数据结构- 平衡二叉树AVL树(左旋、右旋、双旋转)

深藏阁楼爱情的钟 2023-07-03 08:06 38阅读 0赞

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![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 1]  
**第三棵树根节点的左子树高度为3右子树高度为1，相差为2大于1，所以不是平衡二叉树**  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 2]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 3]  
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//左旋转方法
        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;
            //把当前节点的值换成当前节点的右子节点的值
            value = right.value;
            //把当前节点的右节点设置成右节点的右子树
            right = right.right;
            //把当前节点的左节点设置成新的节点
            left = newNode;
        }

然后把此方法加到add方法里，添加节点的时候就判断  
![在这里插入图片描述][20200204191023787.png]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 5]  
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# 右旋 #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 7]  
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//右旋转方法
        private void rightRotate(){ 
            //创建新节点，值为当前节点节点的值
            Node newNode = new Node(value);
            //让当前节点的右子树挂到新节点上的右节点
            newNode.right = right;
            //让当前节点的左子节点的右子树挂到新节点的左节点
            newNode.left = left.right;
            //把当前节点的值改成左节点的值
            value = left.value;
            //当前节点的左节点执行左节点的左节点
            left = left.left;
            //把新节点挂到当前节点的右节点
            right = newNode;
        }

![在这里插入图片描述][2020020419103850.png]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 9]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 10]

# 但是还不能进行双旋转 #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 11]  
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![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 13]

//当添加完节点，当前节点的右子树的高度比左子树的高度差大于1，就左旋
            if (rightHeight() - leftHeight() > 1){ 
                //如果它的右子树的左子树高度大于它的右子树的右子树高度
                if (right != null && right.leftHeight() > right.rightHeight()){ 
                    //右子树右旋
                    right.rightRotate();
                    //当前节点左旋
                    leftRotate();
                }else { 
                    leftRotate(); // 左旋转
                }
                return; //平衡了就没必要继续走
            }
            //当前节点的左子树的高度比右子树的高度差大于1，就右旋
            if (leftHeight() - rightHeight() > 1){ 
                //如果它的左子树的右子树高度大于它的左子树的左子树的高度
                if (left != null && left.rightHeight() > left.leftHeight()){ 
                    //先对当前节点的左子树进行左旋
                    left.leftRotate();
                    //在对当前节点右旋
                    rightRotate();
                }else { 
                    //直接进行右旋转
                    rightRotate();
                }
            }

# 完整代码 #

package tree.avl;
    
    
    public class AVLTreeDemo { 
        public static void main(String[] args) { 
            //int[] arr = {4, 3, 6, 5, 7, 8};
            //int[] arr = {10, 12, 8, 9, 7, 6};
            int[] arr = { 10, 11, 7, 6, 8, 9};
            AVLTree avlTree = new AVLTree();
            //循环添加节点
            for (int i = 0; i < arr.length; i++) { 
                avlTree.add(new Node(arr[i]));
            }
    
            //中序遍历
            //avlTree.infixOrder();
    
            System.out.println("树的高度：" + avlTree.getRoot().height());
            System.out.println("左子树的高度："+avlTree.getRoot().leftHeight());
            System.out.println("右子树的高度："+avlTree.getRoot().rightHeight());
    
        }
    }
    
    //创建AVL树
    class AVLTree{ 
        private Node root;
    
        public Node getRoot() { 
            return root;
        }
    
        //查找要删除的节点
        public Node search(int value){ 
            if (root == null){ 
                return null;
            }else { 
                return root.search(value);
            }
        }
    
        //查找父节点
        public Node searchParent(int value){ 
            if (root == null){ 
                return null;
            }else{ 
                return root.searchParent(value);
            }
        }
    
        //编写一个方法,查找以传入节点为根节点的二叉排序树中的最小节点的值，并删除此节点
        public int delRightTreeMin(Node node){ 
            Node target = node;
            //循环查找左节点，就会找到最小值
            while(target.left != null){ 
                target = target.left;
            }
            //删除最小节点
            delNode(target.value);
            return target.value;
        }
    
        //删除节点
        public void delNode(int value){ 
            if (root == null){ 
                return;
            }else { 
                //1.找到要删除的节点
                Node targetNode = search(value);
                if (targetNode == null){ 
                    return;
                }
                //如果二叉排序树只有一个节点，并且删除的此节点
                if (root.left == null && root.right == null){ 
                    root = null;
                    return;
                }
    
                //找到父节点
                Node parent = searchParent(value);
    
