Java数据结构之TreeMap

一、源码注释

/**
 * TreeMap基于NavigableMap 的一个红黑树的实现。TreeMap会根据比较器comparator对键值对的key进行比较进行排序，如果没有比较器就是用key的自然排序进行排序，这取决你用什么构造器
 * TreeMap为containsKey、get、put和remove操作提供了保证的log(n)时间开销。
 *
 * TreeMap是非线程安全的，如果多个线程同时访问TreeMap，那必须在外部进行同步，以免出现线程安全问题。
 * 或者通过SortedMap m = Collections.synchronizedSortedMap(new TreeMap(...));来对TreeMap进行包装
 *
 * 集合的视图方法返回的迭代器都是快速失败的，如果在创建迭代器后，任何时候对TreeMap的结构上的 修改（除非通过迭代器的删除方法）,迭代器将抛出ConcurrentModificationException}。
 * 因此，在面对并发修改时，迭代器会快速而干净地失败，而不是在将来某个不确定的时间冒着任意的、不确定的行为的风险。、
 *
 * 所有通过类的方法或者视图的到的 Map.Entry对不支持Entry.setValue 方法。(但是可以使用put更改关联映射中的映射。)
 *
 *
 * @author  Josh Bloch and Doug Lea
 * @see Map
 * @see HashMap
 * @see Hashtable
 * @see Comparable
 * @see Comparator
 * @see Collection
 * @since 1.2
 */

public class TreeMap<K,V>
    extends AbstractMap<K,V>
    implements NavigableMap<K,V>, Cloneable, java.io.Serializable
{
    /**
     * 比较器，用来对TreeMap中的节点进行排序，如果使用key的自然排序comparator就为null
     */
    private final Comparator<? super K> comparator;

    /**
     * 红黑树的根节点
     */
    private transient Entry<K,V> root;

    /**
     * 红黑树的节点总数
     */
    private transient int size = 0;

    /**
     * 结构化修改的次数
     */
    private transient int modCount = 0;

    /**
     * 默认的构造函数，比较器为null，说明按照自然排序
     */
    public TreeMap() {
        comparator = null;
    }

    /**
     * 使用比较器的构造函数
     */
    public TreeMap(Comparator<? super K> comparator) {
        this.comparator = comparator;
    }

    /**
     *
     */
    public TreeMap(Map<? extends K, ? extends V> m) {
        comparator = null;
        putAll(m);
    }

    /**
     * 通过SortMap来创建TreeMap，SortMap中的key必须是可比较的，也就是实现了Comparable接口
     */
    public TreeMap(SortedMap<K, ? extends V> m) {
        comparator = m.comparator();
        try {
            buildFromSorted(m.size(), m.entrySet().iterator(), null, null);
        } catch (java.io.IOException cannotHappen) {
        } catch (ClassNotFoundException cannotHappen) {
        }
    }

    // Query Operations

    /**
     * 返回节点总个数
     */
    public int size() {
        return size;
    }

    /**
     * 是否包含该key
     */
    public boolean containsKey(Object key) {
        return getEntry(key) != null;
    }

    /**
     * 是否包含该value，遍历每个节点，然后去匹配是否存在该value
     */
    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;
    }

    /**
     * 返回key对应的value
     */
    public V get(Object key) {
        Entry<K,V> p = getEntry(key);
        return (p==null ? null : p.value);
    }
    //获取比较器
    public Comparator<? super K> comparator() {
        return comparator;
    }

    /**
     *  获取第一个key，如果TreeMap为空，则抛出异常
     */
    public K firstKey() {
        return key(getFirstEntry());
    }

    /**
     * 返回最后一个key
     */
    public K lastKey() {
        return key(getLastEntry());
    }

    /**
     * 将Map中的所有键值对添加到TreeMap中
     * 如果当前TreeMap中没有节点，并且传入map是SortedMap的实现，并且比较器也一样，这时候直接将map中的键值对拷贝到TreeMap中
     * 否则就循环添加键值对
     */
    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);
    }

