← Microsoft Interview Insights
I went straight to a tree with cached subtree counts per node.
Start by clarifying requirements and scale, then propose a graph-based solution with efficient query and update operations. Discuss trade-offs between different data structures and algorithms, and address edge cases like cycles and consistency.
Pro tip: Mention that you would use a topological ordering or maintain subtree sizes with a balanced tree to achieve O(log n) updates and O(1) queries, showing awareness of real-world performance needs.
Ask about scale (number of employees, frequency of queries vs updates), consistency requirements, and whether the hierarchy is a tree or can have multiple managers.
Propose representing the hierarchy as a directed graph (tree) and discuss options like adjacency lists, parent pointers, or Euler tour trees for efficient subtree size queries.
For queries, explain how to compute the total number of reports using subtree sizes. For updates, describe how to detach and reattach nodes while maintaining subtree sizes and detecting cycles.
Address cycle detection (e.g., using visited sets or union-find), root changes, and concurrent updates. Discuss how to ensure atomicity and consistency.
Compare time and space complexity of your approach with alternatives (e.g., naive traversal vs. augmented trees). Discuss scalability and potential optimizations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.