Question
Count the number of distinct ways to completely tile an m x n grid with 1x2 dominoes (each domino covers two orthogonally adjacent cells), where every cell must be covered exactly once. Return the count. Constraints: 1 <= m <= 12, 1 <= n <= 12, and m*n is processed column-by-column with a broken-profile bitmask DP so the larger dimension can be up to 12.
count_domino_tilings(m: int, n: int) → int[2,3]out3State 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.