Compute height of tree with deleted nodes; minimize deletions
Company: Snowflake
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Technical Screen
You are given a rooted tree (not necessarily binary). Each node has a list of children. Some nodes are marked as `deleted = true`.
Define the **effective tree** as the tree after removing every deleted node and all edges incident to it; nodes that become disconnected from the root are not counted.
1) Compute the **height** of the effective tree (maximum number of nodes on any root-to-leaf path in the effective tree; if the root is deleted, the height is 0).
2) Follow-up: Given an integer `K`, delete the **minimum number of additional nodes** (you may choose any nodes to delete) so that the height of the effective tree is **at most `K`**. Return that minimum number of additional deletions.
Clarify in your solution what “deleting a node” means (assume a deleted node is removed and you cannot traverse through it from the root).
Quick Answer: This question evaluates understanding of tree data structures, connectivity after node deletions, and optimization for minimizing additional removals, and is categorized under Coding & Algorithms. It is commonly asked to assess reasoning about tree pruning and height computation under constraints, testing both conceptual understanding of tree properties and practical algorithmic implementation.