My first instinct was to just iterate over every robot cell and scan outward in four directions each time.
Clarify the problem constraints and edge cases, then propose an efficient solution using precomputed directional distances. Discuss trade-offs between time and space complexity, and outline how to handle large grids.
Pro tip: Mention that you can precompute distances in O(mn) time using dynamic programming, and emphasize the importance of handling obstacles and boundaries uniformly to avoid off-by-one errors.
Ask questions to confirm the grid dimensions, obstacle representation, and whether the distance array is given for a specific robot or is a target profile. Ensure understanding of 'nearest obstacle' including boundaries.
Propose computing the distance to the nearest obstacle in each direction for every cell using dynamic programming. Then compare each robot's distances to the target profile.
State that the solution runs in O(mn) time and O(mn) space, which is optimal for this problem. Discuss potential optimizations if memory is a concern.
Consider grids with no obstacles, all obstacles, or robots on boundaries. Ensure the algorithm correctly treats boundaries as obstacles.
Walk through a small example to verify the logic, such as a 3x3 grid with a central robot and obstacles around, and check that the distances match the profile.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.