Height of Binary Tree After Subtree Removal Queries

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Problem Statement

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 i ^th 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 i ^th 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.

Examples

Example 1

Input: root = [1,3,4,2,null,6,5,null,null,null,null,null,7], queries = [4]
Output: [2]
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]
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 .

2 <= n <= 10 ^5

1 <= Node.val <= n

All the values in the tree are unique .

m == queries.length

1 <= m <= min(n, 10 ^4 )

1 <= queries[i] <= n

queries[i] != root.val

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicTree