← Databricks Interview Insights
Start by clarifying the problem constraints: whether edge weights are non-negative, if the graph is static or dynamic, and the expected scale. Then, propose Dijkstra's algorithm with a priority queue for non-negative weights, and discuss optimizations like A* with a heuristic or bidirectional search for large graphs. Finally, address practical considerations such as memory usage, parallelism, and handling real-time updates.
Pro tip: Mention that for very large graphs, you might use contraction hierarchies or goal-directed techniques like A* to reduce the search space, and note that Databricks' distributed computing could parallelize the algorithm across partitions.
Ask about graph size, edge weight properties (non-negative?), static vs. dynamic, and whether preprocessing is allowed. This shows you consider practical constraints before jumping to a solution.
For non-negative weights, Dijkstra's algorithm is optimal. If weights can be negative, Bellman-Ford is needed. For large graphs, consider A* with a heuristic or bidirectional Dijkstra.
Use a priority queue (min-heap) for efficient extraction of the minimum distance node. Discuss using a Fibonacci heap for theoretical improvement or a binary heap for practical performance.
For massive graphs, discuss partitioning, parallelization (e.g., using Spark), or preprocessing techniques like contraction hierarchies. For dynamic graphs, consider incremental algorithms.
State time complexity O((V+E) log V) with a binary heap, and space complexity O(V). Compare with alternatives like A* (faster with good heuristic) and Bellman-Ford (O(VE)).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where it got interesting and also where I started to sweat a little.
Start by framing the problem as multi-objective shortest path, then discuss two main strategies: scalarization (weighted sum) and Pareto-optimal approaches (e.g., multi-criteria Dijkstra). Explain trade-offs between them, and mention practical considerations like dynamic weights and scalability.
Pro tip: Show awareness that in real systems like Databricks, you often need to balance latency and cost, so being able to tune weights or maintain a Pareto frontier is key. Also, mention that the choice depends on whether the user wants a single best path or a set of trade-off options.
Identify the competing criteria (e.g., time, transfers) and whether they are additive, multiplicative, or have hard constraints. Ask if the goal is a single optimal path or a set of Pareto-optimal paths.
Decide between scalarization (combine criteria into a single weight) or multi-criteria optimization (maintain Pareto frontier). Discuss pros and cons: scalarization is simple but requires weight tuning; Pareto methods are more informative but computationally heavier.
For scalarization, modify edge weights to a weighted sum and run Dijkstra. For Pareto, extend Dijkstra to store non-dominated labels per node, pruning dominated paths.
Discuss how the number of criteria affects complexity. For Pareto, the frontier size can grow exponentially; suggest pruning, approximation, or using A* with heuristics. Mention parallelization or incremental updates if graph is large.
Propose metrics to evaluate solutions (e.g., hypervolume, user satisfaction). Suggest A/B testing or simulation to tune weights or select the best trade-off based on user feedback.
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Didn't see this one coming in the way they framed it.
Start by clarifying that this is a time-dependent graph problem where edge weights are functions of time, so the graph is dynamic. Then discuss modeling approaches such as time-expanded graphs or time-dependent edge weight functions, and algorithms like time-dependent Dijkstra that respect FIFO property. Finally, address practical system design considerations like schedule data representation, caching, and real-time updates.
Pro tip: Mention the FIFO property (waiting longer never gets you there earlier) and how it's required for Dijkstra to work correctly; also note that if the graph is not FIFO, you may need to use time-expanded graphs or more complex algorithms. This shows depth and avoids a common pitfall.
Ask whether edge weights are deterministic functions of time (e.g., schedules) or stochastic, and whether the graph is static otherwise. Confirm if the goal is to find shortest paths at a given departure time or across all times.
Represent each edge weight as a function w(e, t) giving travel time if departing at time t. Alternatively, use a time-expanded graph where each node is duplicated per time step, converting time-dependent edges into static edges between time layers.
For time-dependent graphs with FIFO property, use a time-dependent variant of Dijkstra where the priority queue key is arrival time. For non-FIFO or schedule-based, consider time-expanded graphs with standard Dijkstra or A*.
Discuss how to store and query schedule data efficiently (e.g., GTFS format, interval trees), handle real-time updates (e.g., delays), and cache frequent queries. Consider scalability for large graphs.
Compare time-expanded vs. time-dependent approaches in terms of memory, preprocessing, and query speed. Mention extensions like multi-modal routing, dynamic updates, or handling uncertainty.
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Start by clarifying the requirements and constraints, such as scale, latency, and consistency needs, then propose a high-level architecture that ingests real-time events and updates routes dynamically. Discuss trade-offs between different approaches, focusing on how Databricks' strengths (e.g., Spark, Delta Lake, MLflow) can be leveraged for real-time data processing and machine learning.
Pro tip: Emphasize the importance of handling late or out-of-order events and ensuring idempotency, as these are common pitfalls in real-time systems. Also, mention how you would monitor and evaluate the system's performance and adapt to changing conditions.
Ask questions to understand the scale (number of vehicles, events per second), latency requirements (how quickly routes must update), and consistency needs (e.g., exactly-once processing).
Outline a system that ingests real-time data (e.g., from Kafka), processes it (e.g., using Spark Structured Streaming), and updates routes (e.g., via a routing service). Mention how Databricks services can be integrated.
Explain how to handle events like delays or closures: use stream processing to detect anomalies, trigger re-routing algorithms, and push updates to clients. Discuss state management and fault tolerance.
Discuss trade-offs between latency and accuracy, cost, and complexity. Mention optimizations like caching, incremental computation, and using ML models for prediction.
Describe how to monitor system health, collect metrics, and iterate. Highlight the importance of testing with simulated failures and gradually rolling out changes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.