it.unimi.dsi/fastutil/8.3.0 : it/unimi/dsi/fastutil/objects/Object2ReferenceAVLTreeMap.java

Object2ReferenceAVLTreeMap
http://fastutil.di.unimi.it/: fastutil extends the Java Collections Framework by providing type-specific maps, sets, lists and priority queues with a small memory footprint and fast access and insertion; provides also big (64-bit) arrays, sets and lists, and fast, practical I/O classes for binary and text files.
Apache License, Version 2.0
Sebastiano Vigna
/*
	* Copyright (C) 2002-2019 Sebastiano Vigna
	*
	* Licensed under the Apache License, Version 2.0 (the "License");
	* you may not use this file except in compliance with the License.
	* You may obtain a copy of the License at
	*
	*     http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing, software
	* distributed under the License is distributed on an "AS IS" BASIS,
	* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	* See the License for the specific language governing permissions and
	* limitations under the License.
	*/
package it.unimi.dsi.fastutil.objects;
import it.unimi.dsi.fastutil.objects.AbstractObjectSortedSet;
import it.unimi.dsi.fastutil.objects.ObjectBidirectionalIterator;
import it.unimi.dsi.fastutil.objects.ObjectListIterator;
import it.unimi.dsi.fastutil.objects.ObjectSortedSet;
import it.unimi.dsi.fastutil.objects.ReferenceCollection;
import it.unimi.dsi.fastutil.objects.AbstractReferenceCollection;
import it.unimi.dsi.fastutil.objects.ObjectIterator;
import java.util.Comparator;
import java.util.Iterator;
import java.util.Map;
import java.util.SortedMap;
import java.util.NoSuchElementException;
A type-specific AVL tree map with a fast, small-footprint implementation.
 The iterators provided by the views of this class are type-specific bidirectional
iterators. Moreover, the iterator returned by iterator() can be safely cast to a type-specific list
iterator. /**
 * A type-specific AVL tree map with a fast, small-footprint implementation.
 *
 * <p>
 * The iterators provided by the views of this class are type-specific
 * {@linkplain it.unimi.dsi.fastutil.BidirectionalIterator bidirectional
 * iterators}. Moreover, the iterator returned by {@code iterator()} can be
 * safely cast to a type-specific {@linkplain java.util.ListIterator list
 * iterator}.
 */
public class Object2ReferenceAVLTreeMap<K, V> extends AbstractObject2ReferenceSortedMap<K, V>
		implements
			java.io.Serializable,
			Cloneable {
	A reference to the root entry. /** A reference to the root entry. */
	protected transient Entry<K, V> tree;
	Number of entries in this map. /** Number of entries in this map. */
	protected int count;
	The first key in this map. /** The first key in this map. */
	protected transient Entry<K, V> firstEntry;
	The last key in this map. /** The last key in this map. */
	protected transient Entry<K, V> lastEntry;
	Cached set of entries. /** Cached set of entries. */
	protected transient ObjectSortedSet<Object2ReferenceMap.Entry<K, V>> entries;
	Cached set of keys. /** Cached set of keys. */
	protected transient ObjectSortedSet<K> keys;
	Cached collection of values. /** Cached collection of values. */
	protected transient ReferenceCollection<V> values;
	The value of this variable remembers, after a put() or a remove(), whether the domain of the map has been modified.
/**
	 * The value of this variable remembers, after a {@code put()} or a
	 * {@code remove()}, whether the <em>domain</em> of the map has been modified.
	 */
	protected transient boolean modified;
	This map's comparator, as provided in the constructor. /** This map's comparator, as provided in the constructor. */
	protected Comparator<? super K> storedComparator;
	This map's actual comparator; it may differ from Object2ReferenceAVLTreeMap<K,V>.storedComparator because it is always a type-specific comparator, so it could be derived from the former by wrapping. /**
	 * This map's actual comparator; it may differ from {@link #storedComparator}
	 * because it is always a type-specific comparator, so it could be derived from
	 * the former by wrapping.
	 */
	protected transient Comparator<? super K> actualComparator;
	private static final long serialVersionUID = -7046029254386353129L;
	{
		allocatePaths();
	}
	Creates a new empty tree map.
/**
	 * Creates a new empty tree map.
	 */
	public Object2ReferenceAVLTreeMap() {
		tree = null;
		count = 0;
	}
	Generates the comparator that will be actually used.
 When a given Comparator is specified and stored in Object2ReferenceAVLTreeMap<K,V>.storedComparator, we must check whether it is type-specific. If it is so, we can used directly, and we store it in Object2ReferenceAVLTreeMap<K,V>.actualComparator. Otherwise, we adapt it using a helper static method. /**
	 * Generates the comparator that will be actually used.
	 *
	 * <p>
	 * When a given {@link Comparator} is specified and stored in
	 * {@link #storedComparator}, we must check whether it is type-specific. If it
	 * is so, we can used directly, and we store it in {@link #actualComparator}.
	 * Otherwise, we adapt it using a helper static method.
	 */
	private void setActualComparator() {
		actualComparator = storedComparator;
	}
	Creates a new empty tree map with the given comparator.
Params: c – 
           a (possibly type-specific) comparator./**
	 * Creates a new empty tree map with the given comparator.
	 *
	 * @param c
	 *            a (possibly type-specific) comparator.
	 */
	public Object2ReferenceAVLTreeMap(final Comparator<? super K> c) {
		this();
		storedComparator = c;
		setActualComparator();
	}
	Creates a new tree map copying a given map.
Params: m –  a Map to be copied into the new tree map./**
	 * Creates a new tree map copying a given map.
	 *
	 * @param m
	 *            a {@link Map} to be copied into the new tree map.
	 */
	public Object2ReferenceAVLTreeMap(final Map<? extends K, ? extends V> m) {
		this();
		putAll(m);
	}
	Creates a new tree map copying a given sorted map (and its Comparator). 
Params: m –  a SortedMap to be copied into the new tree map./**
	 * Creates a new tree map copying a given sorted map (and its
	 * {@link Comparator}).
	 *
	 * @param m
	 *            a {@link SortedMap} to be copied into the new tree map.
	 */
	public Object2ReferenceAVLTreeMap(final SortedMap<K, V> m) {
		this(m.comparator());
		putAll(m);
	}
	Creates a new tree map copying a given map.
Params: m – 
           a type-specific map to be copied into the new tree map./**
	 * Creates a new tree map copying a given map.
	 *
	 * @param m
	 *            a type-specific map to be copied into the new tree map.
	 */
	public Object2ReferenceAVLTreeMap(final Object2ReferenceMap<? extends K, ? extends V> m) {
		this();
		putAll(m);
	}
	Creates a new tree map copying a given sorted map (and its Comparator). 
Params: m – 
           a type-specific sorted map to be copied into the new tree map./**
	 * Creates a new tree map copying a given sorted map (and its
	 * {@link Comparator}).
	 *
	 * @param m
	 *            a type-specific sorted map to be copied into the new tree map.
	 */
	public Object2ReferenceAVLTreeMap(final Object2ReferenceSortedMap<K, V> m) {
		this(m.comparator());
		putAll(m);
	}
	Creates a new tree map using the elements of two parallel arrays and the
given comparator.
Params: k – 
           the array of keys of the new tree map.
v – 
           the array of corresponding values in the new tree map.
c – 
           a (possibly type-specific) comparator.
Throws: IllegalArgumentException –  if k and v have different lengths./**
	 * Creates a new tree map using the elements of two parallel arrays and the
	 * given comparator.
	 *
	 * @param k
	 *            the array of keys of the new tree map.
	 * @param v
	 *            the array of corresponding values in the new tree map.
	 * @param c
	 *            a (possibly type-specific) comparator.
	 * @throws IllegalArgumentException
	 *             if {@code k} and {@code v} have different lengths.
	 */
	public Object2ReferenceAVLTreeMap(final K[] k, final V v[], final Comparator<? super K> c) {
		this(c);
		if (k.length != v.length)
			throw new IllegalArgumentException(
					"The key array and the value array have different lengths (" + k.length + " and " + v.length + ")");
		for (int i = 0; i < k.length; i++)
			this.put(k[i], v[i]);
	}
	Creates a new tree map using the elements of two parallel arrays.
