数据结构 - 二叉排序树BST(创建、遍历、删除节点)

红太狼 2023-07-03 07:24 21阅读 0赞

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### 数组与链表区别： ###

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# 二叉排序树的创建和遍历 代码实现 #

package tree.binarysorttree;
    
    public class BinarySortTreeDemo { 
        public static void main(String []args){ 
            int [] arr = { 7,3,10,12,5,1,9};
            BinarySortTree binarySortTree = new BinarySortTree();
            //循环添加节点
            for (int i = 0; i < arr.length; i++) { 
                binarySortTree.add(new Node(arr[i]));
            }
            //中序遍历
            binarySortTree.infixOrder();
        }
    }
    
    //创建二叉排序树
    class BinarySortTree{ 
        private Node root;
        //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;
        }
    
        //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);
                }
            }
        }
    
        //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 +
                    '}';
        }
    }

![在这里插入图片描述][2020020414415975.png]

# 删除： #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 4]  
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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 6]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzczNjA4NA_size_16_color_FFFFFF_t_70 7]

# 编写查找节点的方法 #

//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);
            }
        }

# 删除第三种需要用到的，查找以target.right为根节点节点的树的最小值并删除，然后返回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;
        }

# 删除节点方法 #

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;
                        }
                    }
                }
            }
        }

# 完整代码 #

package tree.binarysorttree;
    
    public class BinarySortTreeDemo { 
        public static void main(String []args){ 
            int [] arr = { 7,3,10,12,5,1,9,2};
            BinarySortTree binarySortTree = new BinarySortTree();
            //循环添加节点
            for (int i = 0; i < arr.length; i++) { 
                binarySortTree.add(new Node(arr[i]));
            }
            //中序遍历
            binarySortTree.infixOrder();
    
            //测试删除
            binarySortTree.delNode(2);
            binarySortTree.delNode(5);
            binarySortTree.delNode(9);
            binarySortTree.delNode(12);
            binarySortTree.delNode(7);
            binarySortTree.delNode(3);
            binarySortTree.delNode(10);
    
            System.out.println();
            binarySortTree.infixOrder();
        }
    }
    
    //创建二叉排序树
    class BinarySortTree{ 
        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;
        }
        //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);
                }
            }
        }
    
        //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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