TreeMap

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TreeMap使用红黑树存储元素，可以保证元素按照key值的大小进行遍历。

其继承关系如下：

TreeMap实现了Map、SortedMap、NavigableMap、Cloneable、Serializable等接口
SortedMap规定了元素可以按key大小来遍历，定义了获取部分map的方法：

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//key的比较器
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();

NavigableMap是对SortedMap的增强，定义了获取离目标key最近的元素的方法：
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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);

TreeMap只使用到了红黑树，故它的时间复杂度为O(logn) 回顾下红黑树的特性：

  1. 每个节点 红色或者黑色
  2. 根节点是黑色
  3. 每个叶子节点是黑色（这里的叶子节点是空节点）
  4. 若一个节点是红色 则它的叶子节点必须是黑色
  5. 从一个节点到该节点的子孙节点的所有路径上包含相同数目的黑节点

主要属性

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public class TreeMap<K,V>
    extends AbstractMap<K,V>
    implements NavigableMap<K,V>, Cloneable, java.io.Serializable
{
    //比较器
    private final Comparator<? super K> comparator;
    //根节点
    private transient Entry<K,V> root;

    //元素个数
    private transient int size = 0;

    //修改次数
    private transient int modCount = 0;
    ... ...   
}

comparator可以通过构造器传入 或者key实现comparable接口

内部类

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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;
        }
        ... ...
}

构造器

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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) {
    }
}

getObject(Object key)

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public V get(Object key) {
    Entry<K,V> p = getEntry(key);
    return (p==null ? null : p.value);
}
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;
}
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;
}

左旋

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/** 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;
    }
}

右旋

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/** 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;
    }
}

插入元素

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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;
}

插入再平衡

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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;
}

删除元素

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

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

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;
        }
    }
}

删除再平衡

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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);
}

总结

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