateException();
1924                 if (m.modCount != expectedModCount)
1925                     throw new ConcurrentModificationException();
1926                 // deleted entries are replaced by their successors
1927                 if (lastReturned.left != null && lastReturned.right != null)
1928                     next = lastReturned;
1929                 m.deleteEntry(lastReturned);
1930                 lastReturned = null;
1931                 expectedModCount = m.modCount;
1932             }
1933 
1934             final void removeDescending() {
1935                 if (lastReturned == null)
1936                     throw new IllegalStateException();
1937                 if (m.modCount != expectedModCount)
1938                     throw new ConcurrentModificationException();
1939                 m.deleteEntry(lastReturned);
1940                 lastReturned = null;
1941                 expectedModCount = m.modCount;
1942             }
1943 
1944         }
1945 
1946         final class SubMapEntryIterator extends SubMapIterator<Map.Entry<K,V>> {
1947             SubMapEntryIterator(TreeMap.Entry<K,V> first,
1948                                 TreeMap.Entry<K,V> fence) {
1949                 super(first, fence);
1950             }
1951             public Map.Entry<K,V> next() {
1952                 return nextEntry();
1953             }
1954             public void remove() {
1955                 removeAscending();
1956             }
1957         }
1958 
1959         final class DescendingSubMapEntryIterator extends SubMapIterator<Map.Entry<K,V>> {
1960             DescendingSubMapEntryIterator(TreeMap.Entry<K,V> last,
1961                                           TreeMap.Entry<K,V> fence) {
1962                 super(last, fence);
1963             }
1964 
1965             public Map.Entry<K,V> next() {
1966                 return prevEntry();
1967             }
1968             public void remove() {
1969                 removeDescending();
1970             }
1971         }
1972 
1973         // Implement minimal Spliterator as KeySpliterator backup
1974         final class SubMapKeyIterator extends SubMapIterator<K>
1975             implements Spliterator<K> {
1976             SubMapKeyIterator(TreeMap.Entry<K,V> first,
1977                               TreeMap.Entry<K,V> fence) {
1978                 super(first, fence);
1979             }
1980             public K next() {
1981                 return nextEntry().key;
1982             }
1983             public void remove() {
1984                 removeAscending();
1985             }
1986             public Spliterator<K> trySplit() {
1987                 return null;
1988             }
1989             public void forEachRemaining(Consumer<? super K> action) {
1990                 while (hasNext())
1991                     action.accept(next());
1992             }
1993             public boolean tryAdvance(Consumer<? super K> action) {
1994                 if (hasNext()) {
1995                     action.accept(next());
1996                     return true;
1997                 }
1998                 return false;
1999             }
2000             public long estimateSize() {
2001                 return Long.MAX_VALUE;
2002             }
2003             public int characteristics() {
2004                 return Spliterator.DISTINCT | Spliterator.ORDERED |
2005                     Spliterator.SORTED;
2006             }
2007             public final Comparator<? super K>  getComparator() {
2008                 return NavigableSubMap.this.comparator();
2009             }
2010         }
2011 
2012         final class DescendingSubMapKeyIterator extends SubMapIterator<K>
2013             implements Spliterator<K> {
2014             DescendingSubMapKeyIterator(TreeMap.Entry<K,V> last,
2015                                         TreeMap.Entry<K,V> fence) {
2016                 super(last, fence);
2017             }
2018             public K next() {
2019                 return prevEntry().key;
2020             }
2021             public void remove() {
2022                 removeDescending();
2023             }
2024             public Spliterator<K> trySplit() {
2025                 return null;
2026             }
2027             public void forEachRemaining(Consumer<? super K> action) {
2028                 while (hasNext())
2029                     action.accept(next());
2030             }
2031             public boolean tryAdvance(Consumer<? super K> action) {
2032                 if (hasNext()) {
2033                     action.accept(next());
2034                     return true;
2035                 }
2036                 return false;
2037             }
2038             public long estimateSize() {
2039                 return Long.MAX_VALUE;
2040             }
2041             public int characteristics() {
2042                 return Spliterator.DISTINCT | Spliterator.ORDERED;
2043             }
2044         }
2045     }
2046 
2047     /**
2048      * @serial include
2049      */
2050     static final class AscendingSubMap<K,V> extends NavigableSubMap<K,V> {
2051         private static final long serialVersionUID = 912986545866124060L;
2052 
2053         AscendingSubMap(TreeMap<K,V> m,
2054                         boolean fromStart, K lo, boolean loInclusive,
2055                         boolean toEnd,     K hi, boolean hiInclusive) {
2056             super(m, fromStart, lo, loInclusive, toEnd, hi, hiInclusive);
2057         }
2058 
2059         public Comparator<? super K> comparator() {
2060             return m.comparator();
2061         }
2062 
2063         public NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
2064                                         K toKey,   boolean toInclusive) {
2065             if (!inRange(fromKey, fromInclusive))
2066                 throw new IllegalArgumentException("fromKey out of range");
2067             if (!inRange(toKey, toInclusive))
2068                 throw new IllegalArgumentException("toKey out of range");
2069             return new AscendingSubMap<>(m,
2070                                          false, fromKey, fromInclusive,
2071                                          false, toKey,   toInclusive);
2072         }
2073 
2074         public NavigableMap<K,V> headMap(K toKey, boolean inclusive) {
2075             if (!inRange(toKey, inclusive))
2076                 throw new IllegalArgumentException("toKey out of range");
2077             return new AscendingSubMap<>(m,
2078                                          fromStart, lo,    loInclusive,
2079                                          false,     toKey, inclusive);
