Clarify the problem constraints (grid size, movement directions, whether diagonal moves are allowed) and then choose an appropriate search algorithm such as BFS or DFS. Implement the search while tracking visited cells to avoid cycles, and return the path once the goal is reached.
Pro tip: In an ML engineering interview at Meta, emphasize that BFS guarantees the shortest path in unweighted grids, which is often preferred, and discuss how this problem relates to pathfinding in reinforcement learning or robotics.
Ask about grid dimensions, movement rules (4-directional or 8-directional), and whether the path needs to be shortest or any valid path suffices.
Select BFS for shortest path or DFS for any path, considering trade-offs in time and space complexity.
Use a queue (BFS) or stack (DFS) to explore cells, marking visited cells and storing parent pointers to reconstruct the path.
Once the goal is found, backtrack using parent pointers to build the path from start to goal, and return it.
State time and space complexity: O(R*C) for both, where R and C are grid dimensions, and discuss potential optimizations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the modified movement rules (e.g., one-way passages, weighted cells) and the objective (e.g., minimize cost, maximize reward). Then, model the maze as a graph where nodes are cells and edges represent allowed movements with associated costs or constraints, and apply an appropriate shortest-path algorithm like Dijkstra's or A* with necessary modifications. Finally, discuss trade-offs between different algorithms and optimizations for large-scale mazes.
Pro tip: Demonstrate awareness of real-world constraints by mentioning how these modifications affect algorithm choice and performance, and propose hybrid approaches (e.g., A* with heuristics) to balance optimality and efficiency.
Ask clarifying questions to understand the exact movement rules (e.g., one-way passages, weighted cells) and whether the goal is to minimize cost, maximize reward, or find any path. Confirm if weights are positive or can be negative.
Represent the maze as a graph: each cell is a node, and allowed movements are directed edges with weights (costs) based on cell weights or passage constraints. For one-way passages, ensure edges are directed accordingly.
Choose a shortest-path algorithm: Dijkstra's for non-negative weights, Bellman-Ford for negative weights, or A* with an admissible heuristic for efficiency. Adapt the algorithm to handle directed edges and weighted nodes (e.g., add node weights to edge costs).
Discuss time and space complexity of the chosen algorithm, and compare alternatives (e.g., BFS for unweighted, Dijkstra vs. A*). Mention potential optimizations like bidirectional search or early termination.
Outline test cases: simple mazes, cycles, negative weights (if allowed), and edge cases like unreachable targets. Validate correctness and performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The wall-breaking variant is basically LC 1293 and I'd seen it before, so I knew the state had to be (cell, walls_remaining) not just the cell.
Model the problem as a state-space search where each state includes position, keys collected, and walls broken. Use BFS for unweighted shortest path, or 0-1 BFS/Dijkstra if breaking walls has a cost, and discuss trade-offs between state space size and optimality.
Pro tip: Clarify constraints early (grid size, number of keys, k value) to choose the right algorithm; mention that for small k, BFS with state (r, c, keys, broken) is fine, but for large k, consider A* with a heuristic or bidirectional search to prune the state space.
Ask whether keys are reusable, if multiple keys of same type exist, and the maximum grid size, number of keys, and k. This determines whether BFS, 0-1 BFS, or Dijkstra is appropriate.
Encode state as (row, col, key_bitmask, walls_broken). Use a bitmask for keys if the number of key types is small (≤20). For walls broken, if k is small, include it as a dimension; otherwise, treat it as a cost.
If all moves have equal cost, use BFS. If breaking a wall costs 1 and moving costs 0, use 0-1 BFS with a deque. If costs vary, use Dijkstra. For large state spaces, consider A* with a heuristic like Manhattan distance to the goal.
When encountering a door, only pass if the corresponding key is in the bitmask. When picking up a key, update the bitmask. Ensure visited states include the key bitmask to avoid revisiting with different keys.
Prune states where walls_broken > k. Discuss time/space complexity: O(R*C*2^K*(k+1)) for BFS. Mention alternatives like bidirectional BFS or A* for performance, and trade-offs between optimality and speed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.