I went with DFS and precomputed parent pointers plus subtree sizes during the build phase, which felt right.
Preprocess the hierarchy using an Euler tour to assign entry/exit times and depths, enabling O(1) ancestor checks and LCA queries via RMQ or binary lifting. For subtree size, compute during a DFS. Then answer each query in O(1) or O(log n) time, and clearly state the trade-offs between preprocessing time and query time.
Pro tip: Mention that the hierarchy may be a forest, so handle multiple roots by adding a virtual super-root or processing each tree separately. Also, discuss how to handle dynamic updates if the hierarchy changes, showing awareness of real-world scenarios.
Ask about the size of the hierarchy, query frequency, whether the hierarchy is static or dynamic, and if it's a tree or forest. Confirm the expected time complexity for queries.
Select an approach: Euler tour + RMQ for LCA, binary lifting for ancestor queries, and subtree sizes via DFS. For forests, add a virtual root or process each tree independently.
For manager chain: use binary lifting to jump up. For LCA: use Euler tour + RMQ or binary lifting. For reports count: use precomputed subtree sizes.
State preprocessing time O(n log n) or O(n), query time O(1) or O(log n), and space O(n log n) or O(n). Compare trade-offs between different methods.
Mention handling dynamic updates (e.g., link-cut trees), memory constraints, and alternative approaches like heavy-light decomposition for path queries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.