2080         }
2081 
2082         public NavigableMap<K,V> tailMap(K fromKey, boolean inclusive) {
2083             if (!inRange(fromKey, inclusive))
2084                 throw new IllegalArgumentException("fromKey out of range");
2085             return new AscendingSubMap<>(m,
2086                                          false, fromKey, inclusive,
2087                                          toEnd, hi,      hiInclusive);
2088         }
2089 
2090         public NavigableMap<K,V> descendingMap() {
2091             NavigableMap<K,V> mv = descendingMapView;
2092             return (mv != null) ? mv :
2093                 (descendingMapView =
2094                  new DescendingSubMap<>(m,
2095                                         fromStart, lo, loInclusive,
2096                                         toEnd,     hi, hiInclusive));
2097         }
2098 
2099         Iterator<K> keyIterator() {
2100             return new SubMapKeyIterator(absLowest(), absHighFence());
2101         }
2102 
2103         Spliterator<K> keySpliterator() {
2104             return new SubMapKeyIterator(absLowest(), absHighFence());
2105         }
2106 
2107         Iterator<K> descendingKeyIterator() {
2108             return new DescendingSubMapKeyIterator(absHighest(), absLowFence());
2109         }
2110 
2111         final class AscendingEntrySetView extends EntrySetView {
2112             public Iterator<Map.Entry<K,V>> iterator() {
2113                 return new SubMapEntryIterator(absLowest(), absHighFence());
2114             }
2115         }
2116 
2117         public Set<Map.Entry<K,V>> entrySet() {
2118             EntrySetView es = entrySetView;
2119             return (es != null) ? es : (entrySetView = new AscendingEntrySetView());
2120         }
2121 
2122         TreeMap.Entry<K,V> subLowest()       { return absLowest(); }
2123         TreeMap.Entry<K,V> subHighest()      { return absHighest(); }
2124         TreeMap.Entry<K,V> subCeiling(K key) { return absCeiling(key); }
2125         TreeMap.Entry<K,V> subHigher(K key)  { return absHigher(key); }
2126         TreeMap.Entry<K,V> subFloor(K key)   { return absFloor(key); }
2127         TreeMap.Entry<K,V> subLower(K key)   { return absLower(key); }
2128     }
2129 
2130     /**
2131      * @serial include
2132      */
2133     static final class DescendingSubMap<K,V>  extends NavigableSubMap<K,V> {
2134         private static final long serialVersionUID = 912986545866120460L;
2135         DescendingSubMap(TreeMap<K,V> m,
2136                         boolean fromStart, K lo, boolean loInclusive,
2137                         boolean toEnd,     K hi, boolean hiInclusive) {
2138             super(m, fromStart, lo, loInclusive, toEnd, hi, hiInclusive);
2139         }
2140 
2141         private final Comparator<? super K> reverseComparator =
2142             Collections.reverseOrder(m.comparator);
2143 
2144         public Comparator<? super K> comparator() {
2145             return reverseComparator;
2146         }
2147 
2148         public NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
2149                                         K toKey,   boolean toInclusive) {
2150             if (!inRange(fromKey, fromInclusive))
2151                 throw new IllegalArgumentException("fromKey out of range");
2152             if (!inRange(toKey, toInclusive))
2153                 throw new IllegalArgumentException("toKey out of range");
2154             return new DescendingSubMap<>(m,
2155                                           false, toKey,   toInclusive,
2156                                           false, fromKey, fromInclusive);
2157         }
2158 
2159         public NavigableMap<K,V> headMap(K toKey, boolean inclusive) {
2160             if (!inRange(toKey, inclusive))
2161                 throw new IllegalArgumentException("toKey out of range");
2162             return new DescendingSubMap<>(m,
2163                                           false, toKey, inclusive,
2164                                           toEnd, hi,    hiInclusive);
2165         }
2166 
2167         public NavigableMap<K,V> tailMap(K fromKey, boolean inclusive) {
2168             if (!inRange(fromKey, inclusive))
2169                 throw new IllegalArgumentException("fromKey out of range");
2170             return new DescendingSubMap<>(m,
2171                                           fromStart, lo, loInclusive,
2172                                           false, fromKey, inclusive);
2173         }
2174 
2175         public NavigableMap<K,V> descendingMap() {
2176             NavigableMap<K,V> mv = descendingMapView;
2177             return (mv != null) ? mv :
2178                 (descendingMapView =
2179                  new AscendingSubMap<>(m,
2180                                        fromStart, lo, loInclusive,
2181                                        toEnd,     hi, hiInclusive));
2182         }
2183 
2184         Iterator<K> keyIterator() {
2185             return new DescendingSubMapKeyIterator(absHighest(), absLowFence());
2186         }
2187 
2188         Spliterator<K> keySpliterator() {
2189             return new DescendingSubMapKeyIterator(absHighest(), absLowFence());
2190         }
2191 
2192         Iterator<K> descendingKeyIterator() {
2193             return new SubMapKeyIterator(absLowest(), absHighFence());
2194         }
2195 
2196         final class DescendingEntrySetView extends EntrySetView {
2197             public Iterator<Map.Entry<K,V>> iterator() {
2198                 return new DescendingSubMapEntryIterator(absHighest(), absLowFence());
2199             }
2200         }
2201 
2202         public Set<Map.Entry<K,V>> entrySet() {
2203             EntrySetView es = entrySetView;
2204             return (es != null) ? es : (entrySetView = new DescendingEntrySetView());
2205         }
2206 
2207         TreeMap.Entry<K,V> subLowest()       { return absHighest(); }
2208         TreeMap.Entry<K,V> subHighest()      { return absLowest(); }
2209         TreeMap.Entry<K,V> subCeiling(K key) { return absFloor(key); }
2210         TreeMap.Entry<K,V> subHigher(K key)  { return absLower(key); }
2211         TreeMap.Entry<K,V> subFloor(K key)   { return absCeiling(key); }
2212         TreeMap.Entry<K,V> subLower(K key)   { return absHigher(key); }
2213     }
2214 
2215     /**
2216      * This class exists solely for the sake of serialization
2217      * compatibility with previous releases of TreeMap that did not
2218      * support NavigableMap.  It translates an old-version SubMap into
2219      * a new-version AscendingSubMap. This class is never otherwise
2220      * used.