Params: k – 
           the array of keys of the new tree map.
v – 
           the array of corresponding values in the new tree map.
Throws: IllegalArgumentException –  if k and v have different lengths./**
	 * Creates a new tree map using the elements of two parallel arrays.
	 *
	 * @param k
	 *            the array of keys of the new tree map.
	 * @param v
	 *            the array of corresponding values in the new tree map.
	 * @throws IllegalArgumentException
	 *             if {@code k} and {@code v} have different lengths.
	 */
	public Object2ReferenceAVLTreeMap(final K[] k, final V v[]) {
		this(k, v, null);
	}
	/*
	 * The following methods implements some basic building blocks used by all
	 * accessors. They are (and should be maintained) identical to those used in
	 * AVLTreeSet.drv.
	 *
	 * The put()/remove() code is derived from Ben Pfaff's GNU libavl
	 * (http://www.msu.edu/~pfaffben/avl/). If you want to understand what's going
	 * on, you should have a look at the literate code contained therein first.
	 */
	Compares two keys in the right way.
 This method uses the Object2ReferenceAVLTreeMap<K,V>.actualComparator if it is non-null. Otherwise, it resorts to primitive type comparisons or to compareTo(). 
Params: k1 – 
           the first key.
k2 – 
           the second key.
Returns: a number smaller than, equal to or greater than 0, as usual (i.e.,
        when k1 < k2, k1 = k2 or k1 > k2, respectively)./**
	 * Compares two keys in the right way.
	 *
	 * <p>
	 * This method uses the {@link #actualComparator} if it is non-{@code null}.
	 * Otherwise, it resorts to primitive type comparisons or to
	 * {@link Comparable#compareTo(Object) compareTo()}.
	 *
	 * @param k1
	 *            the first key.
	 * @param k2
	 *            the second key.
	 * @return a number smaller than, equal to or greater than 0, as usual (i.e.,
	 *         when k1 &lt; k2, k1 = k2 or k1 &gt; k2, respectively).
	 */
	@SuppressWarnings("unchecked")
	final int compare(final K k1, final K k2) {
		return actualComparator == null ? (((Comparable<K>) (k1)).compareTo(k2)) : actualComparator.compare(k1, k2);
	}
	Returns the entry corresponding to the given key, if it is in the tree; null, otherwise. 
Params: k – 
           the key to search for.
Returns: the corresponding entry, or null if no entry with the given key exists./**
	 * Returns the entry corresponding to the given key, if it is in the tree;
	 * {@code null}, otherwise.
	 *
	 * @param k
	 *            the key to search for.
	 * @return the corresponding entry, or {@code null} if no entry with the given
	 *         key exists.
	 */
	final Entry<K, V> findKey(final K k) {
		Entry<K, V> e = tree;
		int cmp;
		while (e != null && (cmp = compare(k, e.key)) != 0)
			e = cmp < 0 ? e.left() : e.right();
		return e;
	}
	Locates a key.
Params: k – 
           a key.
Returns: the last entry on a search for the given key; this will be the given
        key, if it present; otherwise, it will be either the smallest greater
        key or the greatest smaller key./**
	 * Locates a key.
	 *
	 * @param k
	 *            a key.
	 * @return the last entry on a search for the given key; this will be the given
	 *         key, if it present; otherwise, it will be either the smallest greater
	 *         key or the greatest smaller key.
	 */
	final Entry<K, V> locateKey(final K k) {
		Entry<K, V> e = tree, last = tree;
		int cmp = 0;
		while (e != null && (cmp = compare(k, e.key)) != 0) {
			last = e;
			e = cmp < 0 ? e.left() : e.right();
		}
		return cmp == 0 ? e : last;
	}
	This vector remembers the directions followed during the current insertion.
It suffices for about 2³² entries.
/**
	 * This vector remembers the directions followed during the current insertion.
	 * It suffices for about 2<sup>32</sup> entries.
	 */
	private transient boolean dirPath[];
	private void allocatePaths() {
		dirPath = new boolean[48];
	}
	@Override
	public V put(final K k, final V v) {
		Entry<K, V> e = add(k);
		final V oldValue = e.value;
		e.value = v;
		return oldValue;
	}
	Returns a node with key k in the balanced tree, creating one with defRetValue
if necessary.
Params: k – 
           the key
Returns: a node with key k. If a node with key k already exists, then that
        node is returned, otherwise a new node with defRetValue is created
        ensuring that the tree is balanced after creation of the node./**
	 * Returns a node with key k in the balanced tree, creating one with defRetValue
	 * if necessary.
	 *
	 * @param k
	 *            the key
	 * @return a node with key k. If a node with key k already exists, then that
	 *         node is returned, otherwise a new node with defRetValue is created
	 *         ensuring that the tree is balanced after creation of the node.
	 */
	private Entry<K, V> add(final K k) {
		/*
		 * After execution of this method, modified is true iff a new entry has been
		 * inserted.
		 */
		modified = false;
		Entry<K, V> e = null;
		if (tree == null) { // The case of the empty tree is treated separately.
			count++;
			e = tree = lastEntry = firstEntry = new Entry<>(k, defRetValue);
			modified = true;
		} else {
			Entry<K, V> p = tree, q = null, y = tree, z = null, w = null;
			int cmp, i = 0;
			while (true) {
				if ((cmp = compare(k, p.key)) == 0) {
					return p;
				}
				if (p.balance() != 0) {
					i = 0;
					z = q;
					y = p;
				}
				if (dirPath[i++] = cmp > 0) {
					if (p.succ()) {
						count++;
						e = new Entry<>(k, defRetValue);
						modified = true;
						if (p.right == null)
							lastEntry = e;
						e.left = p;
						e.right = p.right;
						p.right(e);
						break;
					}
					q = p;
					p = p.right;
				} else {
					if (p.pred()) {
						count++;
						e = new Entry<>(k, defRetValue);
						modified = true;
						if (p.left == null)
							firstEntry = e;
						e.right = p;
						e.left = p.left;
						p.left(e);
						break;
					}
					q = p;
					p = p.left;
				}
			}
			p = y;
			i = 0;
			while (p != e) {
				if (dirPath[i])
					p.incBalance();
				else
					p.decBalance();
				p = dirPath[i++] ? p.right : p.left;
			}
			if (y.balance() == -2) {
				Entry<K, V> x = y.left;
				if (x.balance() == -1) {
					w = x;
					if (x.succ()) {
						x.succ(false);
						y.pred(x);
					} else
						y.left = x.right;
					x.right = y;
					x.balance(0);
					y.balance(0);
				} else {
					assert x.balance() == 1;
					w = x.right;
					x.right = w.left;
					w.left = x;
					y.left = w.right;
					w.right = y;
					if (w.balance() == -1) {
						x.balance(0);
						y.balance(1);
					} else if (w.balance() == 0) {
						x.balance(0);
						y.balance(0);
					} else {
						x.balance(-1);
						y.balance(0);
					}
					w.balance(0);
					if (w.pred()) {
						x.succ(w);
						w.pred(false);
					}
					if (w.succ()) {
						y.pred(w);
						w.succ(false);
					}
				}
			} else if (y.balance() == +2) {
				Entry<K, V> x = y.right;
				if (x.balance() == 1) {
					w = x;
					if (x.pred()) {
						x.pred(false);
						y.succ(x);
					} else
						y.right = x.left;
					x.left = y;
					x.balance(0);
					y.balance(0);
				} else {
					assert x.balance() == -1;
					w = x.left;
					x.left = w.right;
					w.right = x;
					y.right = w.left;
					w.left = y;
					if (w.balance() == 1) {
						x.balance(0);
						y.balance(-1);
					} else if (w.balance() == 0) {
						x.balance(0);
						y.balance(0);
					} else {
						x.balance(1);
						y.balance(0);
					}
					w.balance(0);
					if (w.pred()) {
						y.succ(w);
						w.pred(false);
					}
					if (w.succ()) {
						x.pred(w);
						w.succ(false);
					}
				}
			} else
				return e;
			if (z == null)
				tree = w;
			else {
				if (z.left == y)
					z.left = w;
				else
					z.right = w;
			}
		}
		return e;
	}
	Finds the parent of an entry.
Params: e – 
           a node of the tree.
Returns: the parent of the given node, or null for the root./**
	 * Finds the parent of an entry.
