I jumped straight to BFS which was right, but I fumbled the neighbor enumeration early on.
Start by clarifying the problem constraints (e.g., grid size, movement allowed, path definition) and then explain the BFS approach: use a queue to explore cells level by level, track visited cells, and store parent pointers to reconstruct the shortest path. Walk through a small example to demonstrate correctness and discuss time/space complexity.
Pro tip: Mention that BFS guarantees the shortest path in unweighted grids, and proactively discuss edge cases like unreachable target, start equals target, and large grids to show thoroughness.
Ask about grid dimensions, movement directions (4-way or 8-way), whether diagonal moves are allowed, and what constitutes a valid path. Confirm that the grid contains only walls and open cells.
Explain that BFS explores cells in increasing distance from the start, ensuring the first time the target is reached, the path is shortest. Use a queue for traversal and a visited set or matrix to avoid cycles.
Describe how to store parent pointers (or previous cell coordinates) for each visited cell. Once the target is found, backtrack from target to start to build the path.
State that time complexity is O(R*C) and space complexity is O(R*C) for the queue and visited structures. Discuss edge cases: start equals target, target unreachable, and empty grid.
Trace BFS on a small grid (e.g., 3x3) to show how the queue evolves and how the path is reconstructed. This demonstrates understanding and catches off-by-one errors.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
They asked this almost as a checklist thing.
Start by clarifying the problem constraints and defining the expected behavior for each edge case. Then systematically walk through each scenario, explaining how your algorithm handles it, and if necessary, propose modifications to ensure correctness and efficiency.
Pro tip: Demonstrate proactive thinking by mentioning that you would write unit tests for these edge cases before coding the solution. This shows you prioritize robustness and test-driven development, which is highly valued at Meta.
Ask the interviewer about the maze representation, movement rules, and expected output for edge cases. Confirm whether start and target are guaranteed to be valid and distinct.
Explicitly state what should happen when start equals target (return 0 or empty path), when the maze is fully blocked (return -1 or no path), and when start or target is a wall (return -1 or handle as invalid input).
Explain how your chosen algorithm (e.g., BFS, DFS, A*) can incorporate early checks for these conditions to avoid unnecessary computation or errors.
Mention that you would write unit tests for these edge cases to ensure the solution behaves as expected and to catch regressions.
Conclude by emphasizing the importance of handling edge cases in production code and how this reflects good software engineering practices.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Said Dijkstra, explained the priority queue swap.
Acknowledge that the problem shifts from BFS to a shortest-path algorithm like Dijkstra's, then discuss the trade-offs between different approaches (e.g., Dijkstra vs. A* vs. Bellman-Ford) based on edge weight properties. Emphasize the need to adapt the data structures (e.g., priority queue) and analyze time/space complexity.
Pro tip: Mention that if edge weights are small integers, you can use Dial's algorithm (bucket queue) for O(V+E) time, showing depth beyond standard Dijkstra. Also, clarify whether negative weights exist, as that would require Bellman-Ford.
Recognize that uniform costs allowed BFS, but weighted edges require a shortest-path algorithm that accounts for varying costs.
Select Dijkstra's algorithm for non-negative weights, A* if a heuristic is available, or Bellman-Ford if negative weights exist. Justify your choice.
Replace the simple queue with a priority queue (min-heap) for Dijkstra, or use a bucket queue if weights are small integers.
Compare time and space complexity of the chosen algorithm (e.g., Dijkstra with binary heap: O((V+E) log V)) and discuss potential optimizations.
Address scenarios like negative weights, zero-weight edges, or large graphs, and how they affect algorithm choice and implementation.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where the conversation got interesting.
Start by acknowledging that memory is the bottleneck and propose memory-efficient strategies like iterative deepening or external memory algorithms. Then compare A* with a heuristic and bidirectional BFS in terms of memory usage, time complexity, and practical applicability, emphasizing trade-offs. Conclude with a recommendation based on the maze's characteristics and available resources.
Pro tip: Mention that bidirectional BFS can be more memory-efficient than A* when the branching factor is high, but A* with a good heuristic often explores fewer nodes. Also, consider using a memory-bounded variant like IDA* to combine the benefits of A* with low memory.
Discuss how large mazes can exceed available memory, leading to swapping or out-of-memory errors. Mention that the frontier (open set) and visited set are the main memory consumers.
Explain that A* stores all generated nodes in memory, which can be prohibitive. However, a good heuristic reduces the number of expanded nodes, potentially saving memory. Mention that memory usage is O(b^d) in the worst case.
Explain that bidirectional BFS expands from both start and goal, potentially reducing the search depth and thus memory. However, it still stores visited nodes from both directions, and memory can be high if the frontiers meet late.
Compare time and memory: A* with a strong heuristic often explores fewer nodes but may still use significant memory; bidirectional BFS can reduce time but may use more memory due to two frontiers. Discuss when each is preferable.
Suggest algorithms like IDA* (Iterative Deepening A*) which uses less memory, or external memory algorithms that store data on disk. Also mention using a memory-bounded heuristic search like SMA*.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.