My first instinct was Dijkstra but then I realized the waiting mechanic made it weird.
Model the problem as a graph where each stop is a node and edges represent either staying on the same train (to the next stop) or transferring to another train at the same station if the departure time is after arrival. Use a time-dependent shortest path algorithm like Dijkstra with priority queue ordered by arrival time, relaxing edges only if they lead to an earlier arrival. Return the earliest arrival at the destination.
Pro tip: Clarify assumptions upfront: whether transfers are allowed, if there's a minimum transfer time, and if the input is static or streaming. This shows you think about real-world constraints and scalability, which is crucial for ML engineers at Glean.
Ask about transfer rules, minimum transfer time, input size, and whether itineraries are static or dynamic. This ensures you're solving the right problem and demonstrates thoroughness.
Represent each stop as a node and create edges for consecutive stops on the same train (with travel time) and for transfers between trains at the same station (if departure >= arrival + min transfer time).
Use Dijkstra's algorithm with a priority queue keyed by arrival time, starting from the start station at the given start time. Alternatively, use a time-expanded graph or label-setting algorithm for time-dependent networks.
When relaxing edges, only consider departures that occur after the current arrival time. For transfers, find the earliest departure from the station after arrival (using binary search on sorted departure times).
Discuss time complexity (e.g., O(E log V) with E edges and V nodes) and potential optimizations like pre-sorting departures, using A* with a heuristic, or parallelizing for large datasets.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the data structures used in the previous solution (e.g., graph of stations, schedules, and algorithm like Dijkstra or BFS). Then, augment the algorithm to store predecessor information and event details (train, wait, transfer) at each step. Finally, backtrack from the destination to reconstruct the full itinerary and format it for printing.
Pro tip: Mention that you would store the path as a list of events (e.g., 'board train X at time T', 'wait until T2', 'transfer to train Y') rather than just stations, to capture all required details. Also, discuss how to handle ties or multiple optimal paths by defining a clear tie-breaking rule.
Briefly restate the algorithm and data structures used to find the optimal route (e.g., Dijkstra with time-dependent edges). Confirm assumptions about input format and constraints.
Modify the algorithm to record, for each visited node, the predecessor node and the action taken (which train, wait time, transfer). Use a dictionary or array to store this metadata.
Starting from the destination, follow the predecessor pointers back to the source, collecting events in reverse order. Then reverse the list to get the chronological itinerary.
Iterate through the events and print each station, time, train taken, waits, and transfers in a clear, readable format. Ensure all required details are included.
Mention memory overhead of storing metadata, handling of multiple optimal paths, and how the approach scales with large networks. Also address potential issues like cycles or unreachable destinations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.