I got the base BFS part fine but then just stared at the cat constraint for a bit.
Reframe the problem as finding the maximum bottleneck path, where the bottleneck is the minimum Manhattan distance to the cat along the path. Use binary search on the distance threshold and check connectivity with BFS/DFS, or use a max-heap variant of Dijkstra to directly compute the optimal path.
Pro tip: Mention that you can precompute the distance from every cell to the cat using multi-source BFS (treating the cat as the only source) to avoid recalculating Manhattan distances on the fly, which improves efficiency and simplifies the code.
Confirm the problem details: grid size, movement allowed, obstacles, and that the cat's cell is impassable. Restate the goal: maximize the minimum Manhattan distance to the cat along a path from S to T.
Recognize that the objective is to maximize the minimum value along the path, which is a classic bottleneck path problem. The value of each cell is its Manhattan distance to the cat.
Decide between binary search + BFS/DFS or a max-heap Dijkstra variant. Discuss trade-offs: binary search is simpler but may be slower; Dijkstra is more efficient but requires careful implementation.
Precompute the Manhattan distance from each cell to the cat, or use multi-source BFS if obstacles affect distance. This step ensures quick access to cell values during the main algorithm.
Implement the chosen algorithm, handle edge cases (e.g., no path, cat blocking), and test with small examples. Analyze time and space complexity.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.