    /**
     * 通过key获取节点。
     */
    final Entry<K,V> getEntry(Object key) {
        // Offload comparator-based version for sake of performance
        if (comparator != null)//存在比较器就通过比较器来进行查找
            return getEntryUsingComparator(key);
        if (key == null)//既没有比较器，此时key还为null就抛出异常
            throw new NullPointerException();
        @SuppressWarnings("unchecked")
            Comparable<? super K> k = (Comparable<? super K>) key;//最后看key是否是可比较的，来进行查找
        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;
    }

    /**
     *    使用比较器的getEntry版本。从getEntry中分离出来以获得性能。(对于不太依赖于比较器性能的大多数方法，这不值得这样做，但在这里是值得的。)
     */
    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;
    }

    /**
     * 返回大于等于key的最小的key所对应的节点
     */
    final Entry<K,V> getCeilingEntry(K key) {
        Entry<K,V> p = root;
        while (p != null) {
            int cmp = compare(key, p.key);
            if (cmp < 0) {//如果要找的key小于当前节点就往左边找，
                if (p.left != null)
                    p = p.left;
                else
                    return p;//找到左节点都没有左节点了都没找到，那么该节点就是大于key的最小左节点
            } else if (cmp > 0) {
                if (p.right != null) {
                    p = p.right;
                } else {
                    Entry<K,V> parent = p.parent;
                    Entry<K,V> ch = p;
                    //能够进入这个循环说明当前节点没有右子节点，并且当前节点是父节点的右子节点，并且当前节点还小于查询的节点
                    //这样就只能找它的父节点来看，一直往上找，直到找到某个节点是其父节点的左节点，那个左节点是大于key的 最小节点
                    //如果往上找，父节点一直都是其父节点的右节点，直到找到root节点，然后返回null。说明没有比key大的节点
                    while (parent != null && ch == parent.right) {
                        ch = parent;
                        parent = parent.parent;
                    }
                    return parent;
                }
            } else
                return p;
        }
        return null;
    }

    /**
     * 返回小于等于key的最大的节点
     */
    final Entry<K,V> getFloorEntry(K key) {
        Entry<K,V> p = root;
        while (p != null) {
            int cmp = compare(key, p.key);
            if (cmp > 0) {//key大于当前节点就往右边继续找
                if (p.right != null)
                    p = p.right;
                else
                    return p;//如果该节点没有右节点，并且此时key还大于当前节点，说明这个节点就是小于key的最大节点了
            } else if (cmp < 0) {//如果key小于当前节点
                if (p.left != null) {//如果还有左节点，就继续往左边找
                    p = p.left;
                } else {
                    //如果当前节点没有左节点了，那么只有两种情况，
                    //一种是当前节点是整个树的最小节点，那说明真个树都没有小于key的节点了，那么就找到root节点，返回root的父节点null
                    //另外一种的就是当前节点不是整个树的 最小节点，那么循环获取父节点的时候，如果某个节点是父节点的右子节点，说明这个该节点的 父节点就是要找的小于key的最大节点
                    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;//等于key的节点

        }
        return null;
    }

    /**
     * 返回大于key的最小节点，如果没有就返回null。和getCeilingEntry一样，只是没有等于
     */
    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;
    }

    /**
     * 返回小于key的最大节点，没有就返回null。和getFloorEntry一样，只是没有等于
     */
    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;
    }

    /**
     * 将键值对放入TreeMap中
     */
    public V put(K key, V value) {
        Entry<K,V> t = root;
        if (t == null) {//如果根节点为null，则将该节点设置为根节点
            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) {//如果有比较器，
            do {//找到key对应的节点，直接将新的值赋给key
                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 {//如果没有比较器，通过key的自身的比较性来进行比较
            if (key == null)
                throw new NullPointerException();
            @SuppressWarnings("unchecked")
                Comparable<? super K> k = (Comparable<? super K>) key;
            do {//找到key对应的节点，直接将新的值赋给key
                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);
        }//如果没有找到key对应的节点，就创建一个新的节点，加在父节点下
        Entry<K,V> e = new Entry<>(key, value, parent);
        if (cmp < 0)
            parent.left = e;
        else
            parent.right = e;
        fixAfterInsertion(e);//加入新的节点后，要对树重新进行整理，来满足红黑树的要求
        size++;
        modCount++;
        return null;
    }

