Leetcode 450. 删除二叉搜索树中的节点

链接：https://leetcode.cn/problems/delete-node-in-a-bst/
二叉搜索树的增删改查都是必会的内容，但是删除相对于其他操作较难一点，可以通过这道题来进行练习。

题目描述

给定一个二叉搜索树的根节点 root 和一个值 key，删除二叉搜索树中的 key 对应的节点，并保证二叉搜索树的性质不变。返回二叉搜索树（有可能被更新）的根节点的引用。

递归解法

class Solution:
    """
    递归解法
    """
    def deleteNode(self, root: Optional[TreeNode], key: int) -> Optional[TreeNode]:
        """
        删除根为root的BST中node.val等于key的节点，返回删除后的根节点（根节点可能变化）
        """
        if not root:
            return None
        if key < root.val:
            root.left = self.deleteNode(root.left, key)
        elif root.val < key:
            root.right = self.deleteNode(root.right, key)
        # # root可能有0或1个孩子节点，但是处理方式相同，返回孩子节点
        elif not root.left or not root.right:
            child = root.left if root.left else root.right
            return child
        else:
            successor = root.right  # 使用后继节点代替root
            while successor.left:
                successor = successor.left
            root.val = successor.val  # root.val赋值为后继节点值
            root.right = self.deleteNode(root.right, successor.val)
        return root

迭代解法

迭代解法基本思路与上相同，就是要多分类讨论删除的节点是不是根节点。

class Solution:
    """
    非递归解法
    """
    def deleteNode(self, root: Optional[TreeNode], key: int) -> Optional[TreeNode]:
        if not root:
            return root
        node, father = self.findNode(root, key)
        if not node:
            return root
        return self.delete(root, father, node)

    def delete(self, root, father, node):
        if node.left and node.right:
            suc_father, successor = self.findSuccessor(node)
            node.val = successor.val
            return self.delete(root, suc_father, successor)
        if not node.left and not node.right:
            if root == node:
                return None
            if father.left == node:
                father.left = None
            else:
                father.right = None
            return root
        child = node.left if node.left else node.right
        if root == node:
            return child
        if father.left == node:
            father.left = child
        else:
            father.right = child
        return root

    def findNode(self, root, key):
        if not root:
            return root
        if root.val == key:
            return root, None
        father = root
        while root:
            if root.val == key:
                return root, father
            elif key < root.val:
                father = root
                root = root.left
            else:
                father = root
                root = root.right
        return None, None

    def findSuccessor(self, root):
        successor = root.right
        father = root
        while successor.left:
            father = successor
            successor = successor.left
        return father, successor