I started with the naive simulation and it felt fine until they asked about doing a thousand operations on a large matrix.
Start by clarifying the problem constraints and expected operation frequency, then outline a naive simulation approach and its O(n^2) per operation cost. Propose an optimized solution using index permutations and an orientation flag to achieve O(1) per operation, and discuss the trade-offs between the two approaches.
Pro tip: Emphasize that the optimized approach is not just about speed but also about scalability and handling large matrices efficiently; mention that it reduces the risk of off-by-one errors in complex simulations.
Ask about matrix size, number of operations, and whether operations are known in advance. Confirm if in-place modification is required or if returning a new matrix is acceptable.
Explain that simulating each operation literally would take O(n^2) time per operation due to copying rows/columns or rotating the entire matrix, leading to O(m * n^2) total time for m operations.
Propose maintaining a mapping of logical indices to physical indices for rows and columns, along with an orientation flag (0, 90, 180, 270 degrees). Each operation updates these mappings in O(1) time.
Explain how each operation translates to updates: swapping rows/columns swaps entries in the mapping; reversing a row/column flips the order in the mapping; rotation updates the orientation flag and may swap row/column mappings.
Compare the two approaches: naive is simpler but slower; optimized is faster but more complex. Mention that the final matrix can be constructed in O(n^2) by applying the mappings and orientation once at the end.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.