The dependency angle is what makes this problem worth thinking about carefully.
Model tasks and subtasks as a directed acyclic graph (DAG) and compute each task's effective deadline as the minimum of its own deadline and the maximum effective deadline of its subtasks. Then use a priority queue (min-heap) to repeatedly schedule the ready task with the smallest effective deadline, updating readiness as subtasks complete. This ensures correct ordering while respecting dependencies.
Pro tip: Explicitly discuss how you would handle dynamic updates (e.g., a subtask's deadline changes) and avoid recomputing the entire graph by using incremental updates or lazy propagation. This shows you think about real-world scalability and maintainability.
Ask about the expected scale (number of tasks/subtasks), whether deadlines can change, and if cycles are possible. Confirm that a task can only be scheduled after all its subtasks are complete.
Represent tasks as a DAG. For each task, compute its effective deadline as the minimum of its own deadline and the maximum effective deadline of its subtasks (propagated bottom-up). This ensures that scheduling a task respects both its own and its subtasks' deadlines.
Use a min-heap keyed by effective deadline to select the next task to schedule. Maintain a count of incomplete subtasks per task; when a subtask completes, decrement the count and if it reaches zero, add the task to the heap.
Discuss handling cycles (detect and reject), tasks with no subtasks, and dynamic changes to deadlines or dependencies. For updates, consider incremental recomputation or lazy evaluation to avoid full graph traversal.
State time complexity: O(V + E log V) for initial computation and scheduling, where V is number of tasks and E is number of dependencies. Mention space complexity O(V + E). Discuss trade-offs between eager vs lazy deadline propagation.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.