2221      *
2222      * @serial include
2223      */
2224     private class SubMap extends AbstractMap<K,V>
2225         implements SortedMap<K,V>, java.io.Serializable {
2226         private static final long serialVersionUID = -6520786458950516097L;
2227         private boolean fromStart = false, toEnd = false;
2228         private K fromKey, toKey;
2229         private Object readResolve() {
2230             return new AscendingSubMap<>(TreeMap.this,
2231                                          fromStart, fromKey, true,
2232                                          toEnd, toKey, false);
2233         }
2234         public Set<Map.Entry<K,V>> entrySet() { throw new InternalError(); }
2235         public K lastKey() { throw new InternalError(); }
2236         public K firstKey() { throw new InternalError(); }
2237         public SortedMap<K,V> subMap(K fromKey, K toKey) { throw new InternalError(); }
2238         public SortedMap<K,V> headMap(K toKey) { throw new InternalError(); }
2239         public SortedMap<K,V> tailMap(K fromKey) { throw new InternalError(); }
2240         public Comparator<? super K> comparator() { throw new InternalError(); }
2241     }
2242 
2243 
2244     // Red-black mechanics
2245 
2246     private static final boolean RED   = false;
2247     private static final boolean BLACK = true;
2248 
2249     /**
2250      * Node in the Tree.  Doubles as a means to pass key-value pairs back to
2251      * user (see Map.Entry).
2252      */
2253 
2254     static final class Entry<K,V> implements Map.Entry<K,V> {
2255         K key;
2256         V value;
2257         Entry<K,V> left;
2258         Entry<K,V> right;
2259         Entry<K,V> parent;
2260         boolean color = BLACK;
2261 
2262         /**
2263          * Make a new cell with given key, value, and parent, and with
2264          * {@code null} child links, and BLACK color.
2265          */
2266         Entry(K key, V value, Entry<K,V> parent) {
2267             this.key = key;
2268             this.value = value;
2269             this.parent = parent;
2270         }
2271 
2272         /**
2273          * Returns the key.
2274          *
2275          * @return the key
2276          */
2277         public K getKey() {
2278             return key;
2279         }
2280 
2281         /**
2282          * Returns the value associated with the key.
2283          *
2284          * @return the value associated with the key
2285          */
2286         public V getValue() {
2287             return value;
2288         }
2289 
2290         /**
2291          * Replaces the value currently associated with the key with the given
2292          * value.
2293          *
2294          * @return the value associated with the key before this method was
2295          *         called
2296          */
2297         public V setValue(V value) {
2298             V oldValue = this.value;
2299             this.value = value;
2300             return oldValue;
2301         }
2302 
2303         public boolean equals(Object o) {
2304             if (!(o instanceof Map.Entry))
2305                 return false;
2306             Map.Entry<?,?> e = (Map.Entry<?,?>)o;
2307 
2308             return valEquals(key,e.getKey()) && valEquals(value,e.getValue());
2309         }
2310 
2311         public int hashCode() {
2312             int keyHash = (key==null ? 0 : key.hashCode());
2313             int valueHash = (value==null ? 0 : value.hashCode());
2314             return keyHash ^ valueHash;
2315         }
2316 
2317         public String toString() {
2318             return key + "=" + value;
2319         }
2320     }
2321 
2322     /**
2323      * Returns the first Entry in the TreeMap (according to the TreeMap's
2324      * key-sort function).  Returns null if the TreeMap is empty.
2325      */
2326     final Entry<K,V> getFirstEntry() {
2327         Entry<K,V> p = root;
2328         if (p != null)
2329             while (p.left != null)
2330                 p = p.left;
2331         return p;
2332     }
2333 
2334     /**
2335      * Returns the last Entry in the TreeMap (according to the TreeMap's
2336      * key-sort function).  Returns null if the TreeMap is empty.
2337      */
2338     final Entry<K,V> getLastEntry() {
2339         Entry<K,V> p = root;
2340         if (p != null)
2341             while (p.right != null)
2342                 p = p.right;
2343         return p;
2344     }
2345 
2346     /**
2347      * Returns the successor of the specified Entry, or null if no such.
2348      */
2349     static <K,V> TreeMap.Entry<K,V> successor(Entry<K,V> t) {
2350         if (t == null)
2351             return null;
2352         else if (t.right != null) {
2353             Entry<K,V> p = t.right;
2354             while (p.left != null)
2355                 p = p.left;
2356             return p;
2357         } else {
2358             Entry<K,V> p = t.parent;
2359             Entry<K,V> ch = t;
2360             while (p != null && ch == p.right) {
2361                 ch = p;
2362                 p = p.parent;
2363             }
2364             return p;
2365         }
2366     }
2367 
2368     /**
2369      * Returns the predecessor of the specified Entry, or null if no such.
2370      */
2371     static <K,V> Entry<K,V> predecessor(Entry<K,V> t) {
2372         if (t == null)
2373             return null;
2374         else if (t.left != null) {
2375             Entry<K,V> p = t.left;
2376             while (p.right != null)
2377                 p = p.right;
2378             return p;
2379         } else {
2380             Entry<K,V> p = t.parent;
2381             Entry<K,V> ch = t;
2382             while (p != null && ch == p.left) {
2383                 ch = p;
2384                 p = p.parent;
2385             }
2386             return p;
2387         }
2388     }
2389 
2390     /**
2391      * Balancing operations.
2392      *
2393      * Implementations of rebalancings during insertion and deletion are
2394      * slightly different than the CLR version.  Rather than using dummy
2395      * nilnodes, we use a set of accessors that deal properly with null.  They
2396      * are used to avoid messiness surrounding nullness checks in the main
2397      * algorithms.
