# 0450. Delete Node in a BST

<https://leetcode.com/problems/delete-node-in-a-bst>

## Description

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.

**Follow up:** Can you solve it with time complexity `O(height of tree)`?

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/09/04/del_node_1.jpg)

```
**Input:** root = [5,3,6,2,4,null,7], key = 3
**Output:** [5,4,6,2,null,null,7]
**Explanation:** 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 above BST.
Please notice that another valid answer is [5,2,6,null,4,null,7] and it's also accepted.
![](https://assets.leetcode.com/uploads/2020/09/04/del_node_supp.jpg)
```

**Example 2:**

```
**Input:** root = [5,3,6,2,4,null,7], key = 0
**Output:** [5,3,6,2,4,null,7]
**Explanation:** The tree does not contain a node with value = 0.
```

**Example 3:**

```
**Input:** root = [], key = 0
**Output:** []
```

**Constraints:**

* The number of nodes in the tree is in the range `[0, 104]`.
* `-105 <= Node.val <= 105`
* Each node has a **unique** value.
* `root` is a valid binary search tree.
* `-105 <= key <= 105`

## ac

```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) {
        // exit
        if (root == null) return root;

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

        return root;        
    }

    private int minValue(TreeNode root) {
        while (root.left != null) {
            root = root.left;
        }
        return root.val;
    }
}

/*
find that value: 1) return null if left/right null; 2) return left if right null; 3) return right if left null; 4) find minValue in right, upate in root.val, delete minValue in right, return root.
*/
```


---

# 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://jaywin.gitbook.io/leetcode/solutions/0450-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.