Java集合之TreeMap

TreeMap与Map的关系如下图：



TreeMap介绍：
（1）TreeMap是一个有序的key-value集合，是通过红黑树来实现的。
（2）TreeMap是继承于AbstractMap，所以他是一个Map，是一个key-value集合。
（3）TreeMap实现了Navigable接口，支持一系列的导航方法，TreeMap是有序集合
（4）实现了Cloneable接口，可以被克隆
（5）TreeMap实现了Serializable接口，它支持序列化
（6）TreeMap基于红黑树数显，映射根据其键的自然排序进行排序

TreeMap主要的API：

Entry<K, V>                ceilingEntry(K key)
K                          ceilingKey(K key)
void                       clear()
Object                     clone()
Comparator<? super K>      comparator()
boolean                    containsKey(Object key)
NavigableSet<K>            descendingKeySet()
NavigableMap<K, V>         descendingMap()
Set<Entry<K, V>>           entrySet()
Entry<K, V>                firstEntry()
K                          firstKey()
Entry<K, V>                floorEntry(K key)
K                          floorKey(K key)
V                          get(Object key)
NavigableMap<K, V>         headMap(K to, boolean inclusive)
SortedMap<K, V>            headMap(K toExclusive)
Entry<K, V>                higherEntry(K key)
K                          higherKey(K key)
boolean                    isEmpty()
Set<K>                     keySet()
Entry<K, V>                lastEntry()
K                          lastKey()
Entry<K, V>                lowerEntry(K key)
K                          lowerKey(K key)
NavigableSet<K>            navigableKeySet()
Entry<K, V>                pollFirstEntry()
Entry<K, V>                pollLastEntry()
V                          put(K key, V value)
V                          remove(Object key)
int                        size()
SortedMap<K, V>            subMap(K fromInclusive, K toExclusive)
NavigableMap<K, V>         subMap(K from, boolean fromInclusive, K to, boolean toInclusive)
NavigableMap<K, V>         tailMap(K from, boolean inclusive)
SortedMap<K, V>            tailMap(K fromInclusive)

TreeMap遍历方式
（1）遍历TreeMap的键值对：根据entrySet()获取TreeMap的“键值对”集合，对键值对集合通过Iterator迭代遍历。

String key=null;
Integer value=null;
Iterator iterator=map.entrySet().iterator();
while(iterator.hasNext())
{
Map.Entry entry=(Map.Entry)iterator.next();
key=(String) entry.getKey();
value=(Integer)entry.getValue();
}

（2）遍历TreeMap的键：根据keySet()获得“键”集合，通过迭代器去遍历键集合。

String key = null;
Integer integ = null;
Iterator iter = map.keySet().iterator();
while (iter.hasNext()) {
// 获取key
key = (String)iter.next();
// 根据key，获取value
integ = (Integer)map.get(key);
}

（3）遍历TreeMap的值：根据values获得值的集合，通过迭代器去遍历值的集合。

Integer value = null;
Collection c = map.values();
Iterator iter= c.iterator();
while (iter.hasNext())
{
value = (Integer)iter.next();
}

TreeMap示例代码：

public class Hello {

public static void main(String[] args) {
testTreeMapOridinaryAPIs();
testSubMapAPIs();
}
private static void testTreeMapOridinaryAPIs() {
// 初始化随机种子
Random r = new Random();
// 新建TreeMap
TreeMap tmap = new TreeMap();
// 添加操作
tmap.put("one", r.nextInt(10));
tmap.put("two", r.nextInt(10));
tmap.put("three", r.nextInt(10));
tmap.put("four", r.nextInt(10));
tmap.put("five", r.nextInt(10));
tmap.put("six", r.nextInt(10));
System.out.printf("\n ---- testTreeMapOridinaryAPIs ----\n");
// 打印出TreeMap
System.out.printf("%s\n",tmap );
// 通过Iterator遍历key-value
Iterator iter = tmap.entrySet().iterator();
while(iter.hasNext()) {
Map.Entry entry = (Map.Entry)iter.next();
System.out.printf("next : %s - %s\n", entry.getKey(), entry.getValue());
}
// TreeMap的键值对个数
System.out.printf("size: %s\n", tmap.size());
// containsKey(Object key) :是否包含键key
System.out.printf("contains key two : %s\n",tmap.containsKey("two"));
System.out.printf("contains key five : %s\n",tmap.containsKey("five"));
// containsValue(Object value) :是否包含值value
System.out.printf("contains value 0 : %s\n",tmap.containsValue(new Integer(0)));
// remove(Object key) ： 删除键key对应的键值对
tmap.remove("three");
System.out.printf("tmap:%s\n",tmap );
// clear() ： 清空TreeMap
tmap.clear();
// isEmpty() : TreeMap是否为空
System.out.printf("%s\n", (tmap.isEmpty()?"tmap is empty":"tmap is not empty") );
}
public static void testSubMapAPIs() {
// 新建TreeMap
TreeMap tmap = new TreeMap();
// 添加“键值对”
tmap.put("a", 101);
tmap.put("b", 102);
tmap.put("c", 103);
tmap.put("d", 104);
tmap.put("e", 105);
System.out.printf("\n ---- testSubMapAPIs ----\n");
// 打印出TreeMap
System.out.printf("tmap:\n\t%s\n", tmap);
// 测试 headMap(K toKey)
System.out.printf("tmap.headMap(\"c\"):\n\t%s\n", tmap.headMap("c"));
// 测试 headMap(K toKey, boolean inclusive)
System.out.printf("tmap.headMap(\"c\", true):\n\t%s\n", tmap.headMap("c", true));
System.out.printf("tmap.headMap(\"c\", false):\n\t%s\n", tmap.headMap("c", false));
// 测试 tailMap(K fromKey)
System.out.printf("tmap.tailMap(\"c\"):\n\t%s\n", tmap.tailMap("c"));
// 测试 tailMap(K fromKey, boolean inclusive)
System.out.printf("tmap.tailMap(\"c\", true):\n\t%s\n", tmap.tailMap("c", true));
System.out.printf("tmap.tailMap(\"c\", false):\n\t%s\n", tmap.tailMap("c", false));
// 测试 subMap(K fromKey, K toKey)
System.out.printf("tmap.subMap(\"a\", \"c\"):\n\t%s\n", tmap.subMap("a", "c"));
// 测试
System.out.printf("tmap.subMap(\"a\", true, \"c\", true):\n\t%s\n",
tmap.subMap("a", true, "c", true));
System.out.printf("tmap.subMap(\"a\", true, \"c\", false):\n\t%s\n",
tmap.subMap("a", true, "c", false));
System.out.printf("tmap.subMap(\"a\", false, \"c\", true):\n\t%s\n",
tmap.subMap("a", false, "c", true));
System.out.printf("tmap.subMap(\"a\", false, \"c\", false):\n\t%s\n",
tmap.subMap("a", false, "c", false));

