0. TreeMap是什么
- 基于红黑树的
NavigableMap实现，排序的依据是创建时指定的Comparator(如果有指定)或者Key的自然顺序(如果key实现了Comparable)。 - 保证了
log(n)时间的添加、删除、查询操作。 - 非同步
1. 实现的本质
红黑树
节点的结构：
包含3个引用：分别指向左子、右子、父节点，以及一个颜色域。
static final class Entry implements Map.Entry {
K key;
V value;
Entry left;
Entry right;
Entry parent;
boolean color = BLACK;
/**
* Make a new cell with given key, value, and parent, and with
* {@code null} child links, and BLACK color.
*/
//新建节点为黑色
Entry(K key, V value, Entry parent) {
this.key = key;
this.value = value;
this.parent = parent;
}
}
2. 常用api解析
2.1 构造函数
//无参
public TreeMap()
//指定comparator
public TreeMap(Comparator comparator)
//参数为Map集合
public TreeMap(Map m)
public TreeMap(SortedMap m)
2.2 put方法
先将节点放入正确位置，此时可能违反红黑树的性质，需要进行调整。
/**
* Associates the specified value with the specified key in this map.
* If the map previously contained a mapping for the key, the old
* value is replaced.
*
* @param key key with which the specified value is to be associated
* @param value value to be associated with the specified key
*
* @return the previous value associated with {@code key}, or
* {@code null} if there was no mapping for {@code key}.
* (A {@code null} return can also indicate that the map
* previously associated {@code null} with {@code key}.)
* @throws ClassCastException if the specified key cannot be compared
* with the keys currently in the map
* @throws NullPointerException if the specified key is null
* and this map uses natural ordering, or its comparator
* does not permit null keys
*/
public V put(K key, V value) {
Entry t = root;
//建立根节点
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 parent;
// split comparator and comparable paths
Comparator cpr = comparator;
//如果指定了comparator，则使用comparator比较
if (cpr != null) {
do {
parent = t;
cmp = cpr.compare(key, t.key);
//小的左转，大的右转
if (cmp < 0)
t = t.left;
else if (cmp > 0)
t = t.right;
else
//找到相当的key时
return t.setValue(value);
} while (t != null);
//循环完成时，t指向要插入的位置，parent指向父节点
}
//未指定comparator时
else {
//key不能为null
if (key == null)
throw new NullPointerException();
@SuppressWarnings("unchecked")
Comparable k = (Comparable) key;
do {
//和上面一样的比较流程
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);
}
//此时t指向要插入的位置，parent指向父节点
Entry e = new Entry<>(key, value, parent);
if (cmp < 0)
parent.left = e;
else
parent.right = e;
//调整
fixAfterInsertion(e);
size++;
modCount++;
return null;
}
/** From CLR */
//x是新插入的节点
private void fixAfterInsertion(Entry x) {
x.color = RED;
//当x的父节点是红色时
while (x != null && x != root && x.parent.color == RED) {
//x的父节点是祖父节点的左孩子
if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {
//y是x的叔叔节点
Entry y = rightOf(parentOf(parentOf(x)));
//如果叔叔节点是红色
if (colorOf(y) == RED) {
//父节点和叔叔节点变黑，祖父节点变红
setColor(parentOf(x), BLACK);
setColor(y, BLACK);
setColor(parentOf(parentOf(x)), RED);
//x指向祖父节点继续循环
x = parentOf(parentOf(x));
//如果叔叔节点是黑色
} else {
//如果x是父节点的右孩子
if (x == rightOf(parentOf(x))) {
//先将父节点左旋
x = parentOf(x);
rotateLeft(x);
}
//左旋之后，x变为左孩子
//x的父节点变黑，祖父节点变红，然后祖父节点右旋
setColor(parentOf(x), BLACK);
setColor(parentOf(parentOf(x)), RED);
rotateRight(parentOf(parentOf(x)));
}
//x的父节点是祖父节点的右孩子，与上面的过程互为镜像
} else {
//y是x的叔叔节点
Entry y = leftOf(parentOf(parentOf(x)));
//如果叔叔节点是红色
if (colorOf(y) == RED) {
//父节点和叔叔节点变黑，祖父节点变红
setColor(parentOf(x), BLACK);
setColor(y, BLACK);
setColor(parentOf(parentOf(x)), RED);
//x指向祖父节点，继续循环
x = parentOf(parentOf(x));
//如果叔叔节点是黑色
} else {
//如果x是父节点的左孩子
if (x == leftOf(parentOf(x))) {
//x指向父节点，然后右旋，右旋后x变为右孩子
x = parentOf(x);
rotateRight(x);
}
//父节点变黑，祖父节点变红，祖父节点左旋
setColor(parentOf(x), BLACK);
setColor(parentOf(parentOf(x)), RED);
rotateLeft(parentOf(parentOf(x)));
}
}
}
//根节点变黑
root.color = BLACK;
}
2.3 get方法
根据key查找value的方法和普通的BST查找节点的方法一样。
/**
* Returns the value to which the specified key is mapped,
* or {@code null} if this map contains no mapping for the key.