	 *
	 * @param e
	 *            a node of the tree.
	 * @return the parent of the given node, or {@code null} for the root.
	 */
	private Entry<K, V> parent(final Entry<K, V> e) {
		if (e == tree)
			return null;
		Entry<K, V> x, y, p;
		x = y = e;
		while (true) {
			if (y.succ()) {
				p = y.right;
				if (p == null || p.left != e) {
					while (!x.pred())
						x = x.left;
					p = x.left;
				}
				return p;
			} else if (x.pred()) {
				p = x.left;
				if (p == null || p.right != e) {
					while (!y.succ())
						y = y.right;
					p = y.right;
				}
				return p;
			}
			x = x.left;
			y = y.right;
		}
	}
	/*
	 * After execution of this method, {@link #modified} is true iff an entry has
	 * been deleted.
	 */
	@SuppressWarnings("unchecked")
	@Override
	public V remove(final Object k) {
		modified = false;
		if (tree == null)
			return defRetValue;
		int cmp;
		Entry<K, V> p = tree, q = null;
		boolean dir = false;
		final K kk = (K) k;
		while (true) {
			if ((cmp = compare(kk, p.key)) == 0)
				break;
			else if (dir = cmp > 0) {
				q = p;
				if ((p = p.right()) == null)
					return defRetValue;
			} else {
				q = p;
				if ((p = p.left()) == null)
					return defRetValue;
			}
		}
		if (p.left == null)
			firstEntry = p.next();
		if (p.right == null)
			lastEntry = p.prev();
		if (p.succ()) {
			if (p.pred()) {
				if (q != null) {
					if (dir)
						q.succ(p.right);
					else
						q.pred(p.left);
				} else
					tree = dir ? p.right : p.left;
			} else {
				p.prev().right = p.right;
				if (q != null) {
					if (dir)
						q.right = p.left;
					else
						q.left = p.left;
				} else
					tree = p.left;
			}
		} else {
			Entry<K, V> r = p.right;
			if (r.pred()) {
				r.left = p.left;
				r.pred(p.pred());
				if (!r.pred())
					r.prev().right = r;
				if (q != null) {
					if (dir)
						q.right = r;
					else
						q.left = r;
				} else
					tree = r;
				r.balance(p.balance());
				q = r;
				dir = true;
			} else {
				Entry<K, V> s;
				while (true) {
					s = r.left;
					if (s.pred())
						break;
					r = s;
				}
				if (s.succ())
					r.pred(s);
				else
					r.left = s.right;
				s.left = p.left;
				if (!p.pred()) {
					p.prev().right = s;
					s.pred(false);
				}
				s.right = p.right;
				s.succ(false);
				if (q != null) {
					if (dir)
						q.right = s;
					else
						q.left = s;
				} else
					tree = s;
				s.balance(p.balance());
				q = r;
				dir = false;
			}
		}
		Entry<K, V> y;
		while (q != null) {
			y = q;
			q = parent(y);
			if (!dir) {
				dir = q != null && q.left != y;
				y.incBalance();
				if (y.balance() == 1)
					break;
				else if (y.balance() == 2) {
					Entry<K, V> x = y.right;
					assert x != null;
					if (x.balance() == -1) {
						Entry<K, V> w;
						assert x.balance() == -1;
						w = x.left;
						x.left = w.right;
						w.right = x;
						y.right = w.left;
						w.left = y;
						if (w.balance() == 1) {
							x.balance(0);
							y.balance(-1);
						} else if (w.balance() == 0) {
							x.balance(0);
							y.balance(0);
						} else {
							assert w.balance() == -1;
							x.balance(1);
							y.balance(0);
						}
						w.balance(0);
						if (w.pred()) {
							y.succ(w);
							w.pred(false);
						}
						if (w.succ()) {
							x.pred(w);
							w.succ(false);
						}
						if (q != null) {
							if (dir)
								q.right = w;
							else
								q.left = w;
						} else
							tree = w;
					} else {
						if (q != null) {
							if (dir)
								q.right = x;
							else
								q.left = x;
						} else
							tree = x;
						if (x.balance() == 0) {
							y.right = x.left;
							x.left = y;
							x.balance(-1);
							y.balance(+1);
							break;
						}
						assert x.balance() == 1;
						if (x.pred()) {
							y.succ(true);
							x.pred(false);
						} else
							y.right = x.left;
						x.left = y;
						y.balance(0);
						x.balance(0);
					}
				}
			} else {
				dir = q != null && q.left != y;
				y.decBalance();
				if (y.balance() == -1)
					break;
				else if (y.balance() == -2) {
					Entry<K, V> x = y.left;
					assert x != null;
					if (x.balance() == 1) {
						Entry<K, V> w;
						assert x.balance() == 1;
						w = x.right;
						x.right = w.left;
						w.left = x;
						y.left = w.right;
						w.right = y;
						if (w.balance() == -1) {
							x.balance(0);
							y.balance(1);
						} else if (w.balance() == 0) {
							x.balance(0);
							y.balance(0);
						} else {
							assert w.balance() == 1;
							x.balance(-1);
							y.balance(0);
						}
						w.balance(0);
						if (w.pred()) {
							x.succ(w);
							w.pred(false);
						}
						if (w.succ()) {
							y.pred(w);
							w.succ(false);
						}
						if (q != null) {
							if (dir)
								q.right = w;
							else
								q.left = w;
						} else
							tree = w;
					} else {
						if (q != null) {
							if (dir)
								q.right = x;
							else
								q.left = x;
						} else
							tree = x;
						if (x.balance() == 0) {
							y.left = x.right;
							x.right = y;
							x.balance(+1);
							y.balance(-1);
							break;
						}
						assert x.balance() == -1;
						if (x.succ()) {
							y.pred(true);
							x.succ(false);
						} else
							y.left = x.right;
						x.right = y;
						y.balance(0);
						x.balance(0);
					}
				}
			}
		}
		modified = true;
		count--;
		return p.value;
	}
	@Override
	public boolean containsValue(final Object v) {
		final ValueIterator i = new ValueIterator();
		V ev;
		int j = count;
		while (j-- != 0) {
			ev = i.next();
			if (((ev) == (v)))
				return true;
		}
		return false;
	}
	@Override
	public void clear() {
		count = 0;
		tree = null;
		entries = null;
		values = null;
		keys = null;
		firstEntry = lastEntry = null;
	}
	This class represent an entry in a tree map.
 We use the only "metadata", i.e., info, to store information about balance, predecessor status and successor status. 

Note that since the class is recursive, it can be considered equivalently a
tree.
/**
	 * This class represent an entry in a tree map.
	 *
	 * <p>
	 * We use the only "metadata", i.e., {@link Entry#info}, to store information
	 * about balance, predecessor status and successor status.
	 *
	 * <p>
	 * Note that since the class is recursive, it can be considered equivalently a
	 * tree.
	 */
	private static final class Entry<K, V> extends AbstractObject2ReferenceMap.BasicEntry<K, V> implements Cloneable {
		If the bit in this mask is true, Entry<K,V>.right points to a successor. /** If the bit in this mask is true, {@link #right} points to a successor. */
		private static final int SUCC_MASK = 1 << 31;
		If the bit in this mask is true, Entry<K,V>.left points to a predecessor. /** If the bit in this mask is true, {@link #left} points to a predecessor. */
		private static final int PRED_MASK = 1 << 30;
		The bits in this mask hold the node balance info. You can get it just by
casting to byte.
/**
		 * The bits in this mask hold the node balance info. You can get it just by
		 * casting to byte.
		 */
		private static final int BALANCE_MASK = 0xFF;
		The pointers to the left and right subtrees. /** The pointers to the left and right subtrees. */
		Entry<K, V> left, right;
		This integers holds different information in different bits (see Entry<K,V>.SUCC_MASK, Entry<K,V>.PRED_MASK and Entry<K,V>.BALANCE_MASK). /**
		 * This integers holds different information in different bits (see
		 * {@link #SUCC_MASK}, {@link #PRED_MASK} and {@link #BALANCE_MASK}).
		 */
		int info;
		Entry() {
			super((null), (null));
		}
		Creates a new entry with the given key and value.
Params: k – 
           a key.
v – 
           a value./**
		 * Creates a new entry with the given key and value.