// 测试 navigableKeySet()
System.out.printf("tmap.navigableKeySet():\n\t%s\n", tmap.navigableKeySet());
// 测试 descendingKeySet()
System.out.printf("tmap.descendingKeySet():\n\t%s\n", tmap.descendingKeySet());
}
public static void testNavigableMapAPIs() {
// 新建TreeMap
NavigableMap nav = new TreeMap();
// 添加“键值对”
nav.put("aaa", 111);
nav.put("bbb", 222);
nav.put("eee", 333);
nav.put("ccc", 555);
nav.put("ddd", 444);

System.out.printf("\n ---- testNavigableMapAPIs ----\n");
// 打印出TreeMap
System.out.printf("Whole list:%s%n", nav);

// 获取第一个key、第一个Entry
System.out.printf("First key: %s\tFirst entry: %s%n",nav.firstKey(), nav.firstEntry());

// 获取最后一个key、最后一个Entry
System.out.printf("Last key: %s\tLast entry: %s%n",nav.lastKey(), nav.lastEntry());

// 获取“小于/等于bbb”的最大键值对
System.out.printf("Key floor before bbb: %s%n",nav.floorKey("bbb"));

// 获取“小于bbb”的最大键值对
System.out.printf("Key lower before bbb: %s%n", nav.lowerKey("bbb"));

// 获取“大于/等于bbb”的最小键值对
System.out.printf("Key ceiling after ccc: %s%n",nav.ceilingKey("ccc"));

// 获取“大于bbb”的最小键值对
System.out.printf("Key higher after ccc: %s%n\n",nav.higherKey("ccc"));
}

}

运行结果：
---- testTreeMapOridinaryAPIs ----
{five=5, four=5, one=3, six=8, three=1, two=0}
next : five - 5
next : four - 5
next : one - 3
next : six - 8
next : three - 1
next : two - 0
size: 6
contains key two : true
contains key five : true
contains value 0 : true
tmap:{five=5, four=5, one=3, six=8, two=0}
tmap is empty

---- testSubMapAPIs ----
tmap:
{a=101, b=102, c=103, d=104, e=105}
tmap.headMap("c"):
{a=101, b=102}
tmap.headMap("c", true):
{a=101, b=102, c=103}
tmap.headMap("c", false):
{a=101, b=102}
tmap.tailMap("c"):
{c=103, d=104, e=105}
tmap.tailMap("c", true):
{c=103, d=104, e=105}
tmap.tailMap("c", false):
{d=104, e=105}
tmap.subMap("a", "c"):
{a=101, b=102}
tmap.subMap("a", true, "c", true):
{a=101, b=102, c=103}
tmap.subMap("a", true, "c", false):
{a=101, b=102}
tmap.subMap("a", false, "c", true):
{b=102, c=103}
tmap.subMap("a", false, "c", false):
{b=102}
tmap.navigableKeySet():
[a, b, c, d, e]
tmap.descendingKeySet():
[e, d, c, b, a]
基于Java8的SortedMap接口源代码：

public interface SortedMap<K,V> extends Map<K,V> {
Comparator<? super K> comparator();
SortedMap<K,V> subMap(K fromKey, K toKey);
SortedMap<K,V> headMap(K toKey);
SortedMap<K,V> tailMap(K fromKey);
K firstKey();
K lastKey();
Set<K> keySet();
Collection<V> values();
Set<Map.Entry<K, V>> entrySet();
}

