# 0510. Inorder Successor in BST II

<https://leetcode.com/problems/inorder-successor-in-bst-ii>

## Description

Given a `node` in a binary search tree, return *the in-order successor of that node in the BST*. If that node has no in-order successor, return `null`.

The successor of a `node` is the node with the smallest key greater than `node.val`.

You will have direct access to the node but not to the root of the tree. Each node will have a reference to its parent node. Below is the definition for `Node`:

```
class Node {
    public int val;
    public Node left;
    public Node right;
    public Node parent;
}
```

**Example 1:**

![](https://assets.leetcode.com/uploads/2019/01/23/285_example_1.PNG)

```
**Input:** tree = [2,1,3], node = 1
**Output:** 2
**Explanation:** 1's in-order successor node is 2. Note that both the node and the return value is of Node type.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2019/01/23/285_example_2.PNG)

```
**Input:** tree = [5,3,6,2,4,null,null,1], node = 6
**Output:** null
**Explanation:** There is no in-order successor of the current node, so the answer is null.
```

**Example 3:**

![](https://assets.leetcode.com/uploads/2019/02/02/285_example_34.PNG)

```
**Input:** tree = [15,6,18,3,7,17,20,2,4,null,13,null,null,null,null,null,null,null,null,9], node = 15
**Output:** 17
```

**Example 4:**

![](https://assets.leetcode.com/uploads/2019/02/02/285_example_34.PNG)

```
**Input:** tree = [15,6,18,3,7,17,20,2,4,null,13,null,null,null,null,null,null,null,null,9], node = 13
**Output:** 15
```

**Example 5:**

```
**Input:** tree = [0], node = 0
**Output:** null
```

**Constraints:**

* The number of nodes in the tree is in the range `[1, 104]`.
* `-105 <= Node.val <= 105`
* All Nodes will have unique values.

**Follow up:** Could you solve it without looking up any of the node's values?

## ac

```java
```