The no-AI constraint on Q1 felt like a vibe check more than anything.
Clarify the problem constraints (grid size, movement allowed, path definition) and then implement BFS from the start to the goal, tracking parent pointers to reconstruct the shortest path. Explain the algorithm's time and space complexity and discuss potential optimizations or edge cases.
Pro tip: Mention that BFS guarantees the shortest path in unweighted grids, and proactively discuss how you would handle very large grids (e.g., using bidirectional BFS or A* with Manhattan distance) to show depth beyond the basic solution.
Ask about grid size, allowed moves (4-directional vs 8-directional), whether diagonal moves have different costs, and what to return if no path exists. Confirm that the path should be a list of coordinates.
Select BFS because it finds the shortest path in an unweighted grid. If the grid is very large, consider bidirectional BFS or A* with Manhattan distance as a heuristic.
Use a queue to explore cells level by level, a visited set to avoid revisiting, and a parent map to record how each cell was reached. When the goal is found, backtrack from the goal to the start to build the path.
State that time and space complexity are O(R*C) for an R x C grid. Discuss edge cases: start equals goal, no path exists, start or goal is a wall, and grid boundaries.
Walk through a small example to verify correctness. Mention possible optimizations like early exit when the goal is dequeued, using a 1D array for visited, or switching to A* for performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify that the maze is unweighted (or treat it as such) and that 'shortest' means minimum number of steps. Then, modify BFS to record all predecessors for each node when a shortest path is found, and finally backtrack from the goal to reconstruct all paths. Discuss complexity and potential optimizations like bidirectional BFS.
Pro tip: Mention that the number of shortest paths can be exponential, so returning all paths may be impractical; instead, you can return the count or a compressed representation. This shows awareness of real-world constraints.
Confirm that the maze is a grid with obstacles, movement is in 4 directions (or 8), and 'shortest' means minimum number of steps. Ask if all paths need to be explicitly listed or if a count is sufficient.
Explain that BFS is ideal for unweighted graphs to find shortest distances. Run BFS from start to compute distances to all reachable cells.
During BFS, for each cell, maintain a list of predecessors that lead to it via a shortest path. When exploring neighbors, if a neighbor is unvisited or at the same distance level, add the current cell as a predecessor.
After BFS, start from the goal and recursively (or iteratively) backtrack using the predecessor lists to build all paths from start to goal. Use DFS with memoization or iterative stack to avoid recursion depth issues.
Discuss time and space complexity: O(V+E) for BFS plus O(P * L) for output, where P is number of paths and L is path length. Mention edge cases: no path, start equals goal, multiple paths due to cycles of same length.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I went with weighted cells and picked Dijkstra.
Choose one meaningful extension (e.g., weighted movement costs) and clearly define how it changes the problem. Then compare BFS, Dijkstra, and A* based on the new problem characteristics, justify your algorithm choice with complexity and optimality arguments, and outline how you would implement and test it.
Pro tip: Tie your choice to the specific extension: for weighted costs, Dijkstra or A* is appropriate; for multiple goals, consider multi-source BFS or A* with a heuristic to the nearest goal. Mention that A* requires an admissible heuristic to guarantee optimality, and that in ML engineering, the same trade-offs appear in graph-based models and search problems.
Pick one extension (e.g., weighted movement costs) and precisely describe how it modifies the maze: edges have non-negative weights, or teleporters add zero-cost edges, or multiple goals exist.
Determine if edge weights are uniform or non-uniform, if the graph is unweighted or weighted, and if there are multiple targets. This dictates which algorithms are applicable.
Evaluate BFS, Dijkstra, and A* against the new problem: BFS works for unweighted graphs; Dijkstra handles non-negative weights; A* adds a heuristic for faster search when a good heuristic exists.
Select the most suitable algorithm and justify it with complexity, optimality, and practical considerations (e.g., memory, heuristic availability).
Briefly describe how you would implement the chosen algorithm and test it with edge cases (e.g., unreachable goals, zero-weight edges).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem variant (e.g., dynamic walls or batched queries) and state assumptions. Then outline an algorithm that handles the changes efficiently, analyze its time and space complexity, and describe a validation strategy that combines automated testing with manual reasoning, especially when AI-generated code is involved.
Pro tip: Emphasize that you treat AI-generated code as a draft: you always write unit tests for edge cases and manually trace the algorithm on small examples to catch subtle bugs. This shows you're both efficient and rigorous.
Ask clarifying questions to pin down the variant: do walls change over time (dynamic) or are there batched queries? What are the constraints (grid size, number of updates/queries)? This ensures you solve the right problem.
Outline an approach that handles the variant efficiently. For dynamic walls, consider incremental updates or periodic recomputation; for batched queries, consider precomputation or offline processing. Explain why it's suitable.
Derive the time and space complexity of your algorithm, including the cost per update/query and overall. Compare with naive approaches to highlight trade-offs.
Describe how you'd validate the solution, especially if AI wrote most of the code: write unit tests for edge cases, use property-based testing, manually trace small examples, and cross-check with a brute-force implementation.
Mention alternative approaches and their trade-offs (e.g., time vs. space, simplicity vs. performance). If relevant, discuss how the solution scales or could be extended.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.