TreeMap 红黑树实现

TreeMap 是一个有序的key-value集合，它是通过 红黑树 实现的。

TreeMap 继承于AbstractMap，所以它是一个Map，即一个key-value集合。

TreeMap 实现了NavigableMap，Cloneable和Serializable接口。

TreeMap的基本操作 containsKey、get、put 和 remove 的时间复杂度是 log(n) 。

首先是TreeMap的构造方法：

　　public TreeMap() {
        comparator = null;
    }

    /**
     * Constructs a new, empty tree map, ordered according to the given comparator. 
     */
    public TreeMap(Comparator<? super K> comparator) {
        this.comparator = comparator;
    }

    /**
     * Constructs a new tree map containing the same mappings as the given
     * map, ordered according to the <em>natural ordering</em> of its keys.
     */
    public TreeMap(Map<? extends K, ? extends V> m) {
        comparator = null;
        putAll(m);
    }

    /**
     * Constructs a new tree map containing the same mappings and
     * using the same ordering as the specified sorted map.  This
     * method runs in linear time.
     */
    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) {
        }
    }

TreeMap是基于红黑树实现的，以下是树结点的定义，主要key(键)、value(值)、left(左孩子)、right(右孩子)、parent(父节点)、color(颜色)六个字段，根据key的值进行排序。该内部类比较简单，不做分析。

    static final class Entry<K,V> implements Map.Entry<K,V> {
        K key;
        V value;
        Entry<K,V> left = null;
        Entry<K,V> right = null;
        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;
        }

        ......
　　}

以下是红黑树的插入put和删除deleteEntry操作，以及执行插入删除时需要用到的操作：左旋rotateLeft、右旋rotateRight、插入修正fixAfterInsertion和删除修正fixAfterDeletion。

插入操作，先找到要插入的位置，插入新结点，调用fixAfterInsertion对插入结果进行修正：

    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();
            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;
    }

 fixAfterInsertion操作，保证插入节点之后，仍然是一棵红黑树：

     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;
    }

之中用到了leftRotate和rightRotate操作，这里先介绍这两个操作，在fixAfterDeletion中也会用到：

    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;
        }
    }

    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;
        }
    }

删除操作，先按二叉查找树的方法删除节点，然后调用fixAfterDeletion使得树保持红黑树性质：

    private void deleteEntry(Entry<K, V> p) {
        modCount++;
        size--;
        if (p.left != null && p.right != null) {
            Entry<K, V> s = successor(p);
            p.key = s.key;
            p.value = s.value;
            p = s;
        }

        Entry<K,V> replacement = p.left != null ? p.left : p.right;
        if (replacement != null) {
            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;
            p.left = p.right = p.parent = null;
            if (p.COLOR == BLACK)
                fixAfterDeletion(replacement);
        } else if (p.parent == NULL) {
            root = null;
        } else {
            if (p.color == BLACK)
                fixAfterDeletion(p);
            if (p.parent != null) {
                if (p ==p.parent.left)
                    p.parent.left = null;
                else
                    p.parent.right = null;
                p.parent = null;
            }
        }
    }