I went with DFS first because it's the quickest to write under pressure, got through the base case fine.
Start by clarifying the problem and edge cases, then explain a standard solution using DFS/BFS to count islands in the base grid. For the follow-up variant, adapt the approach by modifying the traversal or using a set to track distinct island shapes, ensuring to discuss time and space complexity.
Pro tip: Demonstrate proactive communication by asking clarifying questions about the follow-up variant before diving into the solution, and relate the problem to real-world applications like image processing or social network analysis to show depth.
Ask about grid dimensions, input format, and the exact follow-up variant. Confirm whether diagonal connections count and if the grid can be modified.
Explain that you'll iterate through each cell, and when encountering a '1', perform DFS/BFS to mark all connected land cells as visited, incrementing the island count.
For counting distinct islands, during traversal record the relative shape (e.g., using coordinates or directions) and store it in a set to avoid duplicates. Alternatively, if the variant is about max area or perimeter, adjust the traversal to compute the required metric.
State that time complexity is O(M*N) for grid traversal, and space complexity is O(M*N) in worst case for recursion/queue. Mention edge cases like empty grid, all water, or all land.
Walk through a small example to validate the approach, and if time permits, discuss potential optimizations like union-find or iterative DFS to avoid stack overflow.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.