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Databricks·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Databricks software engineer interview with a grid-based pathfinding problem that looked deceptively clean on the surface but had enough edge cases to keep you busy for a while. The twist of handling multiple transport modes with separate time and cost constraints made it more interesting than a standard BFS.

Questions Asked (1)

Q1

Given a 2D city grid where each cell is labeled with a transport mode (walk, bike, car, train), blocked cells, a start, and a destination, find the fastest transport mode from start to destination. Each mode can only traverse cells matching its own label. Break ties in minimum time by minimum total cost.

Algorithms & Data StructuresSystem Design
Author's notes

The problem reads like a normal BFS grid question until you realize each transport mode is essentially its own separate graph traversal.

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AI HintsAI Generated

Suggested Approach

Model the grid as a graph where each cell is a node, and edges connect adjacent cells with the same transport mode. For each mode, run a shortest path algorithm (e.g., Dijkstra) from start to destination, considering time as primary weight and cost as secondary. Compare the results across modes and select the one with minimum time, breaking ties by minimum cost.

Pro tip: Clarify upfront whether the mode is fixed for the entire trip or can change per cell; if it can change, the problem becomes a multi-layer graph where each layer represents a mode, and you must account for switching costs or constraints.

1. Clarify problem constraints

Ask about mode switching, tie-breaking rules, movement directions, and whether time/cost are per-cell or per-edge. Confirm if blocked cells are impassable for all modes.

2. Model as a graph

Represent each cell as a node. For each mode, create edges between adjacent cells that share the same mode. If mode switching is allowed, use a multi-layer graph with inter-layer edges.

3. Choose and justify algorithm

Use Dijkstra's algorithm for each mode (or on the multi-layer graph) with a composite key (time, cost). Explain why BFS is insufficient if edge weights vary.

4. Handle tie-breaking and compare results

For each mode, compute the optimal path. Compare modes by minimum time, then by minimum cost. Return the best mode and optionally the path.

5. Analyze complexity and edge cases

Discuss time and space complexity. Address unreachable destination, multiple optimal paths, and large grids. Suggest optimizations like bidirectional search or A* if needed.

Key Points to Mention

  • Graph representation: cells as nodes, adjacency based on same transport mode.
  • Dijkstra's algorithm with a priority queue keyed by (time, cost) for lexicographic ordering.
  • Multi-layer graph if mode switching is allowed, with switching costs or constraints.
  • Tie-breaking: compare modes by time first, then cost; ensure the algorithm respects this.
  • Complexity: O(M * N log(MN)) per mode, where MxN is grid size; space O(MN).
  • Edge cases: start/destination blocked, no path, multiple modes with same time but different costs.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.