Matrix and Grid Simulation Patterns

Grid problems reward a small set of mechanical patterns: walk a spiral by shrinking four boundaries, rotate a square in place with a transpose-then-reverse, and mark state inside the grid itself to keep extra space at O(1). The hard part is index bookkeeping, not algorithms. Interviews probe these because off-by-one errors on boundaries are where most candidates lose points, and in-place tricks test whether you can avoid an obvious extra-memory copy.