Databricks·Software Engineer·Technical Phone Screen·Senior

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Jun 2026Remote

Summary

Databricks technical phone screen, one meaty graph problem that took up most of the time. The multi-modal twist is what makes it interesting, otherwise it's just shortest path.

Questions Asked (1)

Given a 2D grid with a start, a destination, open cells, and blocked cells, find the minimum-cost path where you can switch between multiple transportation modes (each with different step costs and movement constraints), and switching modes at a cell also carries a cost.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

The key insight I kept circling around was that you can't just track position, you have to track (position, current mode) as your state.

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AI HintsAI Generated

Suggested Approach

Model the problem as a shortest path search on an expanded state space where each state is (cell, mode). Use Dijkstra's algorithm to handle non-negative edge weights, including mode-switch costs. Discuss how movement constraints and mode-switch costs affect the graph and algorithm choice.

Pro tip: Clarify assumptions early: are mode-switch costs uniform? Can you switch modes only at certain cells? This shows you think about edge cases and practical constraints, which is crucial for real-world systems like Databricks.

1. Clarify problem constraints

Ask about grid size, number of modes, movement rules (e.g., 4-directional vs. 8-directional), mode-switch costs, and whether switching is allowed anywhere or only at specific cells.

2. Define state space

Represent each state as (row, col, mode). This captures both position and current transportation mode, allowing correct cost accounting for moves and switches.

3. Construct graph edges

For each state, add edges for moving to adjacent cells using the same mode (cost = mode's step cost) and for switching modes at the same cell (cost = switch cost). Ensure blocked cells are excluded.

4. Apply shortest path algorithm

Use Dijkstra's algorithm since all edge weights are non-negative. Initialize distances to infinity, set start state distance to 0, and process nodes in order of increasing distance.

5. Analyze complexity and optimizations

Time complexity is O((R*C*M) log(R*C*M)) for R rows, C columns, M modes. Discuss potential optimizations like bidirectional search or A* with a heuristic if applicable.

Key Points to Mention

State space expansion: (cell, mode) to handle mode-dependent costs and constraints.
Dijkstra's algorithm for non-negative edge weights; mention why BFS won't work if costs vary.
Mode-switch costs as additional edges; consider if switching is allowed only at certain cells.
Movement constraints: different modes may have different step costs or allowed directions.
Complexity analysis: O(R*C*M log(R*C*M)) time, O(R*C*M) space.
Edge cases: unreachable destination, start equals destination, blocked start/destination, zero-cost switches.

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