		 *
		 * @param k
		 *            a key.
		 * @param v
		 *            a value.
		 */
		Entry(final K k, final V v) {
			super(k, v);
			info = SUCC_MASK | PRED_MASK;
		}
		Returns the left subtree.
Returns: the left subtree (null if the left subtree is empty)./**
		 * Returns the left subtree.
		 *
		 * @return the left subtree ({@code null} if the left subtree is empty).
		 */
		Entry<K, V> left() {
			return (info & PRED_MASK) != 0 ? null : left;
		}
		Returns the right subtree.
Returns: the right subtree (null if the right subtree is empty)./**
		 * Returns the right subtree.
		 *
		 * @return the right subtree ({@code null} if the right subtree is empty).
		 */
		Entry<K, V> right() {
			return (info & SUCC_MASK) != 0 ? null : right;
		}
		Checks whether the left pointer is really a predecessor.
Returns: true if the left pointer is a predecessor./**
		 * Checks whether the left pointer is really a predecessor.
		 * 
		 * @return true if the left pointer is a predecessor.
		 */
		boolean pred() {
			return (info & PRED_MASK) != 0;
		}
		Checks whether the right pointer is really a successor.
Returns: true if the right pointer is a successor./**
		 * Checks whether the right pointer is really a successor.
		 * 
		 * @return true if the right pointer is a successor.
		 */
		boolean succ() {
			return (info & SUCC_MASK) != 0;
		}
		Sets whether the left pointer is really a predecessor.
Params: pred – 
           if true then the left pointer will be considered a predecessor./**
		 * Sets whether the left pointer is really a predecessor.
		 * 
		 * @param pred
		 *            if true then the left pointer will be considered a predecessor.
		 */
		void pred(final boolean pred) {
			if (pred)
				info |= PRED_MASK;
			else
				info &= ~PRED_MASK;
		}
		Sets whether the right pointer is really a successor.
Params: succ – 
           if true then the right pointer will be considered a successor./**
		 * Sets whether the right pointer is really a successor.
		 * 
		 * @param succ
		 *            if true then the right pointer will be considered a successor.
		 */
		void succ(final boolean succ) {
			if (succ)
				info |= SUCC_MASK;
			else
				info &= ~SUCC_MASK;
		}
		Sets the left pointer to a predecessor.
Params: pred – 
           the predecessr./**
		 * Sets the left pointer to a predecessor.
		 * 
		 * @param pred
		 *            the predecessr.
		 */
		void pred(final Entry<K, V> pred) {
			info |= PRED_MASK;
			left = pred;
		}
		Sets the right pointer to a successor.
Params: succ – 
           the successor./**
		 * Sets the right pointer to a successor.
		 * 
		 * @param succ
		 *            the successor.
		 */
		void succ(final Entry<K, V> succ) {
			info |= SUCC_MASK;
			right = succ;
		}
		Sets the left pointer to the given subtree.
Params: left – 
           the new left subtree./**
		 * Sets the left pointer to the given subtree.
		 * 
		 * @param left
		 *            the new left subtree.
		 */
		void left(final Entry<K, V> left) {
			info &= ~PRED_MASK;
			this.left = left;
		}
		Sets the right pointer to the given subtree.
Params: right – 
           the new right subtree./**
		 * Sets the right pointer to the given subtree.
		 * 
		 * @param right
		 *            the new right subtree.
		 */
		void right(final Entry<K, V> right) {
			info &= ~SUCC_MASK;
			this.right = right;
		}
		Returns the current level of the node.
Returns: the current level of this node./**
		 * Returns the current level of the node.
		 * 
		 * @return the current level of this node.
		 */
		int balance() {
			return (byte) info;
		}
		Sets the level of this node.
Params: level – 
           the new level of this node./**
		 * Sets the level of this node.
		 * 
		 * @param level
		 *            the new level of this node.
		 */
		void balance(int level) {
			info &= ~BALANCE_MASK;
			info |= (level & BALANCE_MASK);
		}
		Increments the level of this node. /** Increments the level of this node. */
		void incBalance() {
			info = info & ~BALANCE_MASK | ((byte) info + 1) & 0xFF;
		}
		Decrements the level of this node. /** Decrements the level of this node. */
		protected void decBalance() {
			info = info & ~BALANCE_MASK | ((byte) info - 1) & 0xFF;
		}
		Computes the next entry in the set order.
Returns: the next entry (null) if this is the last entry)./**
		 * Computes the next entry in the set order.
		 *
		 * @return the next entry ({@code null}) if this is the last entry).
		 */
		Entry<K, V> next() {
			Entry<K, V> next = this.right;
			if ((info & SUCC_MASK) == 0)
				while ((next.info & PRED_MASK) == 0)
					next = next.left;
			return next;
		}
		Computes the previous entry in the set order.
Returns: the previous entry (null) if this is the first entry)./**
		 * Computes the previous entry in the set order.
		 *
		 * @return the previous entry ({@code null}) if this is the first entry).
		 */
		Entry<K, V> prev() {
			Entry<K, V> prev = this.left;
			if ((info & PRED_MASK) == 0)
				while ((prev.info & SUCC_MASK) == 0)
					prev = prev.right;
			return prev;
		}
		@Override
		public V setValue(final V value) {
			final V oldValue = this.value;
			this.value = value;
			return oldValue;
		}
		@Override
		@SuppressWarnings("unchecked")
		public Entry<K, V> clone() {
			Entry<K, V> c;
			try {
				c = (Entry<K, V>) super.clone();
			} catch (CloneNotSupportedException cantHappen) {
				throw new InternalError();
			}
			c.key = key;
			c.value = value;
			c.info = info;
			return c;
		}
		@Override
		@SuppressWarnings("unchecked")
		public boolean equals(final Object o) {
			if (!(o instanceof Map.Entry))
				return false;
			Map.Entry<K, V> e = (Map.Entry<K, V>) o;
			return java.util.Objects.equals(key, (e.getKey())) && ((value) == ((e.getValue())));
		}
		@Override
		public int hashCode() {
			return ((key).hashCode()) ^ ((value) == null ? 0 : System.identityHashCode(value));
		}
		@Override
		public String toString() {
			return key + "=>" + value;
		}
		/*
		 * public void prettyPrint() { prettyPrint(0); }
		 * 
		 * public void prettyPrint(int level) { if (pred()) { for (int i = 0; i < level;
		 * i++) System.err.print("  "); System.err.println("pred: " + left); } else if
		 * (left != null) left.prettyPrint(level +1); for (int i = 0; i < level; i++)
		 * System.err.print("  "); System.err.println(key + "=" + value + " (" +
		 * balance() + ")"); if (succ()) { for (int i = 0; i < level; i++)
		 * System.err.print("  "); System.err.println("succ: " + right); } else if
		 * (right != null) right.prettyPrint(level + 1); }
		 */
	}
	/*
	 * public void prettyPrint() { System.err.println("size: " + count); if (tree !=
	 * null) tree.prettyPrint(); }
	 */
	@SuppressWarnings("unchecked")
	@Override
	public boolean containsKey(final Object k) {
		return findKey((K) k) != null;
	}
	@Override
	public int size() {
		return count;
	}
	@Override
	public boolean isEmpty() {
		return count == 0;
	}
	@SuppressWarnings("unchecked")
	@Override
	public V get(final Object k) {
		final Entry<K, V> e = findKey((K) k);
		return e == null ? defRetValue : e.value;
	}
	@Override
	public K firstKey() {
		if (tree == null)
			throw new NoSuchElementException();
		return firstEntry.key;
	}
	@Override
	public K lastKey() {
		if (tree == null)
			throw new NoSuchElementException();
		return lastEntry.key;
	}
	An abstract iterator on the whole range.

This class can iterate in both directions on a threaded tree.
/**
	 * An abstract iterator on the whole range.
	 *
	 * <p>
	 * This class can iterate in both directions on a threaded tree.
	 */
	private class TreeIterator {
		The entry that will be returned by the next call to ListIterator.previous() (or null if no previous entry exists). /**
		 * The entry that will be returned by the next call to
		 * {@link java.util.ListIterator#previous()} (or {@code null} if no previous
		 * entry exists).
