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# 0701. Insert into a Binary Search Tree

<https://leetcode.com/problems/insert-into-a-binary-search-tree>

## Description

You are given the `root` node of a binary search tree (BST) and a `value` to insert into the tree. Return *the root node of the BST after the insertion*. It is **guaranteed** that the new value does not exist in the original BST.

**Notice** that there may exist multiple valid ways for the insertion, as long as the tree remains a BST after insertion. You can return **any of them**.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/10/05/insertbst.jpg)

```
**Input:** root = [4,2,7,1,3], val = 5
**Output:** [4,2,7,1,3,5]
**Explanation:** Another accepted tree is:
![](https://assets.leetcode.com/uploads/2020/10/05/bst.jpg)
```

**Example 2:**

```
**Input:** root = [40,20,60,10,30,50,70], val = 25
**Output:** [40,20,60,10,30,50,70,null,null,25]
```

**Example 3:**

```
**Input:** root = [4,2,7,1,3,null,null,null,null,null,null], val = 5
**Output:** [4,2,7,1,3,5]
```

**Constraints:**

* The number of nodes in the tree will be in the range `[0, 104]`.
* `-108 <= Node.val <= 108`
* All the values `Node.val` are **unique**.
* `-108 <= val <= 108`
* It's **guaranteed** that `val` does not exist in the original BST.

## ac

```java
```