*
* More formally, if this map contains a mapping from a key
* {@code k} to a value {@code v} such that {@code key} compares
* equal to {@code k} according to the map's ordering, then this
* method returns {@code v}; otherwise it returns {@code null}.
* (There can be at most one such mapping.)
*
*
A return value of {@code null} does not necessarily
* indicate that the map contains no mapping for the key; it's also
* possible that the map explicitly maps the key to {@code null}.
* The {@link #containsKey containsKey} operation may be used to
* distinguish these two cases.
*
* @throws ClassCastException if the specified key cannot be compared
* with the keys currently in the map
* @throws NullPointerException if the specified key is null
* and this map uses natural ordering, or its comparator
* does not permit null keys
*/
public V get(Object key) {
Entry p = getEntry(key);
return (p==null ? null : p.value);
}
/**
* Returns this map's entry for the given key, or {@code null} if the map
* does not contain an entry for the key.
*
* @return this map's entry for the given key, or {@code null} if the map
* does not contain an entry for the key
* @throws ClassCastException if the specified key cannot be compared
* with the keys currently in the map
* @throws NullPointerException if the specified key is null
* and this map uses natural ordering, or its comparator
* does not permit null keys
*/
final Entry 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 k = (Comparable) key;
Entry 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;
}
2.4 remove方法
/**
* Removes the mapping for this key from this TreeMap if present.
*
* @param key key for which mapping should be removed
* @return the previous value associated with {@code key}, or
* {@code null} if there was no mapping for {@code key}.
* (A {@code null} return can also indicate that the map
* previously associated {@code null} with {@code key}.)
* @throws ClassCastException if the specified key cannot be compared
* with the keys currently in the map
* @throws NullPointerException if the specified key is null
* and this map uses natural ordering, or its comparator
* does not permit null keys
*/
public V remove(Object key) {
//找到正确的节点
Entry p = getEntry(key);
if (p == null)
return null;
V oldValue = p.value;
//删除节点p
deleteEntry(p);
return oldValue;
}
/**
* Delete node p, and then rebalance the tree.
*/
private void deleteEntry(Entry p) {
modCount++;
size--;
// If strictly internal, copy successor's element to p and then make p
// point to successor.
//如果p的左右孩子都不为空
if (p.left != null && p.right != null) {
//s指向p的后继节点
Entry s = successor(p);
//后继节点的值放到当前节点
p.key = s.key;
p.value = s.value;
//然后将p指向后继节点
p = s;
} // p has 2 children
// Start fixup at replacement node, if it exists.
//此时p是真正要删除的节点，并且p只有左子或右子或都为空
Entry replacement = (p.left != null ? p.left : p.right);
//只有左子或右子时，左子或右子取代当前节点
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
//如果删除的是红节点，不影响红黑树的性质，如果是黑节点，则需要进行调整
if (p.color == BLACK)
fixAfterDeletion(replacement);
//如果p是根节点
} else if (p.parent == null) { // return if we are the only node.
root = null;
//如果p没有子节点
} 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;
}
}
}
/**
* Returns the successor of the specified Entry, or null if no such.
