2458 - Height of Binary Tree After Subtree Removal Queries\.

Hard

You are given the root of a binary tree with n nodes. Each node is assigned a unique value from 1 to n. You are also given an array queries of size m.

You have to perform m independent queries on the tree where in the <code>i^th</code> query you do the following:

• Remove the subtree rooted at the node with the value queries[i] from the tree. It is guaranteed that queries[i] will not be equal to the value of the root.

Return an array answer of size m where answer[i] is the height of the tree after performing the <code>i^th</code> query.

Note:

• The queries are independent, so the tree returns to its initial state after each query.

• The height of a tree is the number of edges in the longest simple path from the root to some node in the tree.

Example 1:

Input: root = 1,3,4,2,null,6,5,null,null,null,null,null,7, queries = 4

Output: 2

Explanation: The diagram above shows the tree after removing the subtree rooted at node with value 4. The height of the tree is 2 (The path 1 -> 3 -> 2).

Example 2:

Input: root = 5,8,9,2,1,3,7,4,6, queries = 3,2,4,8

Output: 3,2,3,2

Explanation: We have the following queries:

• Removing the subtree rooted at node with value 3. The height of the tree becomes 3 (The path 5 -> 8 -> 2 -> 4).

• Removing the subtree rooted at node with value 2. The height of the tree becomes 2 (The path 5 -> 8 -> 1).

• Removing the subtree rooted at node with value 4. The height of the tree becomes 3 (The path 5 -> 8 -> 2 -> 6).

• Removing the subtree rooted at node with value 8. The height of the tree becomes 2 (The path 5 -> 9 -> 3).

Constraints:

• The number of nodes in the tree is n.

• <code>2 <= n <= 10⁵</code>

• 1 <= Node.val <= n

• All the values in the tree are unique.

• m == queries.length

• <code>1 <= m <= min(n, 10⁴)</code>

• 1 <= queries[i] <= n

• queries[i] != root.val