Started with Kahn's algorithm because tracking in-degrees felt cleaner to explain out loud.
Recognize this as a topological sort problem on a directed graph. Use Kahn's algorithm (BFS with in-degree tracking) to produce a valid order and detect cycles when the output size is less than the number of tasks. Alternatively, use DFS with recursion stack for cycle detection, but Kahn's is often preferred for its simplicity and explicit cycle detection.
Pro tip: Mention that Kahn's algorithm naturally detects cycles: if the topological order doesn't include all nodes, a cycle exists. Also, clarify that multiple valid orders may exist, so any correct order is acceptable.
Confirm that tasks are nodes and dependencies are directed edges. Ask about input format (adjacency list or edge list), whether tasks are labeled, and if multiple valid orders are acceptable.
Select Kahn's algorithm (BFS-based) for its intuitive cycle detection, or DFS with recursion stack. Explain the trade-offs: Kahn's is iterative and avoids recursion depth issues; DFS can be simpler for some but requires careful cycle detection.
For Kahn's: compute in-degrees, enqueue nodes with in-degree 0, then repeatedly dequeue and reduce in-degrees of neighbors. For DFS: perform depth-first search, tracking visited and recursion stack to detect back edges.
If using Kahn's, after processing, check if the result contains all tasks; if not, a cycle exists. If using DFS, a back edge indicates a cycle. Report the DAG as invalid in either case.
State time complexity O(V+E) and space O(V+E). Discuss edge cases: empty graph, single node, disconnected components, and self-loops.
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This one tripped me up more than I expected.
First, clarify the task dependency model and whether the worker pool should be static or dynamic. Then, describe a topological sort with in-degree tracking to identify ready tasks, and batch them into groups of up to k for parallel execution. Finally, explain how to handle dynamic insertion by updating dependencies and re-evaluating ready tasks without restarting the entire process.
Pro tip: Emphasize that the batch size should be min(k, number of ready tasks) to avoid underutilization, and discuss how dynamic insertion can be handled with a thread-safe queue and condition variables to wake up idle workers.
Ask about the task graph structure (DAG?), whether tasks have uniform execution time, and if dynamic insertion can add dependencies to existing tasks. This shows you think about edge cases before diving into the solution.
Explain that you'll use a worker pool of size k and a thread-safe ready queue. Use topological sort with in-degree counts to identify tasks with no pending dependencies, and batch them into groups of up to k for simultaneous execution.
Describe how to integrate new tasks: update the dependency graph, adjust in-degrees, and if a new task has no dependencies, add it to the ready queue. Use synchronization primitives like mutexes and condition variables to safely notify workers.
Compare static batching vs. dynamic scheduling, and mention potential bottlenecks like lock contention. Suggest optimizations such as work-stealing or using a concurrent queue to improve throughput.
Recap the approach, highlighting how it ensures correctness and scalability. Ask if the interviewer wants to dive deeper into any specific aspect, showing collaborative problem-solving.
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