← Databricks Interview Insights
My first instinct was to throw everything into one big multi-modal graph and run Dijkstra once.
Model the multimodal network as a time-dependent graph where each mode has its own cost function (time, distance, cost) and transfer penalties at mode-switch nodes. Then run a multi-criteria shortest path algorithm (e.g., Dijkstra with Pareto-optimal labels) to find the best route according to user preferences. Discuss scalability and how to handle dynamic updates for a production system.
Pro tip: Acknowledge that 'optimal' is subjective—clarify the objective (fastest, cheapest, greenest) and show how to parameterize the algorithm to support multiple criteria. This demonstrates product thinking and avoids over-engineering a single solution.
Ask about the objective (minimize time, cost, transfers, etc.), graph size, whether modes can be combined, and if real-time updates are needed. State assumptions to scope the problem.
Represent the city as a graph where nodes are locations and edges are mode-specific with associated costs. Add transfer edges between modes at the same location with a penalty (e.g., time to park, wait for transit).
Use Dijkstra's algorithm with a priority queue, but extend it to handle multiple criteria (e.g., Pareto-optimal labels) or use A* with a heuristic. For dynamic costs, consider time-dependent edges or contraction hierarchies.
Compare approaches: single-criterion vs. multi-criteria, exact vs. approximate, precomputation vs. on-the-fly. Address scalability (e.g., partitioning, caching) and real-time updates (e.g., incremental recomputation).
Sketch how this fits into a larger system: data ingestion (traffic, schedules), API design, user preferences, and monitoring. Mention potential use of distributed graph processing if the graph is huge.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Walked through it fine for the per-mode case.
First, clarify the definitions of 'per-mode approach' and 'combined multi-modal graph approach' to ensure alignment. Then, systematically derive time and space complexities for each, considering graph construction, traversal, and query operations. Finally, compare the trade-offs and discuss scenarios where each approach is preferable.
Pro tip: Demonstrate awareness that real-world factors like graph density, query patterns, and hardware constraints often dominate asymptotic complexity, and mention how Databricks' unified platform might influence these trade-offs.
Define what 'per-mode' and 'combined multi-modal graph' mean in this context, including assumptions about data representation and operations.
Derive time and space complexities for building and querying separate graphs for each mode, considering factors like number of modes and graph sizes.
Derive time and space complexities for building and querying a single multi-modal graph, accounting for cross-mode edges and unified traversal.
Compare the complexities, highlighting scenarios where one approach outperforms the other in terms of time, space, or scalability.
Discuss real-world implications such as query flexibility, maintenance overhead, and suitability for Databricks' distributed environment.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This one tripped me up more than it should have.
Clarify what 'equivalent' means and the data types involved, then propose a hash-based approach (e.g., hash set or hash map) to achieve O(n) average time. Discuss trade-offs like hash collisions, memory usage, and worst-case O(n) with perfect hashing or balanced trees.
Pro tip: Mention that while hash-based deduplication is O(n) on average, worst-case can degrade to O(n^2) with many collisions; suggest using a cryptographic hash or a balanced BST if worst-case guarantees are needed, but note that BST gives O(n log n).
Ask the interviewer to define 'equivalent' (e.g., exact match, custom equality) and confirm that sorting is not allowed. Also check if additional memory is permitted.
Propose using a hash set (or hash map) to track seen elements. For each element, compute its hash and check for existence; if not present, add it to the set and output it.
Explain that hash collisions are resolved via equals() or a custom comparator. For complex objects, ensure hashCode() and equals() are consistent.
State that average time is O(n) with O(n) extra space. Acknowledge worst-case O(n^2) due to collisions, but note that good hash functions make this unlikely.
Mention that if worst-case O(n) is required, perfect hashing or a trie (for strings) could be used, but they may have limitations. Compare with sorting-based O(n log n) approach.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Pretty much a 'did you think about this' check.
Start by clarifying the problem context—likely a graph-based routing or pathfinding scenario with multiple modes (e.g., walking, driving, transit). Then systematically address each edge case: unreachable modes, equal-cost paths, and prohibited transfers, explaining how to detect and handle them in the algorithm. Emphasize robustness, correctness, and trade-offs between simplicity and performance.
Pro tip: Show that you think about edge cases upfront by designing the data model and algorithm to handle them naturally, rather than patching them later. Mention that you'd write unit tests for each edge case to ensure correctness.
Ask questions to understand the graph structure, mode definitions, cost functions, and transfer rules. Confirm whether modes are nodes, edges, or separate layers.
Detect unreachable modes by checking connectivity or running a reachability analysis. Decide whether to exclude them, return an error, or provide a fallback (e.g., default mode).
Define a tie-breaking strategy (e.g., prefer fewer transfers, faster mode, or lexicographic order) and implement it consistently in the priority queue or comparison function.
Model transfer restrictions as constraints in the graph (e.g., disallow certain edges or add penalty costs). Ensure the algorithm respects them during path exploration.
Write unit tests for each edge case and use property-based testing to ensure the algorithm behaves correctly under various scenarios.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.