		 */
		Entry<K, V> prev;
		The entry that will be returned by the next call to ListIterator.next() (or null if no next entry exists). /**
		 * The entry that will be returned by the next call to
		 * {@link java.util.ListIterator#next()} (or {@code null} if no next entry
		 * exists).
		 */
		Entry<K, V> next;
		The last entry that was returned (or null if we did not iterate or used remove()). /**
		 * The last entry that was returned (or {@code null} if we did not iterate or
		 * used {@link #remove()}).
		 */
		Entry<K, V> curr;
		The current index (in the sense of a ListIterator). Note that this value is not meaningful when this TreeIterator has been created using the nonempty constructor. /**
		 * The current index (in the sense of a {@link java.util.ListIterator}). Note
		 * that this value is not meaningful when this {@link TreeIterator} has been
		 * created using the nonempty constructor.
		 */
		int index = 0;
		TreeIterator() {
			next = firstEntry;
		}
		TreeIterator(final K k) {
			if ((next = locateKey(k)) != null) {
				if (compare(next.key, k) <= 0) {
					prev = next;
					next = next.next();
				} else
					prev = next.prev();
			}
		}
		public boolean hasNext() {
			return next != null;
		}
		public boolean hasPrevious() {
			return prev != null;
		}
		void updateNext() {
			next = next.next();
		}
		Entry<K, V> nextEntry() {
			if (!hasNext())
				throw new NoSuchElementException();
			curr = prev = next;
			index++;
			updateNext();
			return curr;
		}
		void updatePrevious() {
			prev = prev.prev();
		}
		Entry<K, V> previousEntry() {
			if (!hasPrevious())
				throw new NoSuchElementException();
			curr = next = prev;
			index--;
			updatePrevious();
			return curr;
		}
		public int nextIndex() {
			return index;
		}
		public int previousIndex() {
			return index - 1;
		}
		public void remove() {
			if (curr == null)
				throw new IllegalStateException();
			/*
			 * If the last operation was a next(), we are removing an entry that preceeds
			 * the current index, and thus we must decrement it.
			 */
			if (curr == prev)
				index--;
			next = prev = curr;
			updatePrevious();
			updateNext();
			Object2ReferenceAVLTreeMap.this.remove(curr.key);
			curr = null;
		}
		public int skip(final int n) {
			int i = n;
			while (i-- != 0 && hasNext())
				nextEntry();
			return n - i - 1;
		}
		public int back(final int n) {
			int i = n;
			while (i-- != 0 && hasPrevious())
				previousEntry();
			return n - i - 1;
		}
	}
	An iterator on the whole range.

This class can iterate in both directions on a threaded tree.
/**
	 * An iterator on the whole range.
	 *
	 * <p>
	 * This class can iterate in both directions on a threaded tree.
	 */
	private class EntryIterator extends TreeIterator implements ObjectListIterator<Object2ReferenceMap.Entry<K, V>> {
		EntryIterator() {
		}
		EntryIterator(final K k) {
			super(k);
		}
		@Override
		public Object2ReferenceMap.Entry<K, V> next() {
			return nextEntry();
		}
		@Override
		public Object2ReferenceMap.Entry<K, V> previous() {
			return previousEntry();
		}
		@Override
		public void set(Object2ReferenceMap.Entry<K, V> ok) {
			throw new UnsupportedOperationException();
		}
		@Override
		public void add(Object2ReferenceMap.Entry<K, V> ok) {
			throw new UnsupportedOperationException();
		}
	}
	@Override
	public ObjectSortedSet<Object2ReferenceMap.Entry<K, V>> object2ReferenceEntrySet() {
		if (entries == null)
			entries = new AbstractObjectSortedSet<Object2ReferenceMap.Entry<K, V>>() {
				final Comparator<? super Object2ReferenceMap.Entry<K, V>> comparator = (Comparator<Object2ReferenceMap.Entry<K, V>>) (
						x, y) -> Object2ReferenceAVLTreeMap.this.actualComparator.compare(x.getKey(), y.getKey());
				@Override
				public Comparator<? super Object2ReferenceMap.Entry<K, V>> comparator() {
					return comparator;
				}
				@Override
				public ObjectBidirectionalIterator<Object2ReferenceMap.Entry<K, V>> iterator() {
					return new EntryIterator();
				}
				@Override
				public ObjectBidirectionalIterator<Object2ReferenceMap.Entry<K, V>> iterator(
						final Object2ReferenceMap.Entry<K, V> from) {
					return new EntryIterator(from.getKey());
				}
				@Override
				@SuppressWarnings("unchecked")
				public boolean contains(final Object o) {
					if (!(o instanceof Map.Entry))
						return false;
					final Map.Entry<?, ?> e = (Map.Entry<?, ?>) o;
					final Entry<K, V> f = findKey(((K) e.getKey()));
					return e.equals(f);
				}
				@Override
				@SuppressWarnings("unchecked")
				public boolean remove(final Object o) {
					if (!(o instanceof Map.Entry))
						return false;
					final Map.Entry<?, ?> e = (Map.Entry<?, ?>) o;
					final Entry<K, V> f = findKey(((K) e.getKey()));
					if (f == null || !((f.getValue()) == ((e.getValue()))))
						return false;
					Object2ReferenceAVLTreeMap.this.remove(f.key);
					return true;
				}
				@Override
				public int size() {
					return count;
				}
				@Override
				public void clear() {
					Object2ReferenceAVLTreeMap.this.clear();
				}
				@Override
				public Object2ReferenceMap.Entry<K, V> first() {
					return firstEntry;
				}
				@Override
				public Object2ReferenceMap.Entry<K, V> last() {
					return lastEntry;
				}
				@Override
				public ObjectSortedSet<Object2ReferenceMap.Entry<K, V>> subSet(Object2ReferenceMap.Entry<K, V> from,
						Object2ReferenceMap.Entry<K, V> to) {
					return subMap(from.getKey(), to.getKey()).object2ReferenceEntrySet();
				}
				@Override
				public ObjectSortedSet<Object2ReferenceMap.Entry<K, V>> headSet(Object2ReferenceMap.Entry<K, V> to) {
					return headMap(to.getKey()).object2ReferenceEntrySet();
				}
				@Override
				public ObjectSortedSet<Object2ReferenceMap.Entry<K, V>> tailSet(Object2ReferenceMap.Entry<K, V> from) {
					return tailMap(from.getKey()).object2ReferenceEntrySet();
				}
			};
		return entries;
	}
	An iterator on the whole range of keys.
 This class can iterate in both directions on the keys of a threaded tree. We simply override the ListIterator.next()/ListIterator.previous() methods (and possibly their type-specific counterparts) so that they return keys instead of entries. /**
	 * An iterator on the whole range of keys.
	 *
	 * <p>
	 * This class can iterate in both directions on the keys of a threaded tree. We
	 * simply override the
	 * {@link java.util.ListIterator#next()}/{@link java.util.ListIterator#previous()}
	 * methods (and possibly their type-specific counterparts) so that they return
	 * keys instead of entries.
	 */
	private final class KeyIterator extends TreeIterator implements ObjectListIterator<K> {
		public KeyIterator() {
		}
		public KeyIterator(final K k) {
			super(k);
		}
		@Override
		public K next() {
			return nextEntry().key;
		}
		@Override
		public K previous() {
			return previousEntry().key;
		}
	}
	A keyset implementation using a more direct implementation for iterators. /** A keyset implementation using a more direct implementation for iterators. */
	private class KeySet extends AbstractObject2ReferenceSortedMap<K, V>.KeySet {
		@Override
		public ObjectBidirectionalIterator<K> iterator() {
			return new KeyIterator();
		}
		@Override
		public ObjectBidirectionalIterator<K> iterator(final K from) {
			return new KeyIterator(from);
		}
	}
	Returns a type-specific sorted set view of the keys contained in this map.
 In addition to the semantics of Map.keySet(), you can safely cast the set returned by this call to a type-specific sorted set interface. 
Returns: a type-specific sorted set view of the keys contained in this map./**
	 * Returns a type-specific sorted set view of the keys contained in this map.
	 *
	 * <p>
	 * In addition to the semantics of {@link java.util.Map#keySet()}, you can
	 * safely cast the set returned by this call to a type-specific sorted set
	 * interface.
	 *
	 * @return a type-specific sorted set view of the keys contained in this map.