    /**
     * 删除节点
     */
    public V remove(Object key) {
        Entry<K,V> p = getEntry(key);
        if (p == null)
            return null;

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

    /**
     * 清空整个TreeMap
     */
    public void clear() {
        modCount++;
        size = 0;
        root = null;
    }

    /**
     * 浅克隆
     */
    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 返回第一个节点
     */
    public Map.Entry<K,V> firstEntry() {
        return exportEntry(getFirstEntry());
    }

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

    /**
     * @since 1.6 返回并删除第一个节点
     */
    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 返回并删除最后一个节点
     */
    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;
    }

    /**
     * 返回小于key的最大节点
     * @since 1.6
     */
    public Map.Entry<K,V> lowerEntry(K key) {
        return exportEntry(getLowerEntry(key));
    }

    /**
     * 返回小于key的最大的 key
     * @since 1.6
     */
    public K lowerKey(K key) {
        return keyOrNull(getLowerEntry(key));
    }

    /**
     * 返回小于等于key的最大节点
     */
    public Map.Entry<K,V> floorEntry(K key) {
        return exportEntry(getFloorEntry(key));
    }

    /**
     * 返回小于等于key的最大key
     * @since 1.6
     */
    public K floorKey(K key) {
        return keyOrNull(getFloorEntry(key));
    }

    /**
     * 返回大于等于key的最小节点
     * @since 1.6
     */
    public Map.Entry<K,V> ceilingEntry(K key) {
        return exportEntry(getCeilingEntry(key));
    }

    /**
     * 返回大于等于key的最小key
     * @since 1.6
     */
    public K ceilingKey(K key) {
        return keyOrNull(getCeilingEntry(key));
    }

    /**
     * 返回大于key的最小节点
     * @since 1.6
     */
    public Map.Entry<K,V> higherEntry(K key) {
        return exportEntry(getHigherEntry(key));
    }

    /**
     * 返回大于key的最小key
     * @since 1.6
     */
    public K higherKey(K key) {
        return keyOrNull(getHigherEntry(key));
    }

    // Views

    /**
     * 在第一次请求此视图时，创建这些视图。视图是无状态的，因此没有理由创建多个视图。
     */
    private transient EntrySet entrySet;
    private transient KeySet<K> navigableKeySet;
    private transient NavigableMap<K,V> descendingMap;

    /**
     * 返回key的Set集合，Set中的key按照升序排列
     * Set集合的修改会反馈到TreeMap中，同样TreeMap的修改也反馈到Set集合上
     */
    public Set<K> keySet() {
        return navigableKeySet();
    }

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

    /**
     * 返回key的Set集合，Set中的key按照降序排列
     * NavigableSet集合的修改会反馈到TreeMap中，同样TreeMap的修改也反馈到NavigableSet集合上
     * @since 1.6
     */
    public NavigableSet<K> descendingKeySet() {
        return descendingMap().navigableKeySet();
    }

    /**
     * 返回TreeMap中所有的value，不会对value去重
     * value集合的修改会反馈到TreeMap中，同样TreeMap的修改也反馈到value集合上
     */
    public Collection<V> values() {
        Collection<V> vs = values;
        if (vs == null) {
            vs = new Values();
            values = vs;
        }
        return vs;
    }

    /**
     * 返回键值对的集合
     */
    public Set<Map.Entry<K,V>> entrySet() {
        EntrySet es = entrySet;
        return (es != null) ? es : (entrySet = new EntrySet());
    }

