My first instinct was BFS and I started coding before fully thinking through what 'maximize the minimum distance' actually means.
Model the problem as a graph where each cell is a node, and the 'safety' of a path is the minimum distance to the cat along that path. Use binary search on the safety value combined with BFS/DFS to check if a path exists using only cells with distance to cat >= safety, or use a max-min path algorithm like Dijkstra with a modified priority (maximizing the minimum).
Pro tip: Clarify assumptions upfront: whether the cat is stationary, whether diagonal moves are allowed, and whether the cat can move. This shows you think about edge cases and problem constraints before diving into the algorithm.
Ask about grid size, movement rules (4-directional vs 8-directional), whether the cat is stationary, and if the cat can move. Confirm that the goal is to maximize the minimum distance to the cat along the path.
Run BFS from the cat's position to compute the shortest distance from every cell to the cat. This gives a distance map that will be used to evaluate path safety.
Use binary search on the safety threshold combined with BFS/DFS to check connectivity, or use a modified Dijkstra that maximizes the minimum distance. Explain the trade-offs between approaches.
Code the chosen algorithm, ensuring to handle cases where no path exists, the rat or bread is unreachable, or the cat blocks all paths. Consider obstacles and boundaries.
Discuss time and space complexity. For binary search + BFS, it's O(log(maxDist) * (R*C)). For modified Dijkstra, it's O(R*C log(R*C)). Mention potential optimizations like early termination.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.