基于Java8的Navigable接口源代码：

public interface NavigableMap<K,V> extends SortedMap<K,V> {
Map.Entry<K,V> lowerEntry(K key);
K lowerKey(K key);
Map.Entry<K,V> floorEntry(K key);
K floorKey(K key);
Map.Entry<K,V> ceilingEntry(K key);
K ceilingKey(K key);
Map.Entry<K,V> higherEntry(K key);
K higherKey(K key);
Map.Entry<K,V> firstEntry();
Map.Entry<K,V> lastEntry();
Map.Entry<K,V> pollFirstEntry();
Map.Entry<K,V> pollLastEntry();
NavigableMap<K,V> descendingMap();
NavigableSet<K> navigableKeySet();
NavigableSet<K> descendingKeySet();
NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
K toKey,   boolean toInclusive);
NavigableMap<K,V> headMap(K toKey, boolean inclusive);
NavigableMap<K,V> tailMap(K fromKey, boolean inclusive);
SortedMap<K,V> subMap(K fromKey, K toKey);
SortedMap<K,V> headMap(K toKey);
SortedMap<K,V> tailMap(K fromKey);
}

基于Java8的TreeMap源代码：

public class TreeMap<K,V>extends AbstractMap<K,V>
implements NavigableMap<K,V>, Cloneable, java.io.Serializable
{
private final Comparator<? super K> comparator;//比较器
private transient Entry<K,V> root;//根节点
private transient int size = 0;//起始个数
private transient int modCount = 0;//tree改变次数
public TreeMap() {
comparator = null;
}
public TreeMap(Comparator<? super K> comparator) {
this.comparator = comparator;
}
public TreeMap(Map<? extends K, ? extends V> m) {
comparator = null;
putAll(m);
}
public TreeMap(SortedMap<K, ? extends V> m) {
comparator = m.comparator();
try {
buildFromSorted(m.size(), m.entrySet().iterator(), null, null);
} catch (java.io.IOException cannotHappen) {
} catch (ClassNotFoundException cannotHappen) {
}
}
//获得个数
public int size() {
return size;
}
//是否含有某个key
public boolean containsKey(Object key) {
return getEntry(key) != null;
}
//是否还有某个值
public boolean containsValue(Object value) {
for (Entry<K,V> e = getFirstEntry(); e != null; e = successor(e))
if (valEquals(value, e.value))
return true;
return false;
}
//通过key获得值
public V get(Object key) {
Entry<K,V> p = getEntry(key);
return (p==null ? null : p.value);
}
//比较器
public Comparator<? super K> comparator() {
return comparator;
}
//获得第一个key
public K firstKey() {
return key(getFirstEntry());
}
//获得最后一个key
public K lastKey() {
return key(getLastEntry());
}

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

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

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

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

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

}
return null;
}

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

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

/**
* Associates the specified value with the specified key in this map.
* If the map previously contained a mapping for the key, the old
* value is replaced.
*
* @param key key with which the specified value is to be associated
* @param value value to be associated with the specified key
*
* @return the previous value associated with {@code key}, or
*         {@code null} if there was no mapping for {@code key}.
*         (A {@code null} return can also indicate that the map
*         previously associated {@code null} with {@code key}.)
* @throws ClassCastException if the specified key cannot be compared
*         with the keys currently in the map
* @throws NullPointerException if the specified key is null
*         and this map uses natural ordering, or its comparator
*         does not permit null keys
*/
//插入key-value值
public V put(K key, V value) {
Entry<K,V> t = root;
if (t == null) {
compare(key, key); // type (and possibly null) check

root = new Entry<>(key, value, null);
size = 1;
modCount++;
return null;
}
int cmp;
Entry<K,V> parent;
// split comparator and comparable paths
Comparator<? super K> cpr = comparator;
if (cpr != null) {
do {
parent = t;
cmp = cpr.compare(key, t.key);
if (cmp < 0)
t = t.left;
else if (cmp > 0)
t = t.right;
else
return t.setValue(value);
} while (t != null);
}
else {
if (key == null)
throw new NullPointerException();
@SuppressWarnings("unchecked")
Comparable<? super K> k = (Comparable<? super K>) key;
do {
parent = t;
cmp = k.compareTo(t.key);
if (cmp < 0)
t = t.left;
else if (cmp > 0)
t = t.right;
else
return t.setValue(value);
} while (t != null);
}
Entry<K,V> e = new Entry<>(key, value, parent);
if (cmp < 0)
parent.left = e;
else
parent.right = e;
fixAfterInsertion(e);
size++;
modCount++;
return null;
}

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

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

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

/**
* Returns a shallow copy of this {@code TreeMap} instance. (The keys and
* values themselves are not cloned.)
*
* @return a shallow copy of this map
*/
//进行克隆，深拷贝
public Object clone() {
TreeMap<?,?> clone;
try {
clone = (TreeMap<?,?>) super.clone();
} catch (CloneNotSupportedException e) {
throw new InternalError(e);
}