    /**
     * 返回TreeMap的倒序Map
     * 先看有没有缓存好的descendingMap，如果没有就创建一个DescendingSubMap返回并缓存
     * @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));
    }

    /**
     * 返回子视图，升序排列，对视图的 修改和对源map的修改都会相互影响对方
     */
    public NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
                                    K toKey,   boolean toInclusive) {
        return new AscendingSubMap<>(this,
                                     false, fromKey, fromInclusive,
                                     false, toKey,   toInclusive);
    }

    /**
     * 返回TreeMap中键小于toKey的所有节点的视图，inclusive表示是否可以等于tokey
     */
    public NavigableMap<K,V> headMap(K toKey, boolean inclusive) {
        return new AscendingSubMap<>(this,
                                     true,  null,  true,
                                     false, toKey, inclusive);
    }

    /**
     * 返回TreeMap中键大于fromKey的所有节点的视图，inclusive表示是否可以等于fromKey
     */
    public NavigableMap<K,V> tailMap(K fromKey, boolean inclusive) {
        return new AscendingSubMap<>(this,
                                     false, fromKey, inclusive,
                                     true,  null,    true);
    }

    /**
     * 返回TreeMap的一个子视图，key大于等于formKey小于toKey
     */
    public SortedMap<K,V> subMap(K fromKey, K toKey) {
        return subMap(fromKey, true, toKey, false);
    }

    /**
     * 返回小于key的节点视图
     */
    public SortedMap<K,V> headMap(K toKey) {
        return headMap(toKey, false);
    }

    /**
     * 返回大于等于key的节点视图
     */
    public SortedMap<K,V> tailMap(K fromKey) {
        return tailMap(fromKey, true);
    }

    /**
     * 替换key和value都匹配的value值
     */
    @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;
    }

    /**
     * 替换key的value，并返回旧的value
     */
    @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;
    }

    /**
     * 遍历TreeMap中的节点并做相关的操作
     */
    @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();
            }
        }
    }

    /**
     * 替换括号中满足条件的键值对的值,新的值通过括号中的表达式计算得到
     */
    @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();
            }
        }
    }

    // TreeMap的值的视图

    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);
        }
    }

    /**
     * TreeMap的键值对视图
     */
    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);
        }
    }

    /**
     * 键迭代器
     */

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

    /**
     * 反向键迭代器
     * @return
     */
    Iterator<K> descendingKeyIterator() {
        return new DescendingKeyIterator(getLastEntry());
    }
    //TreeMap中键的视图
    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);
        }
    }

    /**
     * 键值对迭代器
     */
    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 一些小工具

    /**
     * 比较两个对象，如果有比较器就用比较器，没有就用两个对象的自然排序进行比较
     */
    @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);
    }

    /**
     * 比较两个两个对象是否相等
     */
    static final boolean valEquals(Object o1, Object o2) {
        return (o1==null ? o2==null : o1.equals(o2));
    }

    /**
     * 返回entry的 不可变对象
     */
    static <K,V> Map.Entry<K,V> exportEntry(TreeMap.Entry<K,V> e) {
        return (e == null) ? null :
            new AbstractMap.SimpleImmutableEntry<>(e);
    }

    /**
     * 返回键值对的键
     */
    static <K,V> K keyOrNull(TreeMap.Entry<K,V> e) {
        return (e == null) ? null : e.key;
    }

    /**
     * 返回节点的key，节点为null则报错
     */
    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;