	 */
	@Override
	public ObjectSortedSet<K> keySet() {
		if (keys == null)
			keys = new KeySet();
		return keys;
	}
	An iterator on the whole range of values.
 This class can iterate in both directions on the values of a threaded tree. We simply override the ListIterator.next()/ListIterator.previous() methods (and possibly their type-specific counterparts) so that they return values instead of entries. /**
	 * An iterator on the whole range of values.
	 *
	 * <p>
	 * This class can iterate in both directions on the values of a threaded tree.
	 * We simply override the
	 * {@link java.util.ListIterator#next()}/{@link java.util.ListIterator#previous()}
	 * methods (and possibly their type-specific counterparts) so that they return
	 * values instead of entries.
	 */
	private final class ValueIterator extends TreeIterator implements ObjectListIterator<V> {
		@Override
		public V next() {
			return nextEntry().value;
		}
		@Override
		public V previous() {
			return previousEntry().value;
		}
	}
	Returns a type-specific collection view of the values contained in this map.
 In addition to the semantics of Map.values(), you can safely cast the collection returned by this call to a type-specific collection interface. 
Returns: a type-specific collection view of the values contained in this map./**
	 * Returns a type-specific collection view of the values contained in this map.
	 *
	 * <p>
	 * In addition to the semantics of {@link java.util.Map#values()}, you can
	 * safely cast the collection returned by this call to a type-specific
	 * collection interface.
	 *
	 * @return a type-specific collection view of the values contained in this map.
	 */
	@Override
	public ReferenceCollection<V> values() {
		if (values == null)
			values = new AbstractReferenceCollection<V>() {
				@Override
				public ObjectIterator<V> iterator() {
					return new ValueIterator();
				}
				@Override
				public boolean contains(final Object k) {
					return containsValue(k);
				}
				@Override
				public int size() {
					return count;
				}
				@Override
				public void clear() {
					Object2ReferenceAVLTreeMap.this.clear();
				}
			};
		return values;
	}
	@Override
	public Comparator<? super K> comparator() {
		return actualComparator;
	}
	@Override
	public Object2ReferenceSortedMap<K, V> headMap(K to) {
		return new Submap((null), true, to, false);
	}
	@Override
	public Object2ReferenceSortedMap<K, V> tailMap(K from) {
		return new Submap(from, false, (null), true);
	}
	@Override
	public Object2ReferenceSortedMap<K, V> subMap(K from, K to) {
		return new Submap(from, false, to, false);
	}
	A submap with given range.
 This class represents a submap. One has to specify the left/right limits (which can be set to -∞ or ∞). Since the submap is a view on the map, at a given moment it could happen that the limits of the range are not any longer in the main map. Thus, things such as SortedMap.firstKey() or Collection.size() must be always computed on-the-fly. /**
	 * A submap with given range.
	 *
	 * <p>
	 * This class represents a submap. One has to specify the left/right limits
	 * (which can be set to -&infin; or &infin;). Since the submap is a view on the
	 * map, at a given moment it could happen that the limits of the range are not
	 * any longer in the main map. Thus, things such as
	 * {@link java.util.SortedMap#firstKey()} or {@link java.util.Collection#size()}
	 * must be always computed on-the-fly.
	 */
	private final class Submap extends AbstractObject2ReferenceSortedMap<K, V> implements java.io.Serializable {
		private static final long serialVersionUID = -7046029254386353129L;
		The start of the submap range, unless Submap.bottom is true. /** The start of the submap range, unless {@link #bottom} is true. */
		K from;
		The end of the submap range, unless Submap.top is true. /** The end of the submap range, unless {@link #top} is true. */
		K to;
		If true, the submap range starts from -∞. /** If true, the submap range starts from -&infin;. */
		boolean bottom;
		If true, the submap range goes to ∞. /** If true, the submap range goes to &infin;. */
		boolean top;
		Cached set of entries. /** Cached set of entries. */
		protected transient ObjectSortedSet<Object2ReferenceMap.Entry<K, V>> entries;
		Cached set of keys. /** Cached set of keys. */
		protected transient ObjectSortedSet<K> keys;
		Cached collection of values. /** Cached collection of values. */
		protected transient ReferenceCollection<V> values;
		Creates a new submap with given key range.
Params: from – 
           the start of the submap range.
bottom – 
           if true, the first parameter is ignored and the range starts from
           -∞.
to – 
           the end of the submap range.
top – 
           if true, the third parameter is ignored and the range goes to
           ∞./**
		 * Creates a new submap with given key range.
		 *
		 * @param from
		 *            the start of the submap range.
		 * @param bottom
		 *            if true, the first parameter is ignored and the range starts from
		 *            -&infin;.
		 * @param to
		 *            the end of the submap range.
		 * @param top
		 *            if true, the third parameter is ignored and the range goes to
		 *            &infin;.
		 */
		public Submap(final K from, final boolean bottom, final K to, final boolean top) {
			if (!bottom && !top && Object2ReferenceAVLTreeMap.this.compare(from, to) > 0)
				throw new IllegalArgumentException("Start key (" + from + ") is larger than end key (" + to + ")");
			this.from = from;
			this.bottom = bottom;
			this.to = to;
			this.top = top;
			this.defRetValue = Object2ReferenceAVLTreeMap.this.defRetValue;
		}
		@Override
		public void clear() {
			final SubmapIterator i = new SubmapIterator();
			while (i.hasNext()) {
				i.nextEntry();
				i.remove();
			}
		}
		Checks whether a key is in the submap range.
Params: k – 
           a key.
Returns: true if is the key is in the submap range./**
		 * Checks whether a key is in the submap range.
		 * 
		 * @param k
		 *            a key.
		 * @return true if is the key is in the submap range.
		 */
		final boolean in(final K k) {
			return (bottom || Object2ReferenceAVLTreeMap.this.compare(k, from) >= 0)
					&& (top || Object2ReferenceAVLTreeMap.this.compare(k, to) < 0);
		}
		@Override
		public ObjectSortedSet<Object2ReferenceMap.Entry<K, V>> object2ReferenceEntrySet() {
			if (entries == null)
				entries = new AbstractObjectSortedSet<Object2ReferenceMap.Entry<K, V>>() {
					@Override
					public ObjectBidirectionalIterator<Object2ReferenceMap.Entry<K, V>> iterator() {
						return new SubmapEntryIterator();
					}
					@Override
					public ObjectBidirectionalIterator<Object2ReferenceMap.Entry<K, V>> iterator(
							final Object2ReferenceMap.Entry<K, V> from) {
						return new SubmapEntryIterator(from.getKey());
					}
					@Override
					public Comparator<? super Object2ReferenceMap.Entry<K, V>> comparator() {
						return Object2ReferenceAVLTreeMap.this.object2ReferenceEntrySet().comparator();
					}
					@Override
					@SuppressWarnings("unchecked")
					public boolean contains(final Object o) {
						if (!(o instanceof Map.Entry))
							return false;
						final Map.Entry<?, ?> e = (Map.Entry<?, ?>) o;
						final Object2ReferenceAVLTreeMap.Entry<K, V> f = findKey(((K) e.getKey()));
						return f != null && in(f.key) && e.equals(f);
					}
					@Override
					@SuppressWarnings("unchecked")
					public boolean remove(final Object o) {
						if (!(o instanceof Map.Entry))
							return false;
						final Map.Entry<?, ?> e = (Map.Entry<?, ?>) o;
						final Object2ReferenceAVLTreeMap.Entry<K, V> f = findKey(((K) e.getKey()));
						if (f != null && in(f.key))
							Submap.this.remove(f.key);
						return f != null;
					}
					@Override
					public int size() {
						int c = 0;
						for (Iterator<?> i = iterator(); i.hasNext(); i.next())
							c++;
						return c;
					}
					@Override
					public boolean isEmpty() {
						return !new SubmapIterator().hasNext();
					}
					@Override
					public void clear() {
						Submap.this.clear();
					}
					@Override
					public Object2ReferenceMap.Entry<K, V> first() {
						return firstEntry();
					}
					@Override
					public Object2ReferenceMap.Entry<K, V> last() {