2398      */
2399 
2400     private static <K,V> boolean colorOf(Entry<K,V> p) {
2401         return (p == null ? BLACK : p.color);
2402     }
2403 
2404     private static <K,V> Entry<K,V> parentOf(Entry<K,V> p) {
2405         return (p == null ? null: p.parent);
2406     }
2407 
2408     private static <K,V> void setColor(Entry<K,V> p, boolean c) {
2409         if (p != null)
2410             p.color = c;
2411     }
2412 
2413     private static <K,V> Entry<K,V> leftOf(Entry<K,V> p) {
2414         return (p == null) ? null: p.left;
2415     }
2416 
2417     private static <K,V> Entry<K,V> rightOf(Entry<K,V> p) {
2418         return (p == null) ? null: p.right;
2419     }
2420 
2421     /** From CLR */
2422     private void rotateLeft(Entry<K,V> p) {
2423         if (p != null) {
2424             Entry<K,V> r = p.right;
2425             p.right = r.left;
2426             if (r.left != null)
2427                 r.left.parent = p;
2428             r.parent = p.parent;
2429             if (p.parent == null)
2430                 root = r;
2431             else if (p.parent.left == p)
2432                 p.parent.left = r;
2433             else
2434                 p.parent.right = r;
2435             r.left = p;
2436             p.parent = r;
2437         }
2438     }
2439 
2440     /** From CLR */
2441     private void rotateRight(Entry<K,V> p) {
2442         if (p != null) {
2443             Entry<K,V> l = p.left;
2444             p.left = l.right;
2445             if (l.right != null) l.right.parent = p;
2446             l.parent = p.parent;
2447             if (p.parent == null)
2448                 root = l;
2449             else if (p.parent.right == p)
2450                 p.parent.right = l;
2451             else p.parent.left = l;
2452             l.right = p;
2453             p.parent = l;
2454         }
2455     }
2456 
2457     /** From CLR */
2458     private void fixAfterInsertion(Entry<K,V> x) {
2459         x.color = RED;
2460 
2461         while (x != null && x != root && x.parent.color == RED) {
2462             if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {
2463                 Entry<K,V> y = rightOf(parentOf(parentOf(x)));
2464                 if (colorOf(y) == RED) {
2465                     setColor(parentOf(x), BLACK);
2466                     setColor(y, BLACK);
2467                     setColor(parentOf(parentOf(x)), RED);
2468                     x = parentOf(parentOf(x));
2469                 } else {
2470                     if (x == rightOf(parentOf(x))) {
2471                         x = parentOf(x);
2472                         rotateLeft(x);
2473                     }
2474                     setColor(parentOf(x), BLACK);
2475                     setColor(parentOf(parentOf(x)), RED);
2476                     rotateRight(parentOf(parentOf(x)));
2477                 }
2478             } else {
2479                 Entry<K,V> y = leftOf(parentOf(parentOf(x)));
2480                 if (colorOf(y) == RED) {
2481                     setColor(parentOf(x), BLACK);
2482                     setColor(y, BLACK);
2483                     setColor(parentOf(parentOf(x)), RED);
2484                     x = parentOf(parentOf(x));
2485                 } else {
2486                     if (x == leftOf(parentOf(x))) {
2487                         x = parentOf(x);
2488                         rotateRight(x);
2489                     }
2490                     setColor(parentOf(x), BLACK);
2491                     setColor(parentOf(parentOf(x)), RED);
2492                     rotateLeft(parentOf(parentOf(x)));
2493                 }
2494             }
2495         }
2496         root.color = BLACK;
2497     }
2498 
2499     /**
2500      * Delete node p, and then rebalance the tree.
2501      */
2502     private void deleteEntry(Entry<K,V> p) {
2503         modCount++;
2504         size--;
2505 
2506         // If strictly internal, copy successor's element to p and then make p
2507         // point to successor.
2508         if (p.left != null && p.right != null) {
2509             Entry<K,V> s = successor(p);
2510             p.key = s.key;
2511             p.value = s.value;
2512             p = s;
2513         } // p has 2 children
2514 
2515         // Start fixup at replacement node, if it exists.
2516         Entry<K,V> replacement = (p.left != null ? p.left : p.right);
2517 
2518         if (replacement != null) {
2519             // Link replacement to parent
2520             replacement.parent = p.parent;
2521             if (p.parent == null)
2522                 root = replacement;
2523             else if (p == p.parent.left)
2524                 p.parent.left  = replacement;
2525             else
2526                 p.parent.right = replacement;
2527 
2528             // Null out links so they are OK to use by fixAfterDeletion.
2529             p.left = p.right = p.parent = null;
2530 
2531             // Fix replacement
2532             if (p.color == BLACK)
2533                 fixAfterDeletion(replacement);
2534         } else if (p.parent == null) { // return if we are the only node.
2535             root = null;
2536         } else { //  No children. Use self as phantom replacement and unlink.
2537             if (p.color == BLACK)
2538                 fixAfterDeletion(p);
2539 
2540             if (p.parent != null) {
2541                 if (p == p.parent.left)
2542                     p.parent.left = null;
2543                 else if (p == p.parent.right)
2544                     p.parent.right = null;
2545                 p.parent = null;
2546             }
2547         }
2548     }
2549 
2550     /** From CLR */
2551     private void fixAfterDeletion(Entry<K,V> x) {
2552         while (x != root && colorOf(x) == BLACK) {
2553             if (x == leftOf(parentOf(x))) {
2554                 Entry<K,V> sib = rightOf(parentOf(x));
2555 
2556                 if (colorOf(sib) == RED) {
2557                     setColor(sib, BLACK);
2558                     setColor(parentOf(x), RED);
2559                     rotateLeft(parentOf(x));
2560                     sib = rightOf(parentOf(x));
2561                 }
2562 
2563                 if (colorOf(leftOf(sib))  == BLACK &&
2564                     colorOf(rightOf(sib)) == BLACK) {
2565                     setColor(sib, RED);
2566                     x = parentOf(x);
2567                 } else {
2568                     if (colorOf(rightOf(sib)) == BLACK) {
2569                         setColor(leftOf(sib), BLACK);
2570                         setColor(sib, RED);
2571                         rotateRight(sib);
2572                         sib = rightOf(parentOf(x));
2573                     }
2574                     setColor(sib, colorOf(parentOf(x)));
2575                     setColor(parentOf(x), BLACK);
2576                     setColor(rightOf(sib), BLACK);
2577                     rotateLeft(parentOf(x));
2578                     x = root;
2579                 }
2580             } else { // symmetric
2581                 Entry<K,V> sib = leftOf(parentOf(x));
2582 
2583                 if (colorOf(sib) == RED) {
2584                     setColor(sib, BLACK);
2585                     setColor(parentOf(x), RED);
2586                     rotateRight(parentOf(x));
2587                     sib = leftOf(parentOf(x));
2588                 }
2589 
2590                 if (colorOf(rightOf(sib)) == BLACK &&
2591                     colorOf(leftOf(sib)) == BLACK) {
2592                     setColor(sib, RED);
2593                     x = parentOf(x);
2594                 } else {
2595                     if (colorOf(leftOf(sib)) == BLACK) {
2596                         setColor(rightOf(sib), BLACK);
2597                         setColor(sib, RED);
2598                         rotateLeft(sib);
2599                         sib = leftOf(parentOf(x));
2600                     }
2601                     setColor(sib, colorOf(parentOf(x)));
2602                     setColor(parentOf(x), BLACK);
2603                     setColor(leftOf(sib), BLACK);
2604                     rotateRight(parentOf(x));
2605                     x = root;
2606                 }
2607             }
2608         }
2609 
2610         setColor(x, BLACK);
2611     }
2612 
2613     private static final long serialVersionUID = 919286545866124006L;
2614 
2615     /**
2616      * Save the state of the {@code TreeMap} instance to a stream (i.e.,
2617      * serialize it).