        /**
         * fromStart 是否从第一个节点开始
         * lo    开始节点
         * loInclusive 是否包含lo节点
         *
         * toEnd 是否到最后一个节点
         * hi    结束节点
         * hiInclusive 是否包含hi节点
         */
        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
        //判断key是否小于NavigableSubMap的lo
        final boolean tooLow(Object key) {
            if (!fromStart) {
                int c = m.compare(key, lo);
                if (c < 0 || (c == 0 && !loInclusive))
                    return true;
            }
            return false;
        }
        //判断key是否大于NavigableSubMap的hi
        final boolean tooHigh(Object key) {
            if (!toEnd) {
                int c = m.compare(key, hi);
                if (c > 0 || (c == 0 && !hiInclusive))
                    return true;
            }
            return false;
        }
        //判断key是否在NavigableSubMap的范围之间
        final boolean inRange(Object key) {
            return !tooLow(key) && !tooHigh(key);
        }
        //判断key是否在视图范围之内
        final boolean inClosedRange(Object key) {
            return (fromStart || m.compare(key, lo) >= 0)
                && (toEnd || m.compare(hi, key) >= 0);
        }
        //判断key是否在视图范围之内
        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
         * 视图迭代器
         */
        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;
            }

        }
        //视图Entry迭代器
        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();
            }
        }
        //逆序视图entry迭代器
        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();
            }
        }

        // 简单实现Spliterator来作为KeySpliterator的备份
        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();
            }
        }
        //逆序视图key迭代器
        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;
            }
        }
    }

    /**
     * 正序视图
     */
    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); }
    }

    /**
     * 逆序视图
     */
    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); }
    }

    /**
     * 视图，
     */
    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(); }
    }

    // 表示红黑树接电点的颜色

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

    /**
     * 节点类，用来存储TreeMap每个节点的信息
     */
    static final class Entry<K,V> implements Map.Entry<K,V> {
        K key;//键
        V value;//值
        Entry<K,V> left;//左子节点
        Entry<K,V> right;//右子节点
        Entry<K,V> parent;//父节点
        boolean color = BLACK;//节点颜色，默认为黑色

        /**
         * 构造方法
         */
        Entry(K key, V value, Entry<K,V> parent) {
            this.key = key;
            this.value = value;
            this.parent = parent;
        }

        /**
         * 返回key
         */
        public K getKey() {
            return key;
        }

        /**
         * 返回value
         */
        public V getValue() {
            return value;
        }

        /**
         * 设置value
         */
        public V setValue(V value) {
            V oldValue = this.value;
            this.value = value;
            return oldValue;
        }

        /**
         * 判断节点和对象是否相等
         */
        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());
        }

        /**
         * 返回节点的hashcode值，是节点的key和value的hashcode然后进行与运算
         */
        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;
        }
    }

    /**
     * 获取第一个节点，也是最小的节点
     */
    final Entry<K,V> getFirstEntry() {
        Entry<K,V> p = root;
        if (p != null)
            while (p.left != null)
                p = p.left;
        return p;
    }

    /**
     * 获取最后一个节点，也是最大节点
     */
    final Entry<K,V> getLastEntry() {
        Entry<K,V> p = root;
        if (p != null)
            while (p.right != null)
                p = p.right;
        return p;
    }

    /**
     * 返回节点t的后继节点，也就是大于t节点的最小节点
     */
    static <K,V> TreeMap.Entry<K,V> successor(Entry<K,V> t) {
        if (t == null)
            return null;
        else if (t.right != null) {//如果该节点有右子节点，就找右子节点的 左子节点，一直往下找
            Entry<K,V> p = t.right;
            while (p.left != null)
                p = p.left;
            return p;
        } else {//如果该节点没有右子节点，就向上找
            Entry<K,V> p = t.parent;
            Entry<K,V> ch = t;
            while (p != null && ch == p.right) {//如果当前节点是父节点的右子节点，就一直往上找，直到找到一个节点是其父节点的左子节点，那个父节点就是要找的节点
                ch = p;
                p = p.parent;
            }
            return p;
        }
    }

    /**
     * 返回小于t的最大节点。
     */
    static <K,V> Entry<K,V> predecessor(Entry<K,V> t) {
        if (t == null)
            return null;
        else if (t.left != null) {//如果该节点寸在左子节点，那么要找的节点就是左子节点的右子节点（一直找到最后一个）
            Entry<K,V> p = t.left;
            while (p.right != null)
                p = p.right;
            return p;
        } else {//如果该节点没有左子节点，就一直往上找，直到找到一个节点是其父节点的右子节点，那个父节点就是要找的节点
            Entry<K,V> p = t.parent;
            Entry<K,V> ch = t;
            while (p != null && ch == p.left) {
                ch = p;
                p = p.parent;
            }
            return p;
        }
    }

