I knew it was BFS immediately, which felt good, but I fumbled the setup a bit.
Model the grid as a graph where each cell is a node and edges connect to its 8 neighbors if they are open. Use BFS from the start cell to find the shortest path to the target, as BFS guarantees the minimum number of steps in an unweighted graph. Handle edge cases: if start or target is blocked, return -1 immediately.
Pro tip: In an interview, explicitly state the time and space complexity (O(n^2)) and mention that BFS is optimal for unweighted shortest paths. Also, consider using a deque for BFS and marking visited cells to avoid revisiting.
Confirm the grid size, movement rules, and edge cases (e.g., start or target blocked). Check if the grid is empty or if n=1.
Explain that BFS is ideal for unweighted graphs to find the shortest path. Initialize a queue with the start cell and a distance counter.
For each cell, check all 8 neighboring cells. If a neighbor is open and unvisited, mark it visited and enqueue it with distance+1.
If the target is reached, return the distance. If the queue empties without reaching the target, return -1.
State that time and space complexity are O(n^2). Mention potential optimizations like bidirectional BFS if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Switched BFS to Dijkstra, said it pretty quickly.
Acknowledge that the problem shifts from unweighted to weighted shortest path, requiring a different algorithm like Dijkstra's or A* with a consistent heuristic. Explain how the solution's data structures, complexity, and optimality guarantees change, and discuss trade-offs in implementation and performance.
Pro tip: Mention that if costs are non-negative, Dijkstra's algorithm is optimal, but if negative costs exist, Bellman-Ford is needed; also note that A* with an admissible heuristic can still be used for efficiency. This shows you consider edge cases and practical constraints.
Recognize that the problem becomes a weighted shortest path problem, where each move has an associated cost.
Select an algorithm that handles weighted edges, such as Dijkstra's for non-negative costs or Bellman-Ford for negative costs, and consider A* if a heuristic is available.
Update the data structures (e.g., priority queue for Dijkstra) and analyze the new time and space complexity compared to the unweighted case.
Compare algorithms in terms of performance, memory, and implementation complexity, and mention potential optimizations like bidirectional search or heuristic tuning.
Address scenarios like negative costs, zero costs, or large graphs, and how they affect algorithm choice and correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I said track a parent pointer for each visited cell and reconstruct backwards from the destination.
Explain that to reconstruct the actual path, you need to store parent pointers during the dynamic programming or BFS traversal, then backtrack from the end state to the start. Emphasize that this adds O(n) space but is necessary for path retrieval, and discuss how to adapt the algorithm accordingly.
Pro tip: Mention that you can often avoid storing the full path by using a technique like Hirschberg's algorithm for sequence alignment, which reduces space complexity while still recovering the path. This shows depth and awareness of trade-offs.
Ask whether the path needs to be reconstructed for a single optimal solution or all, and discuss time/space constraints. This ensures you address the right variant.
During the DP table filling, for each cell store which previous cell led to the optimal value (e.g., diagonal, up, left). This allows backtracking.
Starting from the bottom-right cell, follow the stored pointers back to the origin, collecting the decisions (e.g., match, insert, delete) to form the path.
Explain that storing parents adds O(n*m) space, but time remains O(n*m). Mention alternatives like Hirschberg's algorithm for O(min(n,m)) space.
Consider multiple optimal paths, tie-breaking, and whether to store pointers as a separate matrix or encode them in the DP table. Also mention path reconstruction for BFS/DFS in graphs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the original problem and the square-grid solution, then systematically identify where the square assumption is baked in (e.g., dimensions, indexing, neighbor checks, termination). Generalize each component to handle independent row and column bounds, and discuss how the time/space complexity changes with M×N dimensions.
Pro tip: Explicitly state that you would keep the algorithm's core logic unchanged and only adjust boundary conditions and iteration limits—this shows you can separate essential logic from incidental constraints, a key skill for ML engineers who often need to adapt models to varying input shapes.
Briefly summarize the original problem and the square-grid algorithm, highlighting any assumptions like equal dimensions or symmetric neighbor access.
List all places where the code or logic assumes a square (e.g., loops using a single size variable, diagonal moves, boundary checks).
Replace single dimension with separate rows and columns, adjust loops, boundary conditions, and any indexing that relied on symmetry.
Discuss how time and space complexity scale with M and N, and mention edge cases like very thin grids (1×N) or empty grids.
Walk through a small rectangular example to verify correctness, and note any performance or implementation trade-offs compared to the square version.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the grid movement rules and then explain how to adapt pathfinding algorithms to enforce the diagonal restriction. Focus on the algorithmic changes needed, such as modifying neighbor generation and ensuring consistency in cost calculations.
Pro tip: Mention that this rule is common in games to prevent unrealistic corner-cutting and that it can be efficiently implemented by checking adjacent orthogonal cells before allowing a diagonal move.
Restate the rule: diagonal moves are allowed only if both adjacent orthogonal cells are open. Confirm that this applies to all diagonal moves in the grid.
Select a pathfinding algorithm like A* or Dijkstra. Note that the core algorithm remains the same, but neighbor generation must be modified.
When considering diagonal moves, check the two adjacent orthogonal cells. Only include the diagonal neighbor if both are open and within bounds.
Ensure movement costs are consistent (e.g., diagonal cost sqrt(2) if using Euclidean). Heuristics should remain admissible; if using Manhattan distance, it may overestimate, so consider using Euclidean or octile distance.
Test with scenarios where diagonal moves are blocked by closed orthogonal cells. Verify that the algorithm correctly avoids such moves and finds the optimal path.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.