Question
You are paving a straight 1-by-n path using two kinds of pieces: a 1x1 stone, and a 1x2 paver that comes in two colors (red or blue). Pieces of the same kind and color are interchangeable. Return the number of distinct pavings of the whole path. A path of length 0 counts as 1 (lay nothing). For example, n = 2 has 3 pavings: stone+stone, one red paver, or one blue paver.
count_paving_designs(n: int) → int[2]out3[4]out11State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.
Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.