    //返回节点的颜色
    private static <K,V> boolean colorOf(Entry<K,V> p) {
        return (p == null ? BLACK : p.color);
    }
    //返回节点的父节点
    private static <K,V> Entry<K,V> parentOf(Entry<K,V> p) {
        return (p == null ? null: p.parent);
    }
    //设置节点的颜色
    private static <K,V> void setColor(Entry<K,V> p, boolean c) {
        if (p != null)
            p.color = c;
    }
    //返回节点的左子节点
    private static <K,V> Entry<K,V> leftOf(Entry<K,V> p) {
        return (p == null) ? null: p.left;
    }
    //返回节点的右子节点
    private static <K,V> Entry<K,V> rightOf(Entry<K,V> p) {
        return (p == null) ? null: p.right;
    }

    /** From CLR 左旋的过程是将p的右子树绕p逆时针旋转，使得p的右子树成为p的父亲，同时修改相关节点的引用。旋转之后，二叉查找树的属性仍然满足。*/
    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 右旋的过程是将p的左子树绕p顺时针旋转，使得p的左子树成为p的父亲，同时修改相关节点的引用。旋转之后，二叉查找树的属性仍然满足。 */
    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 在加入新的节点后，树的平衡有可能被破坏，所以需要对TreeMap的树结构进行修复*/
    private void fixAfterInsertion(Entry<K,V> x) {
        x.color = RED;//先将当前接节点的颜色设置为红

        while (x != null && x != root && x.parent.color == RED) {//如果父节点是黑色的，那么无需进行任何操作。
            if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {//如果父节点是祖节点的左子节点
                Entry<K,V> y = rightOf(parentOf(parentOf(x)));//祖节点的右子节点，就称为当前节点的叔节点
                if (colorOf(y) == RED) {//如果叔节点的颜色为red，则祖节点肯定为黑色。这样直接将父节点和叔节点都设置为黑色，祖节点设置为红色
                    setColor(parentOf(x), BLACK);
                    setColor(y, BLACK);
                    setColor(parentOf(parentOf(x)), RED);
                    x = parentOf(parentOf(x));//以祖节点为基准点继续上述操作
                } else {//如果叔节点为黑色
                    if (x == rightOf(parentOf(x))) {//如果当前节点是父节点的右子节点，以父节点为基准点，然后对父节点进行左旋。
                        x = parentOf(x);
                        rotateLeft(x);
                    }
                    setColor(parentOf(x), BLACK);//将基准节点的父节点变黑，祖节点变红，对祖节点进行右旋操作
                    setColor(parentOf(parentOf(x)), RED);
                    rotateRight(parentOf(parentOf(x)));
                }
            } else {//如果父节点是祖节点的右子节点
                Entry<K,V> y = leftOf(parentOf(parentOf(x)));
                if (colorOf(y) == RED) {//如果叔节点为红色，就将叔节点和父节点都设置为黑色，祖节点设置为红色。再以祖节点作为基准点继续上述操作
                    setColor(parentOf(x), BLACK);
                    setColor(y, BLACK);
                    setColor(parentOf(parentOf(x)), RED);
                    x = parentOf(parentOf(x));
                } else {//如果叔节点是黑色
                    if (x == leftOf(parentOf(x))) {//如果当前节点是父节点的左子节点，就以父节点为基准节点进行右旋操作。
                        x = parentOf(x);
                        rotateRight(x);
                    }
                    setColor(parentOf(x), BLACK);//将基准点的父节点设置为黑色，祖节点设置为红色。然后对基准点的祖节点进行左旋操作
                    setColor(parentOf(parentOf(x)), RED);
                    rotateLeft(parentOf(parentOf(x)));
                }
            }
        }
        root.color = BLACK;//将根节点设置为黑色
    }

