手写 avl tree

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);
        }
    }
    
    @Override
    public 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();
        }
    }
}