The core trap I nearly fell into was treating this like an undirected graph problem.
Model the schedule as a temporal graph where nodes are (station, time) pairs and edges represent train rides or waiting. Use BFS or DFS to explore reachable states from the start, checking if any state has the destination station. Discuss time complexity and potential optimizations like interval merging or priority queues.
Pro tip: Clarify assumptions about waiting at stations and whether schedules are periodic or one-time. Mention that in real systems, you'd preprocess schedules into a graph or use time-expanded networks for efficient queries.
Ask about schedule format, waiting rules, and whether multiple routes can be combined. Confirm if time is discrete or continuous and if stations are uniquely identified.
Represent each (station, time) as a node. Add edges for train rides (from departure to arrival) and waiting (from time t to t+1 at same station). This captures all possible actions.
Use BFS or DFS to explore reachable nodes from (start, 0). BFS is natural if we want earliest arrival; DFS is simpler if only reachability matters.
Discuss time complexity O(N) where N is total schedule events. Suggest optimizations like merging waiting edges or using interval trees to skip redundant checks.
Consider start equals destination, no routes, unreachable destination, and cycles. Ensure algorithm terminates and handles large time values efficiently.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Thought about this for a second and said something like 'a state is just a station' and the interviewer pushed back immediately.
Define the state as a tuple of (current station, time) and model waiting as self-loop edges with a cost equal to the wait duration. Then discuss how to handle continuous time by discretizing into time steps or using event-based simulation, and analyze the trade-offs between state space size and accuracy.
Pro tip: Mention that waiting can be modeled as zero-cost self-loops if time is not part of the state, but that including time is necessary to capture schedule constraints; then propose a hybrid approach where you only include time when it affects reachability.
Start with a simple state representation: (station, time) where time can be discrete (e.g., minutes since midnight) or continuous. Explain that station alone is insufficient because waiting depends on time.
Add self-loop edges at each station that advance time by a wait duration. If time is discrete, these are edges to (station, t+1); if continuous, they are intervals or events.
Add edges for train departures: from (station, t) to (next_station, t+travel_time) if a train departs at or after t. This creates a time-expanded graph.
Discuss how the state space grows with number of stations and time granularity. Compare explicit time-expanded graph vs. implicit event-based search (e.g., Dijkstra on events) to reduce memory.
Propose optimizations like pruning unreachable states, using interval-based waiting, or applying A* with a heuristic. Validate by checking reachability on small examples.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Rattled off the edge cases pretty well: start equals destination, stations visited multiple times on the same route, trains that loop back.
Start by clearly stating the time and space complexity of your solution using Big-O notation, then explain how you derived it. Next, enumerate the edge cases you considered and how your solution handles them, emphasizing robustness and practical applicability.
Pro tip: Relate the complexity to real-world ML constraints (e.g., dataset size, latency requirements) and mention any trade-offs you made between time and space. Also, proactively discuss how you would test edge cases, showing a testing mindset.
Clearly state the time and space complexity of your solution in Big-O notation, specifying whether it's average or worst-case.
Briefly explain how you arrived at the complexity, referencing key operations (e.g., loops, recursion, data structure operations).
List the edge cases you considered (e.g., empty input, single element, large input, duplicates, invalid data) and how your solution handles them.
Mention any trade-offs between time and space complexity, and why you chose this approach over alternatives.
Relate the complexity and edge cases to ML engineering scenarios, such as scalability, real-time inference, or data preprocessing.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Standard follow-up, just track parent pointers per state.
Explain that the core modification is to track the predecessor of each visited node during the search, then reconstruct the path by backtracking from the target to the source. Emphasize that this works for both BFS and DFS, but the choice of algorithm affects whether the returned path is shortest. Keep the explanation concise and focus on the data structure changes needed.
Pro tip: Mention that if the graph is unweighted, BFS guarantees the shortest path, while DFS does not; if weighted, you'd need Dijkstra or A* with parent tracking. This shows you understand the trade-offs and can adapt the solution to different scenarios.
Ask whether the graph is unweighted or weighted, and whether the path needs to be shortest. This determines whether BFS, DFS, or a weighted algorithm like Dijkstra is appropriate.
During traversal, maintain a dictionary mapping each visited node to the node from which it was discovered. This records the path implicitly.
Once the target is found, backtrack from the target using the parent map until the source is reached, then reverse the sequence to get the path from source to target.
Discuss what happens if no path exists (return empty list or None), and analyze time and space complexity: O(V+E) for traversal plus O(length of path) for reconstruction.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the problem context: what are 'trains' and how are timestamps used? Then, systematically compare the implications of arbitrary timestamps versus route-index-based time across data structures, algorithms, and system design. Finally, discuss trade-offs and potential solutions, emphasizing the impact on ML pipelines and real-time constraints.
Pro tip: Tie your answer back to ML engineering at Glean: arbitrary timestamps introduce non-stationarity and irregular sampling, which affect feature engineering, model retraining, and online serving. Mention concrete techniques like time-window aggregation and event-time processing with watermarking.
Ask clarifying questions to understand what 'trains' and 'timestamps' refer to in this context (e.g., event streams, scheduling, or data pipelines). Confirm whether timestamps are event times or processing times.
Contrast route-index-based time (sequential, predictable) with arbitrary timestamps (non-monotonic, irregular, possibly out-of-order). Highlight how this affects ordering, windowing, and joins.
Discuss changes needed in algorithms: sorting, merging, interval queries, and time-series models. Consider complexity shifts from O(1) index lookups to O(log n) or O(n) timestamp searches.
Explain effects on data pipelines (late data, watermarks), feature stores (point-in-time correctness), and model training (temporal leakage, non-stationarity). Mention trade-offs in latency, accuracy, and complexity.
Suggest approaches like event-time processing, timestamp-based indexing, and robust time-series models. Summarize trade-offs between simplicity, scalability, and correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.