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

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

return clone;
}

// NavigableMap API methods

/**
* @since 1.6
*/
//获得第一个entry
public Map.Entry<K,V> firstEntry() {
return exportEntry(getFirstEntry());
}

/**
* @since 1.6
*/
//最后一个entry
public Map.Entry<K,V> lastEntry() {
return exportEntry(getLastEntry());
}

/**
* @since 1.6
*/
//弹出第一个entry，并删除
public Map.Entry<K,V> pollFirstEntry() {
Entry<K,V> p = getFirstEntry();
Map.Entry<K,V> result = exportEntry(p);
if (p != null)
deleteEntry(p);
return result;
}

/**
* @since 1.6
*/
//弹出最后一个entry，并删除
public Map.Entry<K,V> pollLastEntry() {
Entry<K,V> p = getLastEntry();
Map.Entry<K,V> result = exportEntry(p);
if (p != null)
deleteEntry(p);
return result;
}

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

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

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

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

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

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

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

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

// Views

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

/**
* Returns a {@link Set} view of the keys contained in this map.
*
* <p>The set's iterator returns the keys in ascending order.
* The set's spliterator is
* <em><a href="Spliterator.html#binding">late-binding</a></em>,
* <em>fail-fast</em>, and additionally reports {@link Spliterator#SORTED}
* and {@link Spliterator#ORDERED} with an encounter order that is ascending
* key order.  The spliterator's comparator (see
* {@link java.util.Spliterator#getComparator()}) is {@code null} if
* the tree map's comparator (see {@link #comparator()}) is {@code null}.
* Otherwise, the spliterator's comparator is the same as or imposes the
* same total ordering as the tree map's comparator.
*
* <p>The set is backed by the map, so changes to the map are
* reflected in the set, and vice-versa.  If the map is modified
* while an iteration over the set is in progress (except through
* the iterator's own {@code remove} operation), the results of
* the iteration are undefined.  The set supports element removal,
* which removes the corresponding mapping from the map, via the
* {@code Iterator.remove}, {@code Set.remove},
* {@code removeAll}, {@code retainAll}, and {@code clear}
* operations.  It does not support the {@code add} or {@code addAll}
* operations.
*/
public Set<K> keySet() {
return navigableKeySet();
}

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

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

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

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

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

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

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

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

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

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

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

@Override
public boolean replace(K key, V oldValue, V newValue) {
Entry<K,V> p = getEntry(key);
if (p!=null && Objects.equals(oldValue, p.value)) {
p.value = newValue;
return true;
}
return false;
}

@Override
public V replace(K key, V value) {
Entry<K,V> p = getEntry(key);
if (p!=null) {
V oldValue = p.value;
p.value = value;
return oldValue;
}
return null;
}

@Override
public void forEach(BiConsumer<? super K, ? super V> action) {
Objects.requireNonNull(action);
int expectedModCount = modCount;
for (Entry<K, V> e = getFirstEntry(); e != null; e = successor(e)) {
action.accept(e.key, e.value);

if (expectedModCount != modCount) {
throw new ConcurrentModificationException();
}
}
}

@Override
public void replaceAll(BiFunction<? super K, ? super V, ? extends V> function) {
Objects.requireNonNull(function);
int expectedModCount = modCount;

for (Entry<K, V> e = getFirstEntry(); e != null; e = successor(e)) {
e.value = function.apply(e.key, e.value);

if (expectedModCount != modCount) {
throw new ConcurrentModificationException();
}
}
}

// View class support

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

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

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

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

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

public Spliterator<V> spliterator() {
return new ValueSpliterator<K,V>(TreeMap.this, null, null, 0, -1, 0);
}
}

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

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

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

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

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

public Spliterator<Map.Entry<K,V>> spliterator() {
return new EntrySpliterator<K,V>(TreeMap.this, null, null, 0, -1, 0);
}
}

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

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

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

static final class KeySet<E> extends AbstractSet<E> implements NavigableSet<E> {
private final NavigableMap<E, ?> m;
KeySet(NavigableMap<E,?> map) { m = map; }

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

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

public int size() { return m.size(); }
public boolean isEmpty() { return m.isEmpty(); }
public boolean contains(Object o) { return m.containsKey(o); }
public void clear() { m.clear(); }
public E lower(E e) { return m.lowerKey(e); }
public E floor(E e) { return m.floorKey(e); }
public E ceiling(E e) { return m.ceilingKey(e); }
public E higher(E e) { return m.higherKey(e); }
public E first() { return m.firstKey(); }
public E last() { return m.lastKey(); }
public Comparator<? super E> comparator() { return m.comparator(); }
public E pollFirst() {
Map.Entry<E,?> e = m.pollFirstEntry();
return (e == null) ? null : e.getKey();
}
public E pollLast() {
Map.Entry<E,?> e = m.pollLastEntry();
return (e == null) ? null : e.getKey();
}
public boolean remove(Object o) {
int oldSize = size();
m.remove(o);
return size() != oldSize;
}
public NavigableSet<E> subSet(E fromElement, boolean fromInclusive,
E toElement,   boolean toInclusive) {
return new KeySet<>(m.subMap(fromElement, fromInclusive,
toElement,   toInclusive));
}
public NavigableSet<E> headSet(E toElement, boolean inclusive) {
return new KeySet<>(m.headMap(toElement, inclusive));
}
public NavigableSet<E> tailSet(E fromElement, boolean inclusive) {
return new KeySet<>(m.tailMap(fromElement, inclusive));
}
public SortedSet<E> subSet(E fromElement, E toElement) {
return subSet(fromElement, true, toElement, false);
}
public SortedSet<E> headSet(E toElement) {
return headSet(toElement, false);
}
public SortedSet<E> tailSet(E fromElement) {
return tailSet(fromElement, true);
}
public NavigableSet<E> descendingSet() {
return new KeySet<>(m.descendingMap());
}