2618      *
2619      * @serialData The <em>size</em> of the TreeMap (the number of key-value
2620      *             mappings) is emitted (int), followed by the key (Object)
2621      *             and value (Object) for each key-value mapping represented
2622      *             by the TreeMap. The key-value mappings are emitted in
2623      *             key-order (as determined by the TreeMap's Comparator,
2624      *             or by the keys' natural ordering if the TreeMap has no
2625      *             Comparator).
2626      */
2627     private void writeObject(java.io.ObjectOutputStream s)
2628         throws java.io.IOException {
2629         // Write out the Comparator and any hidden stuff
2630         s.defaultWriteObject();
2631 
2632         // Write out size (number of Mappings)
2633         s.writeInt(size);
2634 
2635         // Write out keys and values (alternating)
2636         for (Map.Entry<K, V> e : entrySet()) {
2637             s.writeObject(e.getKey());
2638             s.writeObject(e.getValue());
2639         }
2640     }
2641 
2642     /**
2643      * Reconstitute the {@code TreeMap} instance from a stream (i.e.,
2644      * deserialize it).
2645      */
2646     private void readObject(final java.io.ObjectInputStream s)
2647         throws java.io.IOException, ClassNotFoundException {
2648         // Read in the Comparator and any hidden stuff
2649         s.defaultReadObject();
2650 
2651         // Read in size
2652         int size = s.readInt();
2653 
2654         buildFromSorted(size, null, s, null);
2655     }
2656 
2657     /** Intended to be called only from TreeSet.readObject */
2658     void readTreeSet(int size, java.io.ObjectInputStream s, V defaultVal)
2659         throws java.io.IOException, ClassNotFoundException {
2660         buildFromSorted(size, null, s, defaultVal);
2661     }
2662 
2663     /** Intended to be called only from TreeSet.addAll */
2664     void addAllForTreeSet(SortedSet<? extends K> set, V defaultVal) {
2665         try {
2666             buildFromSorted(set.size(), set.iterator(), null, defaultVal);
2667         } catch (java.io.IOException | ClassNotFoundException cannotHappen) {
2668         }
2669     }
2670 
2671 
2672     /**
2673      * Linear time tree building algorithm from sorted data.  Can accept keys
2674      * and/or values from iterator or stream. This leads to too many
2675      * parameters, but seems better than alternatives.  The four formats
2676      * that this method accepts are:
2677      *
2678      *    1) An iterator of Map.Entries.  (it != null, defaultVal == null).
2679      *    2) An iterator of keys.         (it != null, defaultVal != null).
2680      *    3) A stream of alternating serialized keys and values.
2681      *                                   (it == null, defaultVal == null).
2682      *    4) A stream of serialized keys. (it == null, defaultVal != null).
2683      *
2684      * It is assumed that the comparator of the TreeMap is already set prior
2685      * to calling this method.
2686      *
2687      * @param size the number of keys (or key-value pairs) to be read from
2688      *        the iterator or stream
2689      * @param it If non-null, new entries are created from entries
2690      *        or keys read from this iterator.
2691      * @param str If non-null, new entries are created from keys and
2692      *        possibly values read from this stream in serialized form.
2693      *        Exactly one of it and str should be non-null.
2694      * @param defaultVal if non-null, this default value is used for
2695      *        each value in the map.  If null, each value is read from
2696      *        iterator or stream, as described above.
2697      * @throws java.io.IOException propagated from stream reads. This cannot
2698      *         occur if str is null.
2699      * @throws ClassNotFoundException propagated from readObject.
2700      *         This cannot occur if str is null.
2701      */
2702     private void buildFromSorted(int size, Iterator<?> it,
2703                                  java.io.ObjectInputStream str,
2704                                  V defaultVal)
2705         throws  java.io.IOException, ClassNotFoundException {
2706         this.size = size;
2707         root = buildFromSorted(0, 0, size-1, computeRedLevel(size),
2708                                it, str, defaultVal);
2709     }
2710 
2711     /**
2712      * Recursive "helper method" that does the real work of the
2713      * previous method.  Identically named parameters have
2714      * identical definitions.  Additional parameters are documented below.
2715      * It is assumed that the comparator and size fields of the TreeMap are
2716      * already set prior to calling this method.  (It ignores both fields.)
2717      *
2718      * @param level the current level of tree. Initial call should be 0.
2719      * @param lo the first element index of this subtree. Initial should be 0.
2720      * @param hi the last element index of this subtree.  Initial should be
2721      *        size-1.
2722      * @param redLevel the level at which nodes should be red.
2723      *        Must be equal to computeRedLevel for tree of this size.
2724      */
2725     @SuppressWarnings("unchecked")
2726     private final Entry<K,V> buildFromSorted(int level, int lo, int hi,
2727                                              int redLevel,
2728                                              Iterator<?> it,
2729                                              java.io.ObjectInputStream str,
2730                                              V defaultVal)
2731         throws  java.io.IOException, ClassNotFoundException {
2732         /*
2733          * Strategy: The root is the middlemost element. To get to it, we
2734          * have to first recursively construct the entire left subtree,
2735          * so as to grab all of its elements. We can then proceed with right
2736          * subtree.
