I jumped straight to BFS which was correct, but I fumbled explaining *why* BFS and not DFS for a second.
Use BFS from the start cell, exploring all four directions level by level, since BFS guarantees the shortest path in an unweighted grid. Track visited cells to avoid cycles, and return the distance when reaching the bottom-right cell, or -1 if the queue is exhausted.
Pro tip: Clarify edge cases upfront (e.g., start or end is a wall, single-cell grid) and mention that BFS is optimal for unweighted grids while DFS would not guarantee shortest path. Also, discuss space-time trade-offs and potential optimizations like bidirectional BFS if the grid is large.
Confirm grid dimensions, movement rules, and what constitutes a valid path. Discuss edge cases: start or end is a wall, grid is 1x1, or no path exists.
State that BFS is ideal for unweighted shortest path because it explores nodes in increasing order of distance from the start. Mention that DFS or Dijkstra would be less efficient or unnecessary.
Initialize a queue with the start cell and a visited set or matrix. While the queue is not empty, dequeue a cell, check if it's the target, and enqueue all valid unvisited neighbors with distance+1.
For each neighbor, check if it's within grid bounds, not a wall ('1'), and not visited. Mark visited upon enqueue to avoid duplicates.
If target is reached, return its distance; otherwise return -1. Analyze time and space complexity: O(R*C) for both, where R and C are grid dimensions.
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Recovered fine on this after the earlier stumble.
First, clarify the problem context and why BFS is suitable (e.g., shortest path in unweighted graph, level-order traversal). Then, derive the time and space complexities based on the graph representation and BFS mechanics, explaining each component.
Pro tip: Mention that BFS is optimal for unweighted graphs but not for weighted graphs (where Dijkstra's is needed), and note that the space complexity can be reduced if the graph is a tree or if we only need to check existence.
Restate the problem to ensure understanding, and identify the key characteristics (e.g., unweighted graph, need shortest path, level-order processing).
Explain why BFS is appropriate: it explores nodes in order of distance from the source, guaranteeing shortest path in unweighted graphs, and naturally handles level-order traversal.
Break down time complexity: O(V + E) for adjacency list, O(V^2) for adjacency matrix. Explain that each vertex and edge is processed once.
Discuss space complexity: O(V) for the queue and visited set, plus O(V + E) for the graph representation if not already given.
Summarize why BFS is the right choice, and briefly compare with alternatives like DFS or Dijkstra's to highlight trade-offs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The multiple shortest paths one was a bit of a curveball.
Start by restating the problem and its constraints, then systematically enumerate edge cases across input dimensions (size, boundaries, obstacles, start/end conditions) and algorithmic concerns (multiple paths, tie-breaking, unreachable targets). For each edge case, briefly explain how your solution handles it and why it matters for correctness or efficiency.
Pro tip: Tie each edge case back to a concrete test you would write, showing you think like a test engineer as well as an algorithm designer. Mention that at Disney, where correctness and reliability are paramount, proactively handling edge cases prevents costly bugs in production.
Restate the problem (e.g., shortest path in a grid) and confirm assumptions about grid size, movement rules, and obstacle representation. This sets the stage for identifying relevant edge cases.
List cases like 1x1 grid, empty grid, start or end blocked, start equals end, no path, and multiple valid shortest paths. Explain how each affects your algorithm.
Discuss cases that impact complexity: large grids, many obstacles, diagonal movement, negative weights (if applicable), and tie-breaking when multiple shortest paths exist.
For each edge case, describe how your solution detects and handles it (e.g., early return, special checks) and what the expected output should be.
Wrap up by emphasizing that these edge cases inform your test suite, ensuring robustness and correctness in production.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Just swap the directions array from 4 neighbors to 8.
Start by clarifying the original solution's context (e.g., grid-based pathfinding, game movement, or matrix traversal) and then systematically identify the components that assume orthogonal movement. Explain how to generalize those components to include diagonal moves, focusing on neighbor generation, cost models, and validity checks, while discussing trade-offs like performance and correctness.
Pro tip: Mention that diagonal movement often requires adjusting cost calculations (e.g., using √2 for Euclidean distance) and handling corner-cutting constraints, which shows you understand real-world implications beyond just adding new directions.
Briefly restate the problem and the current approach, highlighting assumptions about movement (e.g., only up/down/left/right). This ensures you and the interviewer are aligned on the baseline.
List the specific parts that need changes: neighbor generation, movement cost, validity checks (e.g., obstacles, boundaries), and any data structures or algorithms (like BFS, Dijkstra, A*).
Describe how to extend each component: add diagonal offsets to neighbor lists, update cost functions (e.g., √2 for diagonals), and adjust validity checks to prevent corner-cutting if needed.
Address performance implications (e.g., more neighbors increase branching factor), correctness (e.g., ensuring no illegal moves), and potential optimizations (e.g., precomputed directions).
Conclude with a concise summary of changes and suggest testing strategies (e.g., unit tests for diagonal moves, performance benchmarks) to validate the extension.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.