模拟实现二叉搜索树

1、TreeSet和TreeMap插入元素时一定要比较大小，因为其底层是红黑树（由二叉搜索树调整形成）。
2、删除二叉搜索树的目标节点时有三种情况：
（1）cur.left==null
①cur是root，则root=cur.right

②cur不是root，cur是parent.left，则parent.left=cur.right

③cur不是root，cur是parent.right，则parent.right=cur.right

（2）cur.right==null
①cur是root，则root=cur.left

②cur不是root，cur是parent.left，则parent.left = cur.left

③cur不是root，cur是parent.right，parent.right = cur.left

(3)cur.left != null && cur.right != null
这里是在cur节点（要删除的目标节点）的右边找替罪羊，在cur的右子树中找到最左边的节点
①target==targetParent.left，则targetParent.left=target.right

②target==targetParent.right，则targetParent.right=target.right

public class BinarySearchTree {
    static class TreeNode {
        public int key;
        public TreeNode left;
        public TreeNode right;
        TreeNode(int key) {
            this.key = key;
        }
    }

    public TreeNode root;

    //插入一个元素，二叉搜索树不能插入多个相同的数据，插入时是在叶子节点的left和right处插入，每插入一个元素要与之前的元素进行比较
    public boolean insert(int key) {
        TreeNode cur = root;
        TreeNode parent = null;
        TreeNode node = new TreeNode(key);
        if(cur == null) {
           cur = node;
           return true;
        }
        while(cur != null) {
            if(cur.key > key) {
                parent = cur;
                cur = cur.left;
            }else if(cur.key < key) {
                parent = cur;
                cur = cur.right;
            }else {
                break;
            }
        }
        if(parent.key > key) {
            parent.left = node;
        }else {
            parent.right = node;
        }
        return true;
    }

    //查找key是否存在
    public TreeNode search(int key) {
        TreeNode cur = root;
        while(cur != null) {
            if(cur.key > key) {
                cur = cur.left;
            }else if(cur.key < key) {
                cur = cur.right;
            }else {
                return cur;
            }
        }
        return null;//这里已经包含了root==null和找不到两种情况
    }

    //删除key的值
    public boolean remove(int key) {
        TreeNode cur = root;
        TreeNode parent = null;
        while(cur != null) {
            if(cur.key > key) {
                parent = cur;
                cur = cur.left;
            }else if(cur.key < key) {
                parent = cur;
                cur = cur.right;
            }else {
                removeNode(parent, cur);
                return true;
            }
        }
        return false;
    }
    private void removeNode(TreeNode parent, TreeNode cur) {
        if(cur.left == null) {//包括left为空right不为空，left为空right也为空两种情况
            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) {//包括right为空left不为空，right为空left也为空两种情况
            if(cur == root) {
                root = cur.left;
            }else if(cur == parent.left) {
                parent.left = cur.left;
            }else {
                parent.right = cur.left;
            }
        }else {//left和right都不为空，这里是在cur节点（要删除的目标节点）的右边找替罪羊，在cur的右子树中找到最左边的节点
            TreeNode targetParent = cur;
            TreeNode target = cur.right;
            while(target.left != null) {
                targetParent = target;
                target = target.left;
            }
            cur.key = target.key;
            if(target == targetParent.left) {
                targetParent.left = target.right;
            }else {
               targetParent.right = target.right;
            }
        }
    }
}