2737          *
2738          * The lo and hi arguments are the minimum and maximum
2739          * indices to pull out of the iterator or stream for current subtree.
2740          * They are not actually indexed, we just proceed sequentially,
2741          * ensuring that items are extracted in corresponding order.
2742          */
2743 
2744         if (hi < lo) return null;
2745 
2746         int mid = (lo + hi) >>> 1;
2747 
2748         Entry<K,V> left  = null;
2749         if (lo < mid)
2750             left = buildFromSorted(level+1, lo, mid - 1, redLevel,
2751                                    it, str, defaultVal);
2752 
2753         // extract key and/or value from iterator or stream
2754         K key;
2755         V value;
2756         if (it != null) {
2757             if (defaultVal==null) {
2758                 Map.Entry<?,?> entry = (Map.Entry<?,?>)it.next();
2759                 key = (K)entry.getKey();
2760                 value = (V)entry.getValue();
2761             } else {
2762                 key = (K)it.next();
2763                 value = defaultVal;
2764             }
2765         } else { // use stream
2766             key = (K) str.readObject();
2767             value = (defaultVal != null ? defaultVal : (V) str.readObject());
2768         }
2769 
2770         Entry<K,V> middle =  new Entry<>(key, value, null);
2771 
2772         // color nodes in non-full bottommost level red
2773         if (level == redLevel)
2774             middle.color = RED;
2775 
2776         if (left != null) {
2777             middle.left = left;
2778             left.parent = middle;
2779         }
2780 
2781         if (mid < hi) {
2782             Entry<K,V> right = buildFromSorted(level+1, mid+1, hi, redLevel,
2783                                                it, str, defaultVal);
2784             middle.right = right;
2785             right.parent = middle;
2786         }
2787 
2788         return middle;
2789     }
2790 
2791     /**
2792      * Finds the level down to which to assign all nodes BLACK.  This is the
2793      * last `full' level of the complete binary tree produced by buildTree.
2794      * The remaining nodes are colored RED. (This makes a `nice' set of
2795      * color assignments wrt future insertions.) This level number is
2796      * computed by finding the number of splits needed to reach the zeroeth
2797      * node.
2798      *
2799      * @param size the (non-negative) number of keys in the tree to be built
2800      */
2801     private static int computeRedLevel(int size) {
2802         return 31 - Integer.numberOfLeadingZeros(size + 1);
2803     }
2804 
2805     /**
2806      * Currently, we support Spliterator-based versions only for the
2807      * full map, in either plain of descending form, otherwise relying
2808      * on defaults because size estimation for submaps would dominate
2809      * costs. The type tests needed to check these for key views are
2810      * not very nice but avoid disrupting existing class
2811      * structures. Callers must use plain default spliterators if this
2812      * returns null.
2813      */
2814     static <K> Spliterator<K> keySpliteratorFor(NavigableMap<K,?> m) {
2815         if (m instanceof TreeMap) {
2816             @SuppressWarnings("unchecked") TreeMap<K,Object> t =
2817                 (TreeMap<K,Object>) m;
2818             return t.keySpliterator();
2819         }
2820         if (m instanceof DescendingSubMap) {
2821             @SuppressWarnings("unchecked") DescendingSubMap<K,?> dm =
2822                 (DescendingSubMap<K,?>) m;
2823             TreeMap<K,?> tm = dm.m;
2824             if (dm == tm.descendingMap) {
2825                 @SuppressWarnings("unchecked") TreeMap<K,Object> t =
2826                     (TreeMap<K,Object>) tm;
2827                 return t.descendingKeySpliterator();
2828             }
2829         }
2830         @SuppressWarnings("unchecked") NavigableSubMap<K,?> sm =
2831             (NavigableSubMap<K,?>) m;
2832         return sm.keySpliterator();
2833     }
2834 
2835     final Spliterator<K> keySpliterator() {
2836         return new KeySpliterator<>(this, null, null, 0, -1, 0);
2837     }
2838 
2839     final Spliterator<K> descendingKeySpliterator() {
2840         return new DescendingKeySpliterator<>(this, null, null, 0, -2, 0);
2841     }
2842 
2843     /**
2844      * Base class for spliterators.  Iteration starts at a given
2845      * origin and continues up to but not including a given fence (or
2846      * null for end).  At top-level, for ascending cases, the first
2847      * split uses the root as left-fence/right-origin. From there,
2848      * right-hand splits replace the current fence with its left
2849      * child, also serving as origin for the split-off spliterator.
2850      * Left-hands are symmetric. Descending versions place the origin
2851      * at the end and invert ascending split rules.  This base class
2852      * is non-committal about directionality, or whether the top-level
2853      * spliterator covers the whole tree. This means that the actual
2854      * split mechanics are located in subclasses. Some of the subclass
2855      * trySplit methods are identical (except for return types), but
2856      * not nicely factorable.
2857      *
2858      * Currently, subclass versions exist only for the full map
2859      * (including descending keys via its descendingMap).  Others are
2860      * possible but currently not worthwhile because submaps require
2861      * O(n) computations to determine size, which substantially limits
2862      * potential speed-ups of using custom Spliterators versus default
2863      * mechanics.
2864      *
2865      * To boostrap initialization, external constructors use
2866      * negative size estimates: -1 for ascend, -2 for descend.