						return lastEntry();
					}
					@Override
					public ObjectSortedSet<Object2ReferenceMap.Entry<K, V>> subSet(Object2ReferenceMap.Entry<K, V> from,
							Object2ReferenceMap.Entry<K, V> to) {
						return subMap(from.getKey(), to.getKey()).object2ReferenceEntrySet();
					}
					@Override
					public ObjectSortedSet<Object2ReferenceMap.Entry<K, V>> headSet(
							Object2ReferenceMap.Entry<K, V> to) {
						return headMap(to.getKey()).object2ReferenceEntrySet();
					}
					@Override
					public ObjectSortedSet<Object2ReferenceMap.Entry<K, V>> tailSet(
							Object2ReferenceMap.Entry<K, V> from) {
						return tailMap(from.getKey()).object2ReferenceEntrySet();
					}
				};
			return entries;
		}
		private class KeySet extends AbstractObject2ReferenceSortedMap<K, V>.KeySet {
			@Override
			public ObjectBidirectionalIterator<K> iterator() {
				return new SubmapKeyIterator();
			}
			@Override
			public ObjectBidirectionalIterator<K> iterator(final K from) {
				return new SubmapKeyIterator(from);
			}
		}
		@Override
		public ObjectSortedSet<K> keySet() {
			if (keys == null)
				keys = new KeySet();
			return keys;
		}
		@Override
		public ReferenceCollection<V> values() {
			if (values == null)
				values = new AbstractReferenceCollection<V>() {
					@Override
					public ObjectIterator<V> iterator() {
						return new SubmapValueIterator();
					}
					@Override
					public boolean contains(final Object k) {
						return containsValue(k);
					}
					@Override
					public int size() {
						return Submap.this.size();
					}
					@Override
					public void clear() {
						Submap.this.clear();
					}
				};
			return values;
		}
		@Override
		@SuppressWarnings("unchecked")
		public boolean containsKey(final Object k) {
			return in((K) k) && Object2ReferenceAVLTreeMap.this.containsKey(k);
		}
		@Override
		public boolean containsValue(final Object v) {
			final SubmapIterator i = new SubmapIterator();
			Object ev;
			while (i.hasNext()) {
				ev = i.nextEntry().value;
				if (((ev) == (v)))
					return true;
			}
			return false;
		}
		@Override
		@SuppressWarnings("unchecked")
		public V get(final Object k) {
			final Object2ReferenceAVLTreeMap.Entry<K, V> e;
			final K kk = (K) k;
			return in(kk) && (e = findKey(kk)) != null ? e.value : this.defRetValue;
		}
		@Override
		public V put(final K k, final V v) {
			modified = false;
			if (!in(k))
				throw new IllegalArgumentException("Key (" + k + ") out of range ["
						+ (bottom ? "-" : String.valueOf(from)) + ", " + (top ? "-" : String.valueOf(to)) + ")");
			final V oldValue = Object2ReferenceAVLTreeMap.this.put(k, v);
			return modified ? this.defRetValue : oldValue;
		}
		@Override
		@SuppressWarnings("unchecked")
		public V remove(final Object k) {
			modified = false;
			if (!in((K) k))
				return this.defRetValue;
			final V oldValue = Object2ReferenceAVLTreeMap.this.remove(k);
			return modified ? oldValue : this.defRetValue;
		}
		@Override
		public int size() {
			final SubmapIterator i = new SubmapIterator();
			int n = 0;
			while (i.hasNext()) {
				n++;
				i.nextEntry();
			}
			return n;
		}
		@Override
		public boolean isEmpty() {
			return !new SubmapIterator().hasNext();
		}
		@Override
		public Comparator<? super K> comparator() {
			return actualComparator;
		}
		@Override
		public Object2ReferenceSortedMap<K, V> headMap(final K to) {
			if (top)
				return new Submap(from, bottom, to, false);
			return compare(to, this.to) < 0 ? new Submap(from, bottom, to, false) : this;
		}
		@Override
		public Object2ReferenceSortedMap<K, V> tailMap(final K from) {
			if (bottom)
				return new Submap(from, false, to, top);
			return compare(from, this.from) > 0 ? new Submap(from, false, to, top) : this;
		}
		@Override
		public Object2ReferenceSortedMap<K, V> subMap(K from, K to) {
			if (top && bottom)
				return new Submap(from, false, to, false);
			if (!top)
				to = compare(to, this.to) < 0 ? to : this.to;
			if (!bottom)
				from = compare(from, this.from) > 0 ? from : this.from;
			if (!top && !bottom && from == this.from && to == this.to)
				return this;
			return new Submap(from, false, to, false);
		}
		Locates the first entry.
Returns: the first entry of this submap, or null if the submap is empty./**
		 * Locates the first entry.
		 *
		 * @return the first entry of this submap, or {@code null} if the submap is
		 *         empty.
		 */
		public Object2ReferenceAVLTreeMap.Entry<K, V> firstEntry() {
			if (tree == null)
				return null;
			// If this submap goes to -infinity, we return the main map first entry;
			// otherwise, we locate the start of the map.
			Object2ReferenceAVLTreeMap.Entry<K, V> e;
			if (bottom)
				e = firstEntry;
			else {
				e = locateKey(from);
				// If we find either the start or something greater we're OK.
				if (compare(e.key, from) < 0)
					e = e.next();
			}
			// Finally, if this subset doesn't go to infinity, we check that the resulting
			// key isn't greater than the end.
			if (e == null || !top && compare(e.key, to) >= 0)
				return null;
			return e;
		}
		Locates the last entry.
Returns: the last entry of this submap, or null if the submap is empty./**
		 * Locates the last entry.
		 *
		 * @return the last entry of this submap, or {@code null} if the submap is
		 *         empty.
		 */
		public Object2ReferenceAVLTreeMap.Entry<K, V> lastEntry() {
			if (tree == null)
				return null;
			// If this submap goes to infinity, we return the main map last entry;
			// otherwise, we locate the end of the map.
			Object2ReferenceAVLTreeMap.Entry<K, V> e;
			if (top)
				e = lastEntry;
			else {
				e = locateKey(to);
				// If we find something smaller than the end we're OK.
				if (compare(e.key, to) >= 0)
					e = e.prev();
			}
			// Finally, if this subset doesn't go to -infinity, we check that the resulting
			// key isn't smaller than the start.
			if (e == null || !bottom && compare(e.key, from) < 0)
				return null;
			return e;
		}
		@Override
		public K firstKey() {
			Object2ReferenceAVLTreeMap.Entry<K, V> e = firstEntry();
			if (e == null)
				throw new NoSuchElementException();
			return e.key;
		}
		@Override
		public K lastKey() {
			Object2ReferenceAVLTreeMap.Entry<K, V> e = lastEntry();
			if (e == null)
				throw new NoSuchElementException();
			return e.key;
		}
		An iterator for subranges.
 This class inherits from TreeIterator, but overrides the methods that update the pointer after a ListIterator.next() or ListIterator.previous(). If we would move out of the range of the submap we just overwrite the next or previous entry with null. /**
		 * An iterator for subranges.
		 *
		 * <p>
		 * This class inherits from {@link TreeIterator}, but overrides the methods that
		 * update the pointer after a {@link java.util.ListIterator#next()} or
		 * {@link java.util.ListIterator#previous()}. If we would move out of the range
		 * of the submap we just overwrite the next or previous entry with {@code null}.
		 */
		private class SubmapIterator extends TreeIterator {
			SubmapIterator() {
				next = firstEntry();
			}
			SubmapIterator(final K k) {
				this();
				if (next != null) {
					if (!bottom && compare(k, next.key) < 0)
						prev = null;
					else if (!top && compare(k, (prev = lastEntry()).key) >= 0)
						next = null;
					else {
						next = locateKey(k);
						if (compare(next.key, k) <= 0) {
							prev = next;
							next = next.next();
						} else
							prev = next.prev();
					}
				}
			}
			@Override
			void updatePrevious() {
				prev = prev.prev();
				if (!bottom && prev != null && Object2ReferenceAVLTreeMap.this.compare(prev.key, from) < 0)
					prev = null;
			}
			@Override
			void updateNext() {
				next = next.next();
				if (!top && next != null && Object2ReferenceAVLTreeMap.this.compare(next.key, to) >= 0)
					next = null;
			}
		}
		private class SubmapEntryIterator extends SubmapIterator
				implements
					ObjectListIterator<Object2ReferenceMap.Entry<K, V>> {
			SubmapEntryIterator() {
			}
			SubmapEntryIterator(final K k) {
				super(k);
			}
			@Override
			public Object2ReferenceMap.Entry<K, V> next() {
				return nextEntry();
			}
			@Override
			public Object2ReferenceMap.Entry<K, V> previous() {
				return previousEntry();
			}
		}
		An iterator on a subrange of keys.
