# 450 Delete Node in a BST

## 450. [Delete Node in a BST](https://leetcode.com/problems/delete-node-in-a-bst/)

## 1. Question

Given a root node reference of a BST and a key, delete the node with the given key in the BST. Return the root node reference (possibly updated) of the BST.

Basically, the deletion can be divided into two stages:

1. Search for a node to remove.
2. If the node is found, delete the node.

**Note:**Time complexity should be O(height of tree).

**Example:**

```
root = [5,3,6,2,4,null,7]
key = 3

    5
   / \
  3   6
 / \   \
2   4   7

Given key to delete is 3. So we find the node with value 3 and delete it.

One valid answer is [5,4,6,2,null,null,7], shown in the following BST.

    5
   / \
  4   6
 /     \
2       7

Another valid answer is [5,2,6,null,4,null,7].

    5
   / \
  2   6
   \   \
    4   7
```

## 2. Implementation

**(1) Iteration**

```java
class Solution {
    public TreeNode deleteNode(TreeNode root, int key) {
        TreeNode preNode = null, curNode = root;

        while (curNode != null && curNode.val != key) {
            preNode = curNode;
            if (curNode.val < key) {
                curNode = curNode.right;
            }
            else{
                curNode = curNode.left;
            }
        }

        if (preNode == null) {
            return getSuccessor(curNode);
        }
        else if (preNode.left == curNode) {
            preNode.left = getSuccessor(curNode);
        }
        else if (preNode.right == curNode) {
            preNode.right = getSuccessor(curNode);
        }
        return root;
    }

    public TreeNode getSuccessor(TreeNode node) {
        if (node == null) {
            return null;
        }

        if (node.left == null) {
            return node.right;
        }

        if (node.right == null) {
            return node.left;
        }

        TreeNode preNode = null, successor = node.right;

        while (successor.left != null) {
            preNode = successor;
            successor = successor.left;
        }

        successor.left = node.left;
        if (node.right != successor) {
            preNode.left = successor.right;
            successor.right = node.right;
        }
        return successor;
    }
}
```

**（2) Recursion**

```java
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public TreeNode deleteNode(TreeNode root, int key) {
        if (root == null) {
            return null;
        }

        if (root.val < key) {
            root.right = deleteNode(root.right, key);
        }
        else if (root.val > key) {
            root.left = deleteNode(root.left, key);
        }
        else {
            if (root.left == null) {
                return root.right;
            }

            if (root.right == null) {
                return root.left;
            }

            TreeNode successor = getInorderSuccessor(root.right);
            // 注意这一步是改变了原来的数据，面试时不一定被允许
            root.val = successor.val;
            root.right = deleteNode(root.right, root.val);
        }
        return root;
    }

    public TreeNode getInorderSuccessor(TreeNode node) {
        while (node.left != null) {
            node = node.left;
        }
        return node;
    }
}
```

## 3. Time & Space Complexity

**Iteration:**&#x65F6;间复杂度O(h), 空间复杂度O(1)

**Recursion**: 时间复杂度O(h), 空间复杂度O(h)


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://protegejj.gitbook.io/algorithm-practice/leetcode/tree/450-delete-node-in-a-bst.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.