Merge BSTs to Create Single BST

arrayhash tabletree

Problem Statement

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.

Examples

Example 1

Input: trees = [[2,1],[3,2,5],[5,4]]
Output: [3,2,5,1,null,4]
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]].
 
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]].
 
The resulting tree, shown above, is a valid BST, so return its root.

Example 2

Input: trees = [[5,3,8],[3,2,6]]
Output: []
Pick i=0 and j=1 and merge trees[1] into trees[0].
Delete trees[1], 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: []
It is impossible to perform any operations.

Constraints

n == trees.length

1 <= n <= 5 * 10 ^4

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 * 10 ^4 .

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicHash Table