 This class can iterate in both directions on a subrange of the keys of a threaded tree. We simply override the ListIterator.next()/ListIterator.previous() methods (and possibly their type-specific counterparts) so that they return keys instead of entries. /**
		 * An iterator on a subrange of keys.
		 *
		 * <p>
		 * This class can iterate in both directions on a subrange of the keys of a
		 * threaded tree. We simply override the
		 * {@link java.util.ListIterator#next()}/{@link java.util.ListIterator#previous()}
		 * methods (and possibly their type-specific counterparts) so that they return
		 * keys instead of entries.
		 */
		private final class SubmapKeyIterator extends SubmapIterator implements ObjectListIterator<K> {
			public SubmapKeyIterator() {
				super();
			}
			public SubmapKeyIterator(K from) {
				super(from);
			}
			@Override
			public K next() {
				return nextEntry().key;
			}
			@Override
			public K previous() {
				return previousEntry().key;
			}
		};
		An iterator on a subrange of values.
 This class can iterate in both directions on the values of a subrange of the keys of a threaded tree. We simply override the ListIterator.next()/ListIterator.previous() methods (and possibly their type-specific counterparts) so that they return values instead of entries. /**
		 * An iterator on a subrange of values.
		 *
		 * <p>
		 * This class can iterate in both directions on the values of a subrange of the
		 * keys of a threaded tree. We simply override the
		 * {@link java.util.ListIterator#next()}/{@link java.util.ListIterator#previous()}
		 * methods (and possibly their type-specific counterparts) so that they return
		 * values instead of entries.
		 */
		private final class SubmapValueIterator extends SubmapIterator implements ObjectListIterator<V> {
			@Override
			public V next() {
				return nextEntry().value;
			}
			@Override
			public V previous() {
				return previousEntry().value;
			}
		};
	}
	Returns a deep copy of this tree map.

This method performs a deep copy of this tree map; the data stored in the
set, however, is not cloned. Note that this makes a difference only for
object keys.
Returns: a deep copy of this tree map./**
	 * Returns a deep copy of this tree map.
	 *
	 * <p>
	 * This method performs a deep copy of this tree map; the data stored in the
	 * set, however, is not cloned. Note that this makes a difference only for
	 * object keys.
	 *
	 * @return a deep copy of this tree map.
	 */
	@Override
	@SuppressWarnings("unchecked")
	public Object2ReferenceAVLTreeMap<K, V> clone() {
		Object2ReferenceAVLTreeMap<K, V> c;
		try {
			c = (Object2ReferenceAVLTreeMap<K, V>) super.clone();
		} catch (CloneNotSupportedException cantHappen) {
			throw new InternalError();
		}
		c.keys = null;
		c.values = null;
		c.entries = null;
		c.allocatePaths();
		if (count != 0) {
			// Also this apparently unfathomable code is derived from GNU libavl.
			Entry<K, V> e, p, q, rp = new Entry<>(), rq = new Entry<>();
			p = rp;
			rp.left(tree);
			q = rq;
			rq.pred(null);
			while (true) {
				if (!p.pred()) {
					e = p.left.clone();
					e.pred(q.left);
					e.succ(q);
					q.left(e);
					p = p.left;
					q = q.left;
				} else {
					while (p.succ()) {
						p = p.right;
						if (p == null) {
							q.right = null;
							c.tree = rq.left;
							c.firstEntry = c.tree;
							while (c.firstEntry.left != null)
								c.firstEntry = c.firstEntry.left;
							c.lastEntry = c.tree;
							while (c.lastEntry.right != null)
								c.lastEntry = c.lastEntry.right;
							return c;
						}
						q = q.right;
					}
					p = p.right;
					q = q.right;
				}
				if (!p.succ()) {
					e = p.right.clone();
					e.succ(q.right);
					e.pred(q);
					q.right(e);
				}
			}
		}
		return c;
	}
	private void writeObject(java.io.ObjectOutputStream s) throws java.io.IOException {
		int n = count;
		EntryIterator i = new EntryIterator();
		Entry<K, V> e;
		s.defaultWriteObject();
		while (n-- != 0) {
			e = i.nextEntry();
			s.writeObject(e.key);
			s.writeObject(e.value);
		}
	}
	Reads the given number of entries from the input stream, returning the
corresponding tree.
Params: s – 
           the input stream.
n – 
           the (positive) number of entries to read.
pred – 
           the entry containing the key that preceeds the first key in the
           tree.
succ – 
           the entry containing the key that follows the last key in the
           tree./**
	 * Reads the given number of entries from the input stream, returning the
	 * corresponding tree.
	 *
	 * @param s
	 *            the input stream.
	 * @param n
	 *            the (positive) number of entries to read.
	 * @param pred
	 *            the entry containing the key that preceeds the first key in the
	 *            tree.
	 * @param succ
	 *            the entry containing the key that follows the last key in the
	 *            tree.
	 */
	@SuppressWarnings("unchecked")
	private Entry<K, V> readTree(final java.io.ObjectInputStream s, final int n, final Entry<K, V> pred,
			final Entry<K, V> succ) throws java.io.IOException, ClassNotFoundException {
		if (n == 1) {
			final Entry<K, V> top = new Entry<>((K) s.readObject(), (V) s.readObject());
			top.pred(pred);
			top.succ(succ);
			return top;
		}
		if (n == 2) {
			/*
			 * We handle separately this case so that recursion will always* be on nonempty
			 * subtrees.
			 */
			final Entry<K, V> top = new Entry<>((K) s.readObject(), (V) s.readObject());
			top.right(new Entry<>((K) s.readObject(), (V) s.readObject()));
			top.right.pred(top);
			top.balance(1);
			top.pred(pred);
			top.right.succ(succ);
			return top;
		}
		// The right subtree is the largest one.
		final int rightN = n / 2, leftN = n - rightN - 1;
		final Entry<K, V> top = new Entry<>();
		top.left(readTree(s, leftN, pred, top));
		top.key = (K) s.readObject();
		top.value = (V) s.readObject();
		top.right(readTree(s, rightN, top, succ));
		if (n == (n & -n))
			top.balance(1); // Quick test for determining whether n is a power of 2.
		return top;
	}
	private void readObject(java.io.ObjectInputStream s) throws java.io.IOException, ClassNotFoundException {
		s.defaultReadObject();
		/*
		 * The storedComparator is now correctly set, but we must restore on-the-fly the
		 * actualComparator.
		 */
		setActualComparator();
		allocatePaths();
		if (count != 0) {
			tree = readTree(s, count, null, null);
			Entry<K, V> e;
			e = tree;
			while (e.left() != null)
				e = e.left();
			firstEntry = e;
			e = tree;
			while (e.right() != null)
				e = e.right();
			lastEntry = e;
		}
	}
}
Params:	k – the array of keys of the new tree map. v – the array of corresponding values in the new tree map. c – a (possibly type-specific) comparator.
Throws:	IllegalArgumentException – if `k` and `v` have different lengths.
Params:	k1 – the first key. k2 – the second key.
Returns:	a number smaller than, equal to or greater than 0, as usual (i.e., when k1 < k2, k1 = k2 or k1 > k2, respectively).
Params:	k – the key to search for.
Returns:	the corresponding entry, or `null` if no entry with the given key exists.
Params:	k – a key.
Returns:	the last entry on a search for the given key; this will be the given key, if it present; otherwise, it will be either the smallest greater key or the greatest smaller key.
Params:	k – the key
Returns:	a node with key k. If a node with key k already exists, then that node is returned, otherwise a new node with defRetValue is created ensuring that the tree is balanced after creation of the node.
Params:	e – a node of the tree.
Returns:	the parent of the given node, or `null` for the root.
/

it.unimi.dsi/ fastutil/ 8.3.0/ it/unimi/dsi/fastutil/objects/Object2ReferenceAVLTreeMap.java
