二叉搜索树

二叉搜索树：

概念：二叉搜索树又称二叉排序树，它或者是一棵空树，或者是具有以下 性质的二叉树:
1.若它的左子树不为空，则左子树上所有节点的值都小于根节点的值
2.若它的右子树不为空，则右子树上所有节点的值都大于根节点的值
3.它的左右子树也分别为二叉搜索树

二叉搜索树的操作
一：查找
原理：如果查找值小于当前节点的值，就去该节点的左子树去查找，如果查找值大于当前节点的值，就去该节点的右子树去查找

class Node {
        public int val;
        public Node left;
        public Node right;
        public Node(int val) {
            this.val = val;
        }
     public Node search(int key){
        Node cur = root;
        while(cur != null) {
            if (cur.val == key) {
                return cur;
            }else if (key > cur.left.val) {
                cur = cur.right;
            } else {
                cur = cur.left;
            }
        }
        return null;
    }

二：插入
原理：最终插入的一定是该树的叶子节点

class Node {
        public int val;
        public Node left;
        public Node right;
        public Node(int val) {
            this.val = val;
        }
public void insert(int key) {
        Node node = new Node(key);
        if(root == null) {
            root = node;
            return;
        }
        Node cur = root;
        Node parent = cur;
        while (cur != null) {
            if(cur.val == key){
                return;
            }
            if(cur.val < key){
                parent = cur;
                cur = cur.right;
            }else{
                parent = cur;
                cur = cur.left;
            }
        }
        if(parent.val > key){
            parent.left = node;
        }else{
            parent.right = node;
        }

    }        

三：删除
原理：
A. cur.left == null

1. cur 是 root，则 root = cur.right
2. cur 不是 root，cur 是 parent.left，则 parent.left = cur.right
3. cur 不是 root，cur 是 parent.right，则 parent.right = cur.right
   B. cur.right == null
4. cur 是 root，则 root = cur.left
5. cur 不是 root，cur 是 parent.left，则 parent.left = cur.left
6. cur 不是 root，cur 是 parent.right，则 parent.right = cur.left
   C. cur.left != null && cur.right != null
7. 找到右子树最小的值，替换到要删除的节点，然后将找到的最小的值删除掉。

class Node {
        public int val;
        public Node left;
        public Node right;
        public Node(int val) {
            this.val = val;
        }
public void remove(int key) {
        Node cur = root;
        Node parent = null;
        while (cur != null) {
            if(cur.val == key) {
                //删除
                removeNode(parent,cur);
                return;
            }else if(cur.val > key) {
                parent = cur;
                cur = cur.left;
            }else {
                parent = cur;
                cur = cur.right;
            }
        }
    }

    /**
     *
     * @param parent 要删除节点的父亲节点
     * @param cur 代表要删除的节点
     */
    public void removeNode(Node parent,Node cur) {
        if(cur.left == null){
            if(cur == root){
                root = cur.right;
            }else if(cur == parent.left){
                parent.left = cur.right;
            }else{
                parent.right = cur.right;
            }
        }else if(cur.right == null){
            if(cur == root){
                root = cur.left;
            }else if(cur == parent.left){
                parent.left = cur.left;
            }else{
                parent.right = cur.left;
            }
        }else{
            Node targetParent = cur;
            Node target = cur.right;
            while (target.left != null) {
                targetParent = target;
                target = target.left;
            }
            //target->右树当中最小的元素
            cur.val = target.val;
            if(target == targetParent.left) {
                targetParent.left = target.right;
            }else {
                targetParent.right = target.right;
            }
        }

    }