public Spliterator<E> spliterator() {
return keySpliteratorFor(m);
}
}

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

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

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

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

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

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

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

final class ValueIterator extends PrivateEntryIterator<V> {
ValueIterator(Entry<K,V> first) {
super(first);
}
public V next() {
return nextEntry().value;
}
}

final class KeyIterator extends PrivateEntryIterator<K> {
KeyIterator(Entry<K,V> first) {
super(first);
}
public K next() {
return nextEntry().key;
}
}

final class DescendingKeyIterator extends PrivateEntryIterator<K> {
DescendingKeyIterator(Entry<K,V> first) {
super(first);
}
public K next() {
return prevEntry().key;
}
public void remove() {
if (lastReturned == null)
throw new IllegalStateException();
if (modCount != expectedModCount)
throw new ConcurrentModificationException();
deleteEntry(lastReturned);
lastReturned = null;
expectedModCount = modCount;
}
}

// Little utilities

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

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

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

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

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

// SubMaps

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

/**
* @serial include
*/
abstract static class NavigableSubMap<K,V> extends AbstractMap<K,V>
implements NavigableMap<K,V>, java.io.Serializable {
private static final long serialVersionUID = -2102997345730753016L;
/**
* The backing map.
*/
final TreeMap<K,V> m;

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

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

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

// internal utilities

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

abstract TreeMap.Entry<K,V> subLowest();
abstract TreeMap.Entry<K,V> subHighest();
abstract TreeMap.Entry<K,V> subCeiling(K key);
abstract TreeMap.Entry<K,V> subHigher(K key);
abstract TreeMap.Entry<K,V> subFloor(K key);
abstract TreeMap.Entry<K,V> subLower(K key);

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

abstract Spliterator<K> keySpliterator();

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

// public methods

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

// View classes

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

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

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

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

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

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

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

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

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

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

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

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

}

final class SubMapEntryIterator extends SubMapIterator<Map.Entry<K,V>> {
SubMapEntryIterator(TreeMap.Entry<K,V> first,
TreeMap.Entry<K,V> fence) {
super(first, fence);
}
public Map.Entry<K,V> next() {
return nextEntry();
}
public void remove() {
removeAscending();
}
}

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

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

// Implement minimal Spliterator as KeySpliterator backup
final class SubMapKeyIterator extends SubMapIterator<K>
implements Spliterator<K> {
SubMapKeyIterator(TreeMap.Entry<K,V> first,
TreeMap.Entry<K,V> fence) {
super(first, fence);
}
public K next() {
return nextEntry().key;
}
public void remove() {
removeAscending();
}
public Spliterator<K> trySplit() {
return null;
}
public void forEachRemaining(Consumer<? super K> action) {
while (hasNext())
action.accept(next());
}
public boolean tryAdvance(Consumer<? super K> action) {
if (hasNext()) {
action.accept(next());
return true;
}
return false;
}
public long estimateSize() {
return Long.MAX_VALUE;
}
public int characteristics() {
return Spliterator.DISTINCT | Spliterator.ORDERED |
Spliterator.SORTED;
}
public final Comparator<? super K>  getComparator() {
return NavigableSubMap.this.comparator();
}
}

final class DescendingSubMapKeyIterator extends SubMapIterator<K>
implements Spliterator<K> {
DescendingSubMapKeyIterator(TreeMap.Entry<K,V> last,
TreeMap.Entry<K,V> fence) {
super(last, fence);
}
public K next() {
return prevEntry().key;
}
public void remove() {
removeDescending();
}
public Spliterator<K> trySplit() {
return null;
}
public void forEachRemaining(Consumer<? super K> action) {
while (hasNext())
action.accept(next());
}
public boolean tryAdvance(Consumer<? super K> action) {
if (hasNext()) {
action.accept(next());
return true;
}
return false;
}
public long estimateSize() {
return Long.MAX_VALUE;
}
public int characteristics() {
return Spliterator.DISTINCT | Spliterator.ORDERED;
}
}
}

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

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

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

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

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

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

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

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

Spliterator<K> keySpliterator() {
return new SubMapKeyIterator(absLowest(), absHighFence());
}

