BFS felt like the right call immediately and it was.
Clarify the problem constraints (e.g., matrix size, start/end values) and then propose BFS as the optimal solution since all moves have equal cost. Explain how to handle 8-directional movement and avoid revisiting cells, and analyze time and space complexity.
Pro tip: Mention that BFS guarantees the shortest path in an unweighted graph, and proactively discuss edge cases like unreachable destination or start/end being blocked. This shows thoroughness and prevents follow-up questions.
Ask about matrix dimensions, whether start and end are always 0, and if diagonal moves are allowed through corners. Confirm that each move costs 1.
Explain that BFS is ideal because it explores level by level, guaranteeing the shortest path in an unweighted grid. Mention that DFS would not guarantee shortest path.
Initialize a queue with the start cell and a visited set. For each cell, explore all 8 neighbors that are within bounds, have value 0, and are unvisited; mark visited and enqueue. Track distance or use level-order traversal.
Check if start or end is blocked (value 1) and return -1. Also handle cases where the destination is unreachable.
Time complexity is O(R*C) since each cell is visited at most once. Space complexity is O(R*C) for the queue and visited set in the worst case.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Treat the problem as online graph exploration with no prior map, using a systematic traversal strategy like spiral or wall-following with backtracking to ensure full coverage. Emphasize that the robot must maintain its own state (position and orientation) and use a stack to backtrack when stuck, while handling obstacles and avoiding infinite loops.
Pro tip: Mention that in practice, you'd augment the algorithm with sensor fusion or SLAM for robustness, but for this problem, assume perfect odometry and focus on the traversal logic. Also, discuss trade-offs between coverage time and memory usage.
Ask about the robot's movement primitives (e.g., move forward one cell, turn 90 degrees), whether it can detect obstacles, and if it can track its position relative to start. Confirm that the room is bounded and connected.
Select a systematic exploration method such as spiral search, wall-following (e.g., always keep right), or depth-first search with backtracking. Justify why it guarantees coverage.
Outline how the robot maintains its position, orientation, and a stack of visited cells for backtracking. Describe how it decides the next move based on sensor input and coverage status.
Prove that the algorithm visits every reachable cell and terminates. Discuss time complexity (e.g., O(N) moves for N cells) and space complexity (e.g., O(N) for the stack).
Mention potential improvements like using a heuristic to reduce backtracking, or handling dynamic obstacles. Compare with alternative approaches like random walk (not guaranteed) or SLAM-based mapping.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.