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Solution: Height of Binary Tree After Subtree Removal Queries

Explore how to determine the height of a binary tree after subtree removals by using depth-first search to record node depths and heights. Understand how grouping nodes by depth and analyzing their heights enables efficient recalculations for multiple queries, allowing you to solve this problem with optimized time and space complexity.

Statement

We are given the root of a binary tree with nn nodes and an array, queries, of size mm. Each query represents the root of a subtree that should be removed from the tree. The task here is to determine the height of the binary tree after each query, i.e., once a subtree is removed. We'll store the updated heights against each query in an array and return it.

Note: A tree’s height is the number of edges in the longest path from the root to any leaf node in the tree.

A few points to be considered:

  • All the values in the tree are unique.

  • It is guaranteed that queries[i] ...