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, ornull 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:

**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:

**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:

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

Example 4:

**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.

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