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

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

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

TreeMap.Entry<K,V> subLowest()       { return absLowest(); }
TreeMap.Entry<K,V> subHighest()      { return absHighest(); }
TreeMap.Entry<K,V> subCeiling(K key) { return absCeiling(key); }
TreeMap.Entry<K,V> subHigher(K key)  { return absHigher(key); }
TreeMap.Entry<K,V> subFloor(K key)   { return absFloor(key); }
TreeMap.Entry<K,V> subLower(K key)   { return absLower(key); }
}

/**
* @serial include
*/
static final class DescendingSubMap<K,V>  extends NavigableSubMap<K,V> {
private static final long serialVersionUID = 912986545866120460L;
DescendingSubMap(TreeMap<K,V> m,
boolean fromStart, K lo, boolean loInclusive,
boolean toEnd,     K hi, boolean hiInclusive) {
super(m, fromStart, lo, loInclusive, toEnd, hi, hiInclusive);
}

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

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

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

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

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

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

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

Spliterator<K> keySpliterator() {
return new DescendingSubMapKeyIterator(absHighest(), absLowFence());
}

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

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

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

TreeMap.Entry<K,V> subLowest()       { return absHighest(); }
TreeMap.Entry<K,V> subHighest()      { return absLowest(); }
TreeMap.Entry<K,V> subCeiling(K key) { return absFloor(key); }
TreeMap.Entry<K,V> subHigher(K key)  { return absLower(key); }
TreeMap.Entry<K,V> subFloor(K key)   { return absCeiling(key); }
TreeMap.Entry<K,V> subLower(K key)   { return absHigher(key); }
}

/**
* This class exists solely for the sake of serialization
* compatibility with previous releases of TreeMap that did not
* support NavigableMap.  It translates an old-version SubMap into
* a new-version AscendingSubMap. This class is never otherwise
* used.
*
* @serial include
*/
private class SubMap extends AbstractMap<K,V>
implements SortedMap<K,V>, java.io.Serializable {
private static final long serialVersionUID = -6520786458950516097L;
private boolean fromStart = false, toEnd = false;
private K fromKey, toKey;
private Object readResolve() {
return new AscendingSubMap<>(TreeMap.this,
fromStart, fromKey, true,
toEnd, toKey, false);
}
public Set<Map.Entry<K,V>> entrySet() { throw new InternalError(); }
public K lastKey() { throw new InternalError(); }
public K firstKey() { throw new InternalError(); }
public SortedMap<K,V> subMap(K fromKey, K toKey) { throw new InternalError(); }
public SortedMap<K,V> headMap(K toKey) { throw new InternalError(); }
public SortedMap<K,V> tailMap(K fromKey) { throw new InternalError(); }
public Comparator<? super K> comparator() { throw new InternalError(); }
}

// Red-black mechanics

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

setColor(x, BLACK);
}

private static final long serialVersionUID = 919286545866124006L;

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

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

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

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

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

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

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

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

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

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

if (hi < lo) return null;

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

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

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

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

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

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

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

return middle;
}

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

/**
* Currently, we support Spliterator-based versions only for the
* full map, in either plain of descending form, otherwise relying
* on defaults because size estimation for submaps would dominate
* costs. The type tests needed to check these for key views are
* not very nice but avoid disrupting existing class
* structures. Callers must use plain default spliterators if this
* returns null.
*/
static <K> Spliterator<K> keySpliteratorFor(NavigableMap<K,?> m) {
if (m instanceof TreeMap) {
@SuppressWarnings("unchecked") TreeMap<K,Object> t =
(TreeMap<K,Object>) m;
return t.keySpliterator();
}
if (m instanceof DescendingSubMap) {
@SuppressWarnings("unchecked") DescendingSubMap<K,?> dm =
(DescendingSubMap<K,?>) m;
TreeMap<K,?> tm = dm.m;
if (dm == tm.descendingMap) {
@SuppressWarnings("unchecked") TreeMap<K,Object> t =
(TreeMap<K,Object>) tm;
return t.descendingKeySpliterator();
}
}
@SuppressWarnings("unchecked") NavigableSubMap<K,?> sm =
(NavigableSubMap<K,?>) m;
return sm.keySpliterator();
}

final Spliterator<K> keySpliterator() {
return new KeySpliterator<K,V>(this, null, null, 0, -1, 0);
}

final Spliterator<K> descendingKeySpliterator() {
return new DescendingKeySpliterator<K,V>(this, null, null, 0, -2, 0);
}

/**
* Base class for spliterators.  Iteration starts at a given
* origin and continues up to but not including a given fence (or
* null for end).  At top-level, for ascending cases, the first
* split uses the root as left-fence/right-origin. From there,
* right-hand splits replace the current fence with its left
* child, also serving as origin for the split-off spliterator.
* Left-hands are symmetric. Descending versions place the origin
* at the end and invert ascending split rules.  This base class
* is non-commital about directionality, or whether the top-level
* spliterator covers the whole tree. This means that the actual
* split mechanics are located in subclasses. Some of the subclass
* trySplit methods are identical (except for return types), but
* not nicely factorable.
*
* Currently, subclass versions exist only for the full map
* (including descending keys via its descendingMap).  Others are
* possible but currently not worthwhile because submaps require
* O(n) computations to determine size, which substantially limits
* potential speed-ups of using custom Spliterators versus default
* mechanics.
*
* To boostrap initialization, external constructors use
* negative size estimates: -1 for ascend, -2 for descend.
*/
static class TreeMapSpliterator<K,V> {
final TreeMap<K,V> tree;
TreeMap.Entry<K,V> current; // traverser; initially first node in range
TreeMap.Entry<K,V> fence;   // one past last, or null
int side;                   // 0: top, -1: is a left split, +1: right
int est;                    // size estimate (exact only for top-level)
int expectedModCount;       // for CME checks

