I started with the heap and worked outward, which was probably the right instinct.
First, clarify the problem: the min-heap orders tasks by deadline, but dependencies mean a task is only eligible when all its dependencies are consumed. Propose a solution that tracks dependency counts and dependents, uses a ready heap for eligible tasks, and detects cycles via topological sort (Kahn's algorithm). Then discuss how to integrate this with the existing ConsumeTask() method, ensuring tie-breaking by deadline and handling cycles gracefully.
Pro tip: Mention that cycle detection should happen at task addition time to fail fast, and that the ready heap must maintain the same deadline ordering as the original heap to preserve tie-breaking behavior.
Confirm that dependencies are task IDs, tasks are consumed one at a time, and cycles should be detected and reported. Ask if dependencies can be added dynamically or are fixed at task creation.
Use a map from task ID to task, a map for dependency counts (in-degree), and a map for dependents (adjacency list). Maintain a min-heap of ready tasks (no unmet dependencies) ordered by deadline.
When consuming, pop from the ready heap. After consuming, decrement dependency counts of its dependents; if any become zero, push them into the ready heap. Ensure the heap orders by deadline to break ties.
Use Kahn's algorithm: if the number of consumed tasks is less than total tasks after processing, a cycle exists. Alternatively, perform DFS with recursion stack during initialization. Report the cycle and handle gracefully.
Consider performance (O(V+E) for cycle detection, O(log n) heap operations), memory overhead, and concurrency if tasks are added dynamically. Address edge cases like missing dependencies, self-dependencies, and empty heap.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.