← Snowflake Interview Insights
My first instinct was to just brute-force every person-cake pair and compute the distance.
Clarify the problem constraints (grid size, number of people/cakes) and then propose a multi-source BFS from all cakes simultaneously to compute the shortest Manhattan distance to any person. Alternatively, discuss a two-pass dynamic programming approach that computes distances in O(mn) time, which is optimal for large grids.
Pro tip: Mention that multi-source BFS is equivalent to computing the Manhattan distance transform, and that you can optimize memory by using a 2D array of integers or even a single array if the grid is stored row-major. Also, note that if the grid is extremely large and sparse, a k-d tree or sorting-based approach might be more efficient.
Ask about grid dimensions, number of people and cakes, whether movement is allowed only in 4 directions, and if there are no people or no cakes. This ensures you design the right algorithm.
For dense grids, use multi-source BFS from all cakes to compute distances to all cells, then find the minimum among people. For large grids, consider the two-pass dynamic programming (distance transform) approach which runs in O(mn) time and O(mn) space.
Code the BFS with a queue, initializing it with all cake positions. Alternatively, implement the two-pass DP: first pass from top-left to bottom-right, second pass from bottom-right to top-left, updating distances. Use early termination if a person is found at distance 0.
Explain that BFS is O(mn) time and space, and the DP approach is also O(mn) but with lower constant factors. Discuss when to use each (e.g., BFS for sparse cakes, DP for dense).
Walk through a small example to verify correctness, such as a 3x3 grid with one cake and one person. Also test edge cases like no cakes or no people.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.