TreeMapSpliterator(TreeMap<K,V> tree,
TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
int side, int est, int expectedModCount) {
this.tree = tree;
this.current = origin;
this.fence = fence;
this.side = side;
this.est = est;
this.expectedModCount = expectedModCount;
}

final int getEstimate() { // force initialization
int s; TreeMap<K,V> t;
if ((s = est) < 0) {
if ((t = tree) != null) {
current = (s == -1) ? t.getFirstEntry() : t.getLastEntry();
s = est = t.size;
expectedModCount = t.modCount;
}
else
s = est = 0;
}
return s;
}

public final long estimateSize() {
return (long)getEstimate();
}
}

static final class KeySpliterator<K,V>
extends TreeMapSpliterator<K,V>
implements Spliterator<K> {
KeySpliterator(TreeMap<K,V> tree,
TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
int side, int est, int expectedModCount) {
super(tree, origin, fence, side, est, expectedModCount);
}

public KeySpliterator<K,V> trySplit() {
if (est < 0)
getEstimate(); // force initialization
int d = side;
TreeMap.Entry<K,V> e = current, f = fence,
s = ((e == null || e == f) ? null :      // empty
(d == 0)              ? tree.root : // was top
(d >  0)              ? e.right :   // was right
(d <  0 && f != null) ? f.left :    // was left
null);
if (s != null && s != e && s != f &&
tree.compare(e.key, s.key) < 0) {        // e not already past s
side = 1;
return new KeySpliterator<>
(tree, e, current = s, -1, est >>>= 1, expectedModCount);
}
return null;
}

public void forEachRemaining(Consumer<? super K> action) {
if (action == null)
throw new NullPointerException();
if (est < 0)
getEstimate(); // force initialization
TreeMap.Entry<K,V> f = fence, e, p, pl;
if ((e = current) != null && e != f) {
current = f; // exhaust
do {
action.accept(e.key);
if ((p = e.right) != null) {
while ((pl = p.left) != null)
p = pl;
}
else {
while ((p = e.parent) != null && e == p.right)
e = p;
}
} while ((e = p) != null && e != f);
if (tree.modCount != expectedModCount)
throw new ConcurrentModificationException();
}
}

public boolean tryAdvance(Consumer<? super K> action) {
TreeMap.Entry<K,V> e;
if (action == null)
throw new NullPointerException();
if (est < 0)
getEstimate(); // force initialization
if ((e = current) == null || e == fence)
return false;
current = successor(e);
action.accept(e.key);
if (tree.modCount != expectedModCount)
throw new ConcurrentModificationException();
return true;
}

public int characteristics() {
return (side == 0 ? Spliterator.SIZED : 0) |
Spliterator.DISTINCT | Spliterator.SORTED | Spliterator.ORDERED;
}

public final Comparator<? super K>  getComparator() {
return tree.comparator;
}

}

static final class DescendingKeySpliterator<K,V>
extends TreeMapSpliterator<K,V>
implements Spliterator<K> {
DescendingKeySpliterator(TreeMap<K,V> tree,
TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
int side, int est, int expectedModCount) {
super(tree, origin, fence, side, est, expectedModCount);
}

public DescendingKeySpliterator<K,V> trySplit() {
if (est < 0)
getEstimate(); // force initialization
int d = side;
TreeMap.Entry<K,V> e = current, f = fence,
s = ((e == null || e == f) ? null :      // empty
(d == 0)              ? tree.root : // was top
(d <  0)              ? e.left :    // was left
(d >  0 && f != null) ? f.right :   // was right
null);
if (s != null && s != e && s != f &&
tree.compare(e.key, s.key) > 0) {       // e not already past s
side = 1;
return new DescendingKeySpliterator<>
(tree, e, current = s, -1, est >>>= 1, expectedModCount);
}
return null;
}

public void forEachRemaining(Consumer<? super K> action) {
if (action == null)
throw new NullPointerException();
if (est < 0)
getEstimate(); // force initialization
TreeMap.Entry<K,V> f = fence, e, p, pr;
if ((e = current) != null && e != f) {
current = f; // exhaust
do {
action.accept(e.key);
if ((p = e.left) != null) {
while ((pr = p.right) != null)
p = pr;
}
else {
while ((p = e.parent) != null && e == p.left)
e = p;
}
} while ((e = p) != null && e != f);
if (tree.modCount != expectedModCount)
throw new ConcurrentModificationException();
}
}

