简述
何为TreeMap？
TreeMap是一个二叉排序树构成的map。
TreeMap怎么实现二叉树的平衡？
红黑树
综上所属TreeMap是一个map + 红黑树的实现。
源码分析
类图
image.png
根据类图可知TreeMap继承AbstractMap和实现了NavigableMap。通过继承AbstractMap来共用父类的非私有方法，便于维护。通过实现了NavigableMap接口来提供一些便利的查询操作。（这是顺序结构通常需要实现的接口）
数据结构
/**
* 比较器
*/
private final Comparator<? super K> comparator;
/**
* 根节点
*/
private transient Entry<K,V> root;
/**
* The number of entries in the tree
*/
private transient int size = 0;
/**
* 树节点修改次数
*/
private transient int modCount = 0;
节点的数据结构
static final class Entry<K,V> implements Map.Entry<K,V> {
K key;
V value;
Entry<K,V> left;//左节点
Entry<K,V> right;//右节点
Entry<K,V> parent;//父节点
boolean color = BLACK;//颜色标记
}
基本操作
put
public V put(K key, V value) {
Entry<K,V> t = root;
//树为空
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;
//有默认比较器
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);
}
//无默认比较器
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;
//变树，为了保证平衡
fixAfterInsertion(e);
size++;
modCount++;
return null;
}
//插入后维持平衡
private void fixAfterInsertion(Entry<K,V> x) {
// 插入的节点为红色节点
x.color = RED;
while (x != null && x != root && x.parent.color == RED) {
//当前节点为左节点
if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {
Entry<K,V> y = rightOf(parentOf(parentOf(x)));
//叔叔节点是红色
if (colorOf(y) == RED) {
setColor(parentOf(x), BLACK);
setColor(y, BLACK);
setColor(parentOf(parentOf(x)), RED);
x = parentOf(parentOf(x));
} else {//叔叔节点是黑色
if (x == rightOf(parentOf(x))) {
x = parentOf(x);
//左旋
rotateLeft(x);
}
setColor(parentOf(x), BLACK);
setColor(parentOf(parentOf(x)), RED);
//右旋转
rotateRight(parentOf(parentOf(x)));
}
} else {
Entry<K,V> y = leftOf(parentOf(parentOf(x)));
//叔叔节点是红色
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);
//右旋转
rotateRight(x);
}
setColor(parentOf(x), BLACK);
setColor(parentOf(parentOf(x)), RED);
//左旋转
rotateLeft(parentOf(parentOf(x)));
}
}
}
root.color = BLACK;
}
- 先通过查找树的方式找到合适的位置把节点放入
- 新插入的节点可能导致树不平衡
- 根据红黑树的方式变色、左旋、右旋保证树的平衡
remove
public V remove(Object key) {
Entry<K,V> p = getEntry(key);
if (p == null)
return null;
V oldValue = p.value;
deleteEntry(p);
return oldValue;
}
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;
}
private void deleteEntry(Entry<K,V> p) {
modCount++;
size--;
// If strictly internal, copy successor's element to p and then make p
// 如果左右都非空，则找到继承者来代替它的位置
if (p.left != null && p.right != null) {
Entry<K,V> s = successor(p);
p.key = s.key;
p.value = s.value;
p = s;
} // p has 2 children
// Start fixup at replacement node, if it exists.
Entry<K,V> replacement = (p.left != null ? p.left : p.right);
if (replacement != null) {
// Link replacement to parent
replacement.parent = p.parent;
if (p.parent == null)
root = replacement;
else if (p == p.parent.left)
p.parent.left = replacement;
else
p.parent.right = replacement;
// Null out links so they are OK to use by fixAfterDeletion.
p.left = p.right = p.parent = null;
// Fix replacement
if (p.color == BLACK)
fixAfterDeletion(replacement);
} else if (p.parent == null) { // return if we are the only node.
root = null;
} else { // No children. Use self as phantom replacement and unlink.
if (p.color == BLACK)
fixAfterDeletion(p);
if (p.parent != null) {
if (p == p.parent.left)
p.parent.left = null;
else if (p == p.parent.right)
p.parent.right = null;
p.parent = null;
}
}
}
/** From CLR */
private void fixAfterDeletion(Entry<K,V> x) {
while (x != root && colorOf(x) == BLACK) {
if (x == leftOf(parentOf(x))) {
Entry<K,V> sib = rightOf(parentOf(x));
if (colorOf(sib) == RED) {
setColor(sib, BLACK);
setColor(parentOf(x), RED);
rotateLeft(parentOf(x));
sib = rightOf(parentOf(x));
}
if (colorOf(leftOf(sib)) == BLACK &&
colorOf(rightOf(sib)) == BLACK) {
setColor(sib, RED);
x = parentOf(x);
} else {
if (colorOf(rightOf(sib)) == BLACK) {
setColor(leftOf(sib), BLACK);
setColor(sib, RED);
rotateRight(sib);
sib = rightOf(parentOf(x));
}
setColor(sib, colorOf(parentOf(x)));
setColor(parentOf(x), BLACK);
setColor(rightOf(sib), BLACK);
rotateLeft(parentOf(x));
x = root;
}
} else { // symmetric
Entry<K,V> sib = leftOf(parentOf(x));
if (colorOf(sib) == RED) {
setColor(sib, BLACK);
setColor(parentOf(x), RED);
rotateRight(parentOf(x));
sib = leftOf(parentOf(x));
}
if (colorOf(rightOf(sib)) == BLACK &&
colorOf(leftOf(sib)) == BLACK) {
setColor(sib, RED);
x = parentOf(x);
} else {
if (colorOf(leftOf(sib)) == BLACK) {
setColor(rightOf(sib), BLACK);
setColor(sib, RED);
rotateLeft(sib);
sib = leftOf(parentOf(x));
}
setColor(sib, colorOf(parentOf(x)));
setColor(parentOf(x), BLACK);
setColor(leftOf(sib), BLACK);
rotateRight(parentOf(x));
x = root;
}
}
}
setColor(x, BLACK);
}
- 找到需要删除的节点
- 找到它的字节点中能够替换它的节点
- 变树保持平衡
常见问题
树的结构有何优点？
与线性表对比，线性表的平均查找次数=n／2，平衡二叉树平均查找次数=logn。线性表查找只有在极小的数据量下才会有优势。
与hash对比，在查看速度看树可能比不上hash结构。但是二叉树的结构为范围检索提供了方便。
有几种平衡树
二叉树：AVL树、红黑树
n叉树：B-树、B+树
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