    /**
     * 删除节点并重新平衡整棵树，使它符合红黑树
     */
    private void deleteEntry(Entry<K,V> p) {
        modCount++;
        size--;

        //将p的后继节点的key和value赋值给p然后将p指向p的后继节点
        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.
        //开始修正替代节点，如果它存在
        Entry<K,V> replacement = (p.left != null ? p.left : p.right);

        if (replacement != null) {//如果替代节点存在
            // Link replacement to parent
            replacement.parent = p.parent;
            if (p.parent == null)//将p节点的父节点设置为replacement的父节点，如果p节点的父节点不存在，则将replacement设置为根节点
                root = replacement;
            else if (p == p.parent.left)//如果p节点的父节点存在，就将replacement替换掉
                p.parent.left  = replacement;
            else
                p.parent.right = replacement;

            // Null out links so they are OK to use by fixAfterDeletion.
            //将p节点和其他的节点之间断开联系
            p.left = p.right = p.parent = null;

            // Fix replacement
            if (p.color == BLACK)//如果p节点的颜色是黑色，就需要对树结构进行调整
                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 删除节点后将树修复为红黑树结构*/
    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;

    /**
     * 从流中读取对象
     */
    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());
        }
    }

    /**
     * 将对象写入流中
     */
    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;
    }

}

二、TreeMap的特点

　　1、存入TreeMap的键值对的key是要能自然排序的（实现了Comparable接口），否则就要自定义一个比较器Comparator作为参数传入构造函数。

　　2、TreeMap是以红黑树将数据组织在一起，在添加或者删除节点的时候有可能将红黑树的结构破坏了，所以需要判断是否对红黑树进行修复。

　　3、由于底层是红黑树结构，所以TreeMap的基本操作 containsKey、get、put 和 remove 的时间复杂度是 log(n) 。

　　4、由于TreeMap实现了NavigableMap，所以TreeMap有一系列的导航方法。

三、比较器Comparator和实现Comparable接口

　　　TreeMap中的键值对key要么是可比较的，要么就是TreeMap中有比较器，否则无法加入TreeMap中。

　　　1、创建比较器需要实现Comparator接口，然后实现其compare方法。使用比较器的时候只需要创建一个比较器实例然后传入TreeMap的构造器

　　　2、创建一个类实现Comparable接口，然后实现compareTo方法，是对象可比较

　　　3、如果key本身具有自然比较性，同时TreeMap也有比较器那么用比较器进行比较。

　　　4、如果是通过key的自身排序则key不能为null，如果是通过自定义比较器，那么就看自己定义比较器的逻辑了。

//自定义比较器
public class MyComparator implements Comparator<MyEntity> {

    @Override
    public int compare(MyEntity e1, MyEntity e2) {

        int f = e1 == null ? (e2 == null ? 0 : -1) : (e2 == null ? 1 : 2);

        if(f == 2){
            if(e1.getValue() > e2.getValue()){
                return 1;
            }else if(e1.getValue() < e2.getValue()){
                return -1;
            }else{
                return 0;
            }
        }
        return f;
    }

}

　　　　...

//让对象可比较
public class MyEntity implements Comparable<MyEntity>{

    private String name;

    private int value;

    public MyEntity(String name, int value) {
        super();
        this.name = name;
        this.value = value;
    }

    public String getName() {
        return name;
    }

    public void setName(String name) {
        this.name = name;
    }

    public int getValue() {
        return value;
    }

    public void setValue(int value) {
        this.value = value;
    }

    @Override
    public String toString() {
        return "MyEntity [name=" + name + ", value=" + value + "]";
    }

    @Override
    public int compareTo(MyEntity e) {
        if(value > e.getValue()){
            return 1;
        }else if(value < e.getValue()){
            return -1;
        }else{
            return 0;
        }
    }
}