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# 1932. Merge BSTs to Create Single BST

<https://leetcode.com/problems/merge-bsts-to-create-single-bst>

## Description

You are given `n` **BST (binary search tree) root nodes** for `n` separate BSTs stored in an array `trees` (**0-indexed**). Each BST in `trees` has **at most 3 nodes**, and no two roots have the same value. In one operation, you can:

* Select two **distinct** indices `i` and `j` such that the value stored at one of the **leaves** of `trees[i]` is equal to the **root value** of `trees[j]`.
* Replace the leaf node in `trees[i]` with `trees[j]`.
* Remove `trees[j]` from `trees`.

Return *the **root** of the resulting BST if it is possible to form a valid BST after performing* `n - 1` *operations, or*`null` *if it is impossible to create a valid BST*.

A BST (binary search tree) is a binary tree where each node satisfies the following property:

* Every node in the node's left subtree has a value **strictly less** than the node's value.
* Every node in the node's right subtree has a value **strictly greater** than the node's value.

A leaf is a node that has no children.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/06/08/d1.png)

```
**Input:** trees = [[2,1],[3,2,5],[5,4]]
**Output:** [3,2,5,1,null,4]
**Explanation:**
In the first operation, pick i=1 and j=0, and merge trees[0] into trees[1].
Delete trees[0], so trees = [[3,2,5,1],[5,4]].
![](https://assets.leetcode.com/uploads/2021/06/24/diagram.png)
In the second operation, pick i=0 and j=1, and merge trees[1] into trees[0].
Delete trees[1], so trees = [[3,2,5,1,null,4]].
![](https://assets.leetcode.com/uploads/2021/06/24/diagram-2.png)
The resulting tree, shown above, is a valid BST, so return its root.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2021/06/08/d2.png)

```
**Input:** trees = [[5,3,8],[3,2,6]]
**Output:** []
**Explanation:**
Pick i=0 and j=1 and merge trees[1] into trees[0].
Delete trees[1], so trees = [[5,3,8,2,6]].
![](https://assets.leetcode.com/uploads/2021/06/24/diagram-3.png)
The resulting tree is shown above. This is the only valid operation that can be performed, but the resulting tree is not a valid BST, so return null.
```

**Example 3:**

![](https://assets.leetcode.com/uploads/2021/06/08/d3.png)

```
**Input:** trees = [[5,4],[3]]
**Output:** []
**Explanation:** It is impossible to perform any operations.
```

**Example 4:**

![](https://assets.leetcode.com/uploads/2021/06/08/d4.png)

```
**Input:** trees = [[2,1,3]]
**Output:** [2,1,3]
**Explanation:** There is only one tree, and it is already a valid BST, so return its root.
```

**Constraints:**

* `n == trees.length`
* `1 <= n <= 5 * 104`
* The number of nodes in each tree is in the range `[1, 3]`.
* Each node in the input may have children but no grandchildren.
* No two roots of `trees` have the same value.
* All the trees in the input are **valid BSTs**.
* `1 <= TreeNode.val <= 5 * 104`.

## ac

```java
```