I wrote the naive version pretty fast, swapping elements across the diagonal, felt good about it.
Start by writing a clear, correct transpose function for a 2D matrix, then analyze its time and space complexity. Discuss cache performance and potential optimizations like blocked transposition, especially relevant for NVIDIA's GPU and high-performance computing context.
Pro tip: Mention that for large matrices, cache-oblivious or blocked algorithms can significantly improve performance by reducing cache misses, and relate this to GPU memory coalescing if applicable.
Ask about matrix representation (e.g., row-major, contiguous memory), size, and whether it's square or rectangular. This shows attention to detail and avoids incorrect assumptions.
Implement a straightforward transpose using nested loops, swapping elements across the diagonal for square matrices or creating a new matrix for rectangular ones. Ensure code is clean and correct.
State that time complexity is O(n*m) for an n x m matrix, and space complexity is O(1) for in-place square transpose or O(n*m) if allocating a new matrix.
Explain cache behavior: naive transpose has poor spatial locality due to column-wise access. Mention that blocked (tiled) transpose improves cache utilization by processing sub-blocks that fit in cache.
If relevant, mention GPU implementation considerations: memory coalescing, shared memory tiling, and how transpose is a common operation in deep learning and linear algebra libraries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.