为什么需要 avl tree

avl tree 又称 平衡二叉树。主要在排序二叉树的基础上进行的一个优化。避免排序二叉树不平衡，从而严重影响查询效率

avl tree 的特点

平衡二叉树也叫平衡二叉搜索树。
它可以是一颗空树或者它的左右两个子树的高度差的绝对值不超过1，并且左右两个子树都是一颗平衡二叉树

avl tree 实现

/*** @author shengjk1* @date 2020/6/23*/
public class AvlTreeDemo {public static void main(String[] args) {int[] arr = {10, 11, 7, 6, 8, 9};
//		int[] arr = {4, 3, 6, 5, 7, 8};
//		int[] arr = {10, 12, 8, 9, 7, 6};AVLTree avlTree = new AVLTree();for (int i = 0; i < arr.length; i++) {System.out.println(arr[i]);avlTree.add(new Node(arr[i]));}System.out.println("中序遍历");avlTree.infixOrder();System.out.println("在平衡处理~");System.out.println("树的高度=" + avlTree.getRoot().height());System.out.println("树的左子树的高度=" + avlTree.getRoot().leftHight());System.out.println("树的右子树的高度=" + avlTree.getRoot().rightHeight());System.out.println("当前的根节点=" + avlTree.getRoot());}
}class AVLTree {private Node root;public Node getRoot() {return root;}public void add(Node node) {if (root == null) {root = node;} else {root.add(node);}}public void infixOrder() {if (root != null) {root.infixOrder();} else {System.out.println("avl tree is empty");}}
}class Node {int value;Node left;Node right;public Node(int value) {this.value = value;}//返回左子树的高度public int leftHight() {if (left == null) {return 0;}return left.height();}//返回右子树的高度public int rightHeight() {if (right == null) {return 0;}return right.height();}//返回以该节点为根节点的树的高度public int height() {return Math.max(left == null ? 0 : left.height(), right == null ? 0 : right.height()) + 1;}//左旋转private void leftRotate() {//创建新的节点，以当前根节点的值Node newNode = new Node(value);//把新的节点的左子树设置成当前节点的左子树newNode.left = left;//把新的节点的右子树设置成当前节点的右子树的左子树newNode.right = right.left;//把当前节点的值替换为右子节点的值value = right.value;//把当前节点的右子树设置成当前节点右子树的右子树right = right.right;//把当前节点的左子树设置成新的节点left = newNode;}//右旋转private void rightRotate() {Node newNode = new Node(value);newNode.right = right;newNode.left = left.right;value = left.value;left = left.left;right = newNode;}//查找要删除的节点public Node search(int value) {if (value == this.value) {return this;} else if (value < this.value) {if (this.left == null) {return null;}return this.left.search(value);} else {if (this.right == null) {return null;}return this.right.search(value);}}@Overridepublic String toString() {return "Node{" +"value=" + value +'}';}//添加节点//满足二叉排序树public void add(Node node) {if (node == null) {return;}if (node.value < this.value) {if (this.left == null) {this.left = node;} else {this.left.add(node);}} else {if (this.right == null) {this.right = node;} else {this.right.add(node);}}////		//左旋转if (rightHeight() - leftHight() > 1) {//如果它的右子树的左子树的高度大于它的右子树的右子树的高度if (right.leftHight() > right.rightHeight()) {//先对右子节点进行右旋转right.rightRotate();//然后对当前节点进行左旋转leftRotate();} else {//直接进行左旋转leftRotate();}
//			return;} else if (leftHight() - rightHeight() > 1) {if (left.rightHeight() > left.leftHight()) {left.leftRotate();rightRotate();} else {rightRotate();}}}public void infixOrder() {if (this.left != null) {this.left.infixOrder();}System.out.println(this);if (this.right != null) {this.right.infixOrder();}}
}