public boolean tryAdvance(Consumer<? super K> action) {
TreeMap.Entry<K,V> e;
if (action == null)
throw new NullPointerException();
if (est < 0)
getEstimate(); // force initialization
if ((e = current) == null || e == fence)
return false;
current = predecessor(e);
action.accept(e.key);
if (tree.modCount != expectedModCount)
throw new ConcurrentModificationException();
return true;
}

public int characteristics() {
return (side == 0 ? Spliterator.SIZED : 0) |
Spliterator.DISTINCT | Spliterator.ORDERED;
}
}

static final class ValueSpliterator<K,V>
extends TreeMapSpliterator<K,V>
implements Spliterator<V> {
ValueSpliterator(TreeMap<K,V> tree,
TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
int side, int est, int expectedModCount) {
super(tree, origin, fence, side, est, expectedModCount);
}

public ValueSpliterator<K,V> trySplit() {
if (est < 0)
getEstimate(); // force initialization
int d = side;
TreeMap.Entry<K,V> e = current, f = fence,
s = ((e == null || e == f) ? null :      // empty
(d == 0)              ? tree.root : // was top
(d >  0)              ? e.right :   // was right
(d <  0 && f != null) ? f.left :    // was left
null);
if (s != null && s != e && s != f &&
tree.compare(e.key, s.key) < 0) {        // e not already past s
side = 1;
return new ValueSpliterator<>
(tree, e, current = s, -1, est >>>= 1, expectedModCount);
}
return null;
}

public void forEachRemaining(Consumer<? super V> action) {
if (action == null)
throw new NullPointerException();
if (est < 0)
getEstimate(); // force initialization
TreeMap.Entry<K,V> f = fence, e, p, pl;
if ((e = current) != null && e != f) {
current = f; // exhaust
do {
action.accept(e.value);
if ((p = e.right) != null) {
while ((pl = p.left) != null)
p = pl;
}
else {
while ((p = e.parent) != null && e == p.right)
e = p;
}
} while ((e = p) != null && e != f);
if (tree.modCount != expectedModCount)
throw new ConcurrentModificationException();
}
}

public boolean tryAdvance(Consumer<? super V> action) {
TreeMap.Entry<K,V> e;
if (action == null)
throw new NullPointerException();
if (est < 0)
getEstimate(); // force initialization
if ((e = current) == null || e == fence)
return false;
current = successor(e);
action.accept(e.value);
if (tree.modCount != expectedModCount)
throw new ConcurrentModificationException();
return true;
}

public int characteristics() {
return (side == 0 ? Spliterator.SIZED : 0) | Spliterator.ORDERED;
}
}

static final class EntrySpliterator<K,V>
extends TreeMapSpliterator<K,V>
implements Spliterator<Map.Entry<K,V>> {
EntrySpliterator(TreeMap<K,V> tree,
TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
int side, int est, int expectedModCount) {
super(tree, origin, fence, side, est, expectedModCount);
}

public EntrySpliterator<K,V> trySplit() {
if (est < 0)
getEstimate(); // force initialization
int d = side;
TreeMap.Entry<K,V> e = current, f = fence,
s = ((e == null || e == f) ? null :      // empty
(d == 0)              ? tree.root : // was top
(d >  0)              ? e.right :   // was right
(d <  0 && f != null) ? f.left :    // was left
null);
if (s != null && s != e && s != f &&
tree.compare(e.key, s.key) < 0) {        // e not already past s
side = 1;
return new EntrySpliterator<>
(tree, e, current = s, -1, est >>>= 1, expectedModCount);
}
return null;
}

public void forEachRemaining(Consumer<? super Map.Entry<K, V>> action) {
if (action == null)
throw new NullPointerException();
if (est < 0)
getEstimate(); // force initialization
TreeMap.Entry<K,V> f = fence, e, p, pl;
if ((e = current) != null && e != f) {
current = f; // exhaust
do {
action.accept(e);
if ((p = e.right) != null) {
while ((pl = p.left) != null)
p = pl;
}
else {
while ((p = e.parent) != null && e == p.right)
e = p;
}
} while ((e = p) != null && e != f);
if (tree.modCount != expectedModCount)
throw new ConcurrentModificationException();
}
}

public boolean tryAdvance(Consumer<? super Map.Entry<K,V>> action) {
TreeMap.Entry<K,V> e;
if (action == null)
throw new NullPointerException();
if (est < 0)
getEstimate(); // force initialization
if ((e = current) == null || e == fence)
return false;
current = successor(e);
action.accept(e);
if (tree.modCount != expectedModCount)
throw new ConcurrentModificationException();
return true;
}

public int characteristics() {
return (side == 0 ? Spliterator.SIZED : 0) |
Spliterator.DISTINCT | Spliterator.SORTED | Spliterator.ORDERED;
}

@Override
public Comparator<Map.Entry<K, V>> getComparator() {
// Adapt or create a key-based comparator
if (tree.comparator != null) {
return Map.Entry.comparingByKey(tree.comparator);
}
else {
return (Comparator<Map.Entry<K, V>> & Serializable) (e1, e2) -> {
@SuppressWarnings("unchecked")
Comparable<? super K> k1 = (Comparable<? super K>) e1.getKey();
return k1.compareTo(e2.getKey());
};
}
}
}
}