2867      */
2868     static class TreeMapSpliterator<K,V> {
2869         final TreeMap<K,V> tree;
2870         TreeMap.Entry<K,V> current; // traverser; initially first node in range
2871         TreeMap.Entry<K,V> fence;   // one past last, or null
2872         int side;                   // 0: top, -1: is a left split, +1: right
2873         int est;                    // size estimate (exact only for top-level)
2874         int expectedModCount;       // for CME checks
2875 
2876         TreeMapSpliterator(TreeMap<K,V> tree,
2877                            TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
2878                            int side, int est, int expectedModCount) {
2879             this.tree = tree;
2880             this.current = origin;
2881             this.fence = fence;
2882             this.side = side;
2883             this.est = est;
2884             this.expectedModCount = expectedModCount;
2885         }
2886 
2887         final int getEstimate() { // force initialization
2888             int s; TreeMap<K,V> t;
2889             if ((s = est) < 0) {
2890                 if ((t = tree) != null) {
2891                     current = (s == -1) ? t.getFirstEntry() : t.getLastEntry();
2892                     s = est = t.size;
2893                     expectedModCount = t.modCount;
2894                 }
2895                 else
2896                     s = est = 0;
2897             }
2898             return s;
2899         }
2900 
2901         public final long estimateSize() {
2902             return (long)getEstimate();
2903         }
2904     }
2905 
2906     static final class KeySpliterator<K,V>
2907         extends TreeMapSpliterator<K,V>
2908         implements Spliterator<K> {
2909         KeySpliterator(TreeMap<K,V> tree,
2910                        TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
2911                        int side, int est, int expectedModCount) {
2912             super(tree, origin, fence, side, est, expectedModCount);
2913         }
2914 
2915         public KeySpliterator<K,V> trySplit() {
2916             if (est < 0)
2917                 getEstimate(); // force initialization
2918             int d = side;
2919             TreeMap.Entry<K,V> e = current, f = fence,
2920                 s = ((e == null || e == f) ? null :      // empty
2921                      (d == 0)              ? tree.root : // was top
2922                      (d >  0)              ? e.right :   // was right
2923                      (d <  0 && f != null) ? f.left :    // was left
2924                      null);
2925             if (s != null && s != e && s != f &&
2926                 tree.compare(e.key, s.key) < 0) {        // e not already past s
2927                 side = 1;
2928                 return new KeySpliterator<>
2929                     (tree, e, current = s, -1, est >>>= 1, expectedModCount);
2930             }
2931             return null;
2932         }
2933 
2934         public void forEachRemaining(Consumer<? super K> action) {
2935             if (action == null)
2936                 throw new NullPointerException();
2937             if (est < 0)
2938                 getEstimate(); // force initialization
2939             TreeMap.Entry<K,V> f = fence, e, p, pl;
2940             if ((e = current) != null && e != f) {
2941                 current = f; // exhaust
2942                 do {
2943                     action.accept(e.key);
2944                     if ((p = e.right) != null) {
2945                         while ((pl = p.left) != null)
2946                             p = pl;
2947                     }
2948                     else {
2949                         while ((p = e.parent) != null && e == p.right)
2950                             e = p;
2951                     }
2952                 } while ((e = p) != null && e != f);
2953                 if (tree.modCount != expectedModCount)
2954                     throw new ConcurrentModificationException();
2955             }
2956         }
2957 
2958         public boolean tryAdvance(Consumer<? super K> action) {
2959             TreeMap.Entry<K,V> e;
2960             if (action == null)
2961                 throw new NullPointerException();
2962             if (est < 0)
2963                 getEstimate(); // force initialization
2964             if ((e = current) == null || e == fence)
2965                 return false;
2966             current = successor(e);
2967             action.accept(e.key);
2968             if (tree.modCount != expectedModCount)
2969                 throw new ConcurrentModificationException();
2970             return true;
2971         }
2972 
2973         public int characteristics() {
2974             return (side == 0 ? Spliterator.SIZED : 0) |
2975                 Spliterator.DISTINCT | Spliterator.SORTED | Spliterator.ORDERED;
2976         }
2977 
2978         public final Comparator<? super K>  getComparator() {
2979             return tree.comparator;
2980         }
2981 
2982     }
2983 
2984     static final class DescendingKeySpliterator<K,V>
2985         extends TreeMapSpliterator<K,V>
2986         implements Spliterator<K> {
2987         DescendingKeySpliterator(TreeMap<K,V> tree,
2988                                  TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
2989                                  int side, int est, int expectedModCount) {
2990             super(tree, origin, fence, side, est, expectedModCount);
2991         }
2992 
2993         public DescendingKeySpliterator<K,V> trySplit() {
2994             if (est < 0)
2995                 getEstimate(); // force initialization
2996             int d = side;
2997             TreeMap.Entry<K,V> e = current, f = fence,
2998                     s = ((e == null || e == f) ? null :      // empty
2999                          (d == 0)              ? tree.root : // was top
3000                          (d <  0)              ? e.left :    // was left
3001                          (d >  0 && f != null) ? f.right :   // was right
3002                          null);
3003             if (s != null && s != e && s != f &&
3004                 tree.compare(e.key, s.key) > 0) {       // e not already past s
3005                 side = 1;
3006                 return new DescendingKeySpliterator<>
3007                         (tree, e, current = s, -1, est >>>= 1, expectedModCount);
3008             }
3009             return null;
3010         }
3011 
3012         public void forEachRemaining(Consumer<? super K> action) {
3013             if (action == null)
3014                 throw new NullPointerException();
3015             if (est < 0)
3016                 getEstimate(); // force initialization
3017             TreeMap.Entry<K,V> f = fence, e, p, pr;
3018             if ((e = current) != null && e != f) {
3019                 current = f; // exhaust
3020                 do {
3021                     action.accept(e.key);
3022                     if ((p = e.left) != null) {
3023                         while ((pr = p.right) != null)
3024                             p = pr;
3025                     }
3026                     else {
3027                         while ((p = e.parent) != null && e == p.left)
3028                             e = p;
3029                     }
3030                 } while ((e = p) != null && e != f);
3031                 if (tree.modCount != expectedModCount)
3032                     throw new ConcurrentModificationException();
3033             }
3034         }
3035 
3036         public boolean tryAdvance(Consumer<? super K> action) {
3037             TreeMap.Entry<K,V> e;
3038             if (action == null)
3039                 throw new NullPointerException();
3040             if (est < 0)
3041                 getEstimate(); // force initialization