                //如果删除的节点是叶子节点
                if (targetNode.left == null && targetNode.right == null){ //第一种，删除叶子
                    if (targetNode.value < parent.value){  //比较大小判断删除的左叶子还是右叶子
                        parent.left = null;
                    }else { 
                        parent.right = null;
                    }
                }else if (targetNode.left != null && targetNode.right != null){ //删除有两棵子树的(因为第二种判断比较麻烦，所以直接写在else里)
                    //从target的右子树找到最小节点,
                    //用一个临时变量存储这个最小节点的value
                    //删除最小节点
                    int min = delRightTreeMin(targetNode.right);
                    //把最小节点的值赋给targetNode
                    targetNode.value = min;
                }else { //第二种，只有一棵子树
                    //如果要删除的节点有左子节点
                    if (targetNode.left != null){ 
                        //如果只有根节点和一个叶子节点，要删除根节点，那就要判断根节点的父节点是否为空
                        if (parent != null) { 
                            //如果targetNode是parent的左子节点
                            if (parent.left.value == value) { 
                                parent.left = targetNode.left;
                            } else { //targetNode是parent的右子节点
                                parent.right = targetNode.left;
                            }
                        }else { 
                            root = targetNode.left;
                        }
                    }else { //要删除的节点有右子节点
                        if (parent != null) { 
                            if (parent.left.value == value) { 
                                //如果targetNode是parent的左子节点
                                parent.left = targetNode.right;
                            } else { //targetNode是parent的右子节点
                                parent.right = targetNode.right;
                            }
                        }else { 
                            root = targetNode.right;
                        }
                    }
                }
            }
        }
        //添加节点的方法
        public void add(Node node){ 
            if (root == null){ 
                root = node;
            }else { 
                root.add(node);
            }
        }
    
        //中序遍历
        public void infixOrder(){ 
            if (root != null){ 
                root.infixOrder();
            }else { 
                System.out.println("二叉排序树为空,无法遍历");
            }
        }
    }
    
    //创建节点
    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 leftHeight(){ 
            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();
        }
    
        //右旋转方法
        private void rightRotate(){ 
            //创建新节点，值为当前节点节点的值
            Node newNode = new Node(value);
            //让当前节点的右子树挂到新节点上的右节点
            newNode.right = right;
            //让当前节点的左子节点的右子树挂到新节点的左节点
            newNode.left = left.right;
            //把当前节点的值改成左节点的值
            value = left.value;
            //当前节点的左节点执行左节点的左节点
            left = left.left;
            //把新节点挂到当前节点的右节点
            right = newNode;
        }
    
        //左旋转方法
        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;
            //把当前节点的值换成当前节点的右子节点的值
            value = right.value;
            //把当前节点的右节点设置成右节点的右子树
            right = right.right;
            //把当前节点的左节点设置成新的节点
            left = newNode;
        }
    
        //返回当前节点的高度，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;
        }
    
        //查找要删除的节点
        public Node search(int value){ 
            if (value == this.value){ //找到
                return this;
            }else if(value < this.value){ //应该向左继续查找
                //如果左子节点为空就不能找了，说明不存在
                if (this.left == null) { 
                    return null;
                }
                return this.left.search(value);
    
            }else { 
                if (this.right == null){ 
                    return null;
                }
                return this.right.search(value);
            }
        }
    
        //查找要删除节点的父节点
        public Node searchParent(int value){ 
            if ((this.left != null && this.left.value == value)||
                    (this.right != null && this.right.value == value)){ 
                return this;
            }else { 
                //如果查找的值小于当前节点的值，并且当前节点的左子节点不为空
                if (value < this.value && this.left != null){ 
                    return this.left.searchParent(value);//像左子树递归查找
                }else if (value >= this.value && this.right != null){ 
                    return this.right.searchParent(value);//像右子树递归查找
                }else { 
                    return null; //没有父节点
                }
            }
        }
        //添加节点的方法
        //递归的形式添加节点，满足二叉排序树
        public void add(Node node){ 
            if(node == null){ 
                return;
            }
    
            if (node.value < this.value){ 
                //当前节点的左子节点为空直接挂上
                if (this.left == null){ 
                    this.left = node;
                }else { //不为空递归向下
                    this.left.add(node);
                }
            }else {  //添加的节点的值大于等于当前节点的值，右节点为空，挂到右节点
                if (this.right == null){ 
                    this.right = node;
                }else{ //不为空就挂上
                    this.right.add(node);
                }
            }
            //当添加完节点，当前节点的右子树的高度比左子树的高度差大于1，就左旋
            if (rightHeight() - leftHeight() > 1){ 
                //如果它的右子树的左子树高度大于它的右子树的右子树高度
                if (right != null && right.leftHeight() > right.rightHeight()){ 
                    //右子树右旋
                    right.rightRotate();
                    //当前节点左旋
                    leftRotate();
                }else { 
                    leftRotate(); // 左旋转
                }
                return; //平衡了就没必要继续走
            }
            //当前节点的左子树的高度比右子树的高度差大于1，就右旋
            if (leftHeight() - rightHeight() > 1){ 
                //如果它的左子树的右子树高度大于它的左子树的左子树的高度
                if (left != null && left.rightHeight() > left.leftHeight()){ 
                    //先对当前节点的左子树进行左旋
                    left.leftRotate();
                    //在对当前节点右旋
                    rightRotate();
                }else { 
                    //直接进行右旋转
                    rightRotate();
                }
            }
        }
    
        //中序遍历
        public void infixOrder(){ 
            if (this.left != null){ 
                this.left.infixOrder();
            }
    
            System.out.println(this);
    
            if (this.right != null){ 
                this.right.infixOrder();
            }
    
        }
        @Override
        public String toString() { 
            return "Node{" +
                    "value=" + value +
                    '}';
        }
    }

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