*/
//查找节点t的后继节点
static TreeMap.Entry successor(Entry t) {
if (t == null)
return null;
//如果t的右子不为空，右子向左走到底
else if (t.right != null) {
Entry p = t.right;
while (p.left != null)
p = p.left;
return p;
//如果t的右子为空，向上走，到某一个节点是其父节点的左子，该父节点为t的后继
} else {
Entry p = t.parent;
Entry ch = t;
while (p != null && ch == p.right) {
ch = p;
p = p.parent;
}
return p;
}
}
/** From CLR */
private void fixAfterDeletion(Entry x) {
//如果x是黑色，则进行操作
// x节点可能是被删除节点的子节点(可能为红色)，或者其本身(如果它没有子节点)
while (x != root && colorOf(x) == BLACK) {
//如果x是左孩子
if (x == leftOf(parentOf(x))) {
//sib是x的兄弟节点
Entry sib = rightOf(parentOf(x));
//如果兄弟节点是红色
if (colorOf(sib) == RED) {
//交换兄弟节点和父节点的颜色，父节点左旋
setColor(sib, BLACK);
setColor(parentOf(x), RED);
rotateLeft(parentOf(x));
//sib指向新的兄弟节点(必定是黑色)
sib = rightOf(parentOf(x));
}
//如果sib的两个孩子都是黑色
if (colorOf(leftOf(sib)) == BLACK &&
colorOf(rightOf(sib)) == BLACK) {
//sib设为红色，x指向父节点，继续循环
setColor(sib, RED);
x = parentOf(x);
} else {
//如果兄弟节点是左红右黑
if (colorOf(rightOf(sib)) == BLACK) {
//兄弟节点和左孩子颜色互换，然后右旋
setColor(leftOf(sib), BLACK);
setColor(sib, RED);
rotateRight(sib);
//sib指向新的兄弟节点
sib = rightOf(parentOf(x));
}
//此时兄弟节点是左黑右红
//则交换x的父节点和兄弟节点颜色，兄弟右节点设为黑色，父节点左旋
setColor(sib, colorOf(parentOf(x)));
setColor(parentOf(x), BLACK);
setColor(rightOf(sib), BLACK);
rotateLeft(parentOf(x));
//结束循环
x = root;
}
//如果x是右孩子，与if分支对称
} else { // symmetric
//sib是x的兄弟节点
Entry sib = leftOf(parentOf(x));
//如果兄弟节点是红色
if (colorOf(sib) == RED) {
//交换兄弟节点和父节点颜色，父节点右旋
setColor(sib, BLACK);
setColor(parentOf(x), RED);
rotateRight(parentOf(x));
//sib指向新的兄弟节点
sib = leftOf(parentOf(x));
}
//此时sib必定为黑色
//如果sib左右孩子均为黑色
if (colorOf(rightOf(sib)) == BLACK &&
colorOf(leftOf(sib)) == BLACK) {
//将sib设为红色，x指向父节点，继续循环
setColor(sib, RED);
x = parentOf(x);
} else {
//如果兄弟节点的孩子左黑右红
if (colorOf(leftOf(sib)) == BLACK) {
//交换兄弟节点和右孩子颜色，兄弟节点左旋
setColor(rightOf(sib), BLACK);
setColor(sib, RED);
rotateLeft(sib);
//sib指向新的兄弟节点
sib = leftOf(parentOf(x));
}
//此时兄弟节点孩子必定左红右黑
//互换兄弟节点和父节点颜色，兄弟节点左孩子设为黑色，父节点右旋
setColor(sib, colorOf(parentOf(x)));
setColor(parentOf(x), BLACK);
setColor(leftOf(sib), BLACK);
rotateRight(parentOf(x));
//结束循环
x = root;
}
}
}
//如果x是红色，则将x设为黑色即可
setColor(x, BLACK);
}
3. 参考
- TreeMap源码build 1.8.0_121-b13版本
- 二叉树 - 红黑树