1932 - Merge BSTs to Create Single BST.

Hard

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:

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 trees0 into trees1. Delete trees0, so trees = [3,2,5,1,5,4]. In the second operation, pick i=0 and j=1, and merge trees1 into trees0. Delete trees1, so trees = [3,2,5,1,null,4]. 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 trees1 into trees0. Delete trees1, so trees = [5,3,8,2,6]. 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.

Constraints:

• n == trees.length

• <code>1 <= n <= 5 * 10⁴</code>

• 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.

• <code>1 <= TreeNode.val <= 5 * 10⁴</code>.