3042             if ((e = current) == null || e == fence)
3043                 return false;
3044             current = predecessor(e);
3045             action.accept(e.key);
3046             if (tree.modCount != expectedModCount)
3047                 throw new ConcurrentModificationException();
3048             return true;
3049         }
3050 
3051         public int characteristics() {
3052             return (side == 0 ? Spliterator.SIZED : 0) |
3053                 Spliterator.DISTINCT | Spliterator.ORDERED;
3054         }
3055     }
3056 
3057     static final class ValueSpliterator<K,V>
3058             extends TreeMapSpliterator<K,V>
3059             implements Spliterator<V> {
3060         ValueSpliterator(TreeMap<K,V> tree,
3061                          TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
3062                          int side, int est, int expectedModCount) {
3063             super(tree, origin, fence, side, est, expectedModCount);
3064         }
3065 
3066         public ValueSpliterator<K,V> trySplit() {
3067             if (est < 0)
3068                 getEstimate(); // force initialization
3069             int d = side;
3070             TreeMap.Entry<K,V> e = current, f = fence,
3071                     s = ((e == null || e == f) ? null :      // empty
3072                          (d == 0)              ? tree.root : // was top
3073                          (d >  0)              ? e.right :   // was right
3074                          (d <  0 && f != null) ? f.left :    // was left
3075                          null);
3076             if (s != null && s != e && s != f &&
3077                 tree.compare(e.key, s.key) < 0) {        // e not already past s
3078                 side = 1;
3079                 return new ValueSpliterator<>
3080                         (tree, e, current = s, -1, est >>>= 1, expectedModCount);
3081             }
3082             return null;
3083         }
3084 
3085         public void forEachRemaining(Consumer<? super V> action) {
3086             if (action == null)
3087                 throw new NullPointerException();
3088             if (est < 0)
3089                 getEstimate(); // force initialization
3090             TreeMap.Entry<K,V> f = fence, e, p, pl;
3091             if ((e = current) != null && e != f) {
3092                 current = f; // exhaust
3093                 do {
3094                     action.accept(e.value);
3095                     if ((p = e.right) != null) {
3096                         while ((pl = p.left) != null)
3097                             p = pl;
3098                     }
3099                     else {
3100                         while ((p = e.parent) != null && e == p.right)
3101                             e = p;
3102                     }
3103                 } while ((e = p) != null && e != f);
3104                 if (tree.modCount != expectedModCount)
3105                     throw new ConcurrentModificationException();
3106             }
3107         }
3108 
3109         public boolean tryAdvance(Consumer<? super V> action) {
3110             TreeMap.Entry<K,V> e;
3111             if (action == null)
3112                 throw new NullPointerException();
3113             if (est < 0)
3114                 getEstimate(); // force initialization
3115             if ((e = current) == null || e == fence)
3116                 return false;
3117             current = successor(e);
3118             action.accept(e.value);
3119             if (tree.modCount != expectedModCount)
3120                 throw new ConcurrentModificationException();
3121             return true;
3122         }
3123 
3124         public int characteristics() {
3125             return (side == 0 ? Spliterator.SIZED : 0) | Spliterator.ORDERED;
3126         }
3127     }
3128 
3129     static final class EntrySpliterator<K,V>
3130         extends TreeMapSpliterator<K,V>
3131         implements Spliterator<Map.Entry<K,V>> {
3132         EntrySpliterator(TreeMap<K,V> tree,
3133                          TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
3134                          int side, int est, int expectedModCount) {
3135             super(tree, origin, fence, side, est, expectedModCount);
3136         }
3137 
3138         public EntrySpliterator<K,V> trySplit() {
3139             if (est < 0)
3140                 getEstimate(); // force initialization
3141             int d = side;
3142             TreeMap.Entry<K,V> e = current, f = fence,
3143                     s = ((e == null || e == f) ? null :      // empty
3144                          (d == 0)              ? tree.root : // was top
3145                          (d >  0)              ? e.right :   // was right
3146                          (d <  0 && f != null) ? f.left :    // was left
3147                          null);
3148             if (s != null && s != e && s != f &&
3149                 tree.compare(e.key, s.key) < 0) {        // e not already past s
3150                 side = 1;
3151                 return new EntrySpliterator<>
3152                         (tree, e, current = s, -1, est >>>= 1, expectedModCount);
3153             }
3154             return null;
3155         }
3156 
3157         public void forEachRemaining(Consumer<? super Map.Entry<K, V>> action) {
3158             if (action == null)
3159                 throw new NullPointerException();
3160             if (est < 0)
3161                 getEstimate(); // force initialization
3162             TreeMap.Entry<K,V> f = fence, e, p, pl;
3163             if ((e = current) != null && e != f) {
3164                 current = f; // exhaust
3165                 do {
3166                     action.accept(e);
3167                     if ((p = e.right) != null) {
3168                         while ((pl = p.left) != null)
3169                             p = pl;
3170                     }
3171                     else {
3172                         while ((p = e.parent) != null && e == p.right)
3173                             e = p;
3174                     }
3175                 } while ((e = p) != null && e != f);
3176                 if (tree.modCount != expectedModCount)
3177                     throw new ConcurrentModificationException();
3178             }
3179         }
3180 
3181         public boolean tryAdvance(Consumer<? super Map.Entry<K,V>> action) {
3182             TreeMap.Entry<K,V> e;
3183             if (action == null)
3184                 throw new NullPointerException();
3185             if (est < 0)
3186                 getEstimate(); // force initialization
3187             if ((e = current) == null || e == fence)
3188                 return false;
3189             current = successor(e);
3190             action.accept(e);
3191             if (tree.modCount != expectedModCount)
3192                 throw new ConcurrentModificationException();
3193             return true;
3194         }
3195 
3196         public int characteristics() {
3197             return (side == 0 ? Spliterator.SIZED : 0) |
3198                     Spliterator.DISTINCT | Spliterator.SORTED | Spliterator.ORDERED;
3199         }
3200 
3201         @Override
3202         public Comparator<Map.Entry<K, V>> getComparator() {
3203             // Adapt or create a key-based comparator
3204             if (tree.comparator != null) {
3205                 return Map.Entry.comparingByKey(tree.comparator);
3206             }
3207             else {
3208                 return (Comparator<Map.Entry<K, V>> & Serializable) (e1, e2) -> {
3209                     @SuppressWarnings("unchecked")
3210                     Comparable<? super K> k1 = (Comparable<? super K>) e1.getKey();
3211                     return k1.compareTo(e2.getKey());
3212                 };
3213             }
3214         }
3215     }
3216 }