AVLTree(平衡二叉树的实现)

平衡二叉树的实现(Java)

任一节点对应的两棵子树的最大高度差为1。查找、插入和删除在平均和最坏情况下的时间复杂度都是O(log n)

基于BST(二叉搜索树)的基础上实现的

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/**
* @author weijie.zeng
* @create 2022-03-29-19:46
*/
public class AVLTree<E> extends BinarySearchTree<E> implements Tree<E>, BinaryTreeInfo {
public AVLTree() {
this(null);
}

public AVLTree(Comparator<E> comparator) {
super(comparator);
}

@Override
protected void afterAdd(Node<E> node) {
while ((node = node.parent) != null) {
if (isBalanced(node)) {
// 更新高度
updateHeight(node);
} else {
// 恢复平衡
rebalance(node);
// 整棵树恢复平衡
break;
}
}
}

@Override
protected void afterRemove(Node<E> node) {
while ((node = node.parent) != null) {
if (isBalanced(node)) {
// 更新高度
updateHeight(node);
} else {
// 恢复平衡
rebalance(node);
}
}
}

@Override
protected Node<E> createNode(E element, Node<E> parent) {
return new AVLNode<>(element, parent);
}

/**
* 恢复平衡
* @param grand 高度最低的那个不平衡节点
*/
@SuppressWarnings("unused")
private void rebalance2(Node<E> grand) {
Node<E> parent = ((AVLNode<E>)grand).tallerChild();
Node<E> node = ((AVLNode<E>)parent).tallerChild();
if (parent.isLeftChild()) { // L
if (node.isLeftChild()) { // LL
rotateRight(grand);
} else { // LR
rotateLeft(parent);
rotateRight(grand);
}
} else { // R
if (node.isLeftChild()) { // RL
rotateRight(parent);
rotateLeft(grand);
} else { // RR
rotateLeft(grand);
}
}
}
/**
* 恢复平衡
* @param grand 高度最低的那个不平衡节点
*/
private void rebalance(Node<E> grand) {
Node<E> parent = ((AVLNode<E>)grand).tallerChild();
Node<E> node = ((AVLNode<E>)parent).tallerChild();
if (parent.isLeftChild()) { // L
if (node.isLeftChild()) { // LL
rotate(grand, node, node.right, parent, parent.right, grand);
} else { // LR
rotate(grand, parent, node.left, node, node.right, grand);
}
} else { // R
if (node.isLeftChild()) { // RL
rotate(grand, grand, node.left, node, node.right, parent);
} else { // RR
rotate(grand, grand, parent.left, parent, node.left, node);
}
}
}

private void rotate(
Node<E> r, // 子树的根节点
Node<E> b, Node<E> c,
Node<E> d,
Node<E> e, Node<E> f) {
// 让d成为这棵子树的根节点
d.parent = r.parent;
if (r.isLeftChild()) {
r.parent.left = d;
} else if (r.isRightChild()) {
r.parent.right = d;
} else {
root = d;
}

//b-c
b.right = c;
if (c != null) {
c.parent = b;
}
updateHeight(b);

// e-f
f.left = e;
if (e != null) {
e.parent = f;
}
updateHeight(f);

// b-d-f
d.left = b;
d.right = f;
b.parent = d;
f.parent = d;
updateHeight(d);
}

private void rotateLeft(Node<E> grand) {
Node<E> parent = grand.right;
Node<E> child = parent.left;
grand.right = child;
parent.left = grand;
afterRotate(grand, parent, child);
}

private void rotateRight(Node<E> grand) {
Node<E> parent = grand.left;
Node<E> child = parent.right;
grand.left = child;
parent.right = grand;
afterRotate(grand, parent, child);
}

private void afterRotate(Node<E> grand, Node<E> parent, Node<E> child) {
// 让parent称为子树的根节点
parent.parent = grand.parent;
if (grand.isLeftChild()) {
grand.parent.left = parent;
} else if (grand.isRightChild()) {
grand.parent.right = parent;
} else { // grand是root节点
root = parent;
}

// 更新child的parent
if (child != null) {
child.parent = grand;
}

// 更新grand的parent
grand.parent = parent;

// 更新高度
updateHeight(grand);
updateHeight(parent);
}

private boolean isBalanced(Node<E> node) {
return Math.abs(((AVLNode<E>)node).balanceFactor()) <= 1;
}

private void updateHeight(Node<E> node) {
((AVLNode<E>)node).updateHeight();
}

private static class AVLNode<E> extends Node<E> {
int height = 1;

public AVLNode(E element, Node<E> parent) {
super(element, parent);
}

public int balanceFactor() {
int leftHeight = left == null ? 0 : ((AVLNode<E>)left).height;
int rightHeight = right == null ? 0 : ((AVLNode<E>)right).height;
return leftHeight - rightHeight;
}

public void updateHeight() {
int leftHeight = left == null ? 0 : ((AVLNode<E>)left).height;
int rightHeight = right == null ? 0 : ((AVLNode<E>)right).height;
height = 1 + Math.max(leftHeight, rightHeight);
}

public Node<E> tallerChild() {
int leftHeight = left == null ? 0 : ((AVLNode<E>)left).height;
int rightHeight = right == null ? 0 : ((AVLNode<E>)right).height;
if (leftHeight > rightHeight) return left;
if (leftHeight < rightHeight) return right;
return isLeftChild() ? left : right;
}

@Override
public String toString() {
String parentString = "null";
if (parent != null) {
parentString = parent.element.toString();
}
return element + "_p(" + parentString + ")_h(" + height + ")";
}
}
}