The move logic tripped me up more than I'd like to admit.
Start by clarifying requirements and edge cases (e.g., board size, win/lose conditions, scoring). Then outline a clean design: a 2D array for the board, a generic move function that handles all directions via rotation or transformation, and a spawn function that adds a 2 or 4 in a random empty cell. Finally, discuss trade-offs and potential optimizations.
Pro tip: Mention that you can implement a single move function by rotating the board to always slide left, then rotating back—this reduces code duplication and bugs. Also, emphasize testing edge cases like merges at the end of a row and no-op moves.
Ask about board size (typically 4x4), win condition (2048 tile), scoring, and whether moves that don't change the board should spawn a new tile. Confirm input/output expectations.
Use a 2D array (list of lists) to represent the board. Define helper functions: slide and merge a single row left, check for game over, and spawn a random tile.
Write a generic move function that rotates the board so the desired direction becomes 'left', applies slide-and-merge to each row, then rotates back. This avoids duplicating logic for up/down/left/right.
After a successful move, spawn a new tile (90% chance of 2, 10% of 4) in a random empty cell. Check for win (2048 tile) and loss (no empty cells and no merges possible).
Talk about time/space complexity, potential optimizations (e.g., bitboards for 4x4), and how you would test the implementation (unit tests for merge logic, edge cases).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is the part that actually matters in this interview.
First, analyze the information-theoretic requirements: each cell can be empty or one of 11 tile values (2,4,...,2048), so 12 states per cell. Since 12^16 ≈ 2^57.4, a 64-bit integer is sufficient. Then design a mixed-radix encoding where each cell contributes a base-12 digit, and use bitwise operations to pack and unpack the board losslessly.
Pro tip: Mention that you can optimize further by noting that only one new tile appears per move, but for a general lossless encoder, the mixed-radix approach is simple and provably correct. Also, discuss how to handle invalid states (e.g., tiles beyond 2048) by either rejecting or using a sentinel value.
Calculate the number of possible states per cell: empty plus 11 tile values (2^1 to 2^11) = 12 states. With 16 cells, total states = 12^16 ≈ 2^57.4, which fits in 64 bits.
Use a mixed-radix (base-12) encoding: assign each cell a value from 0 to 11 (0 for empty, 1 for 2, 2 for 4, ..., 11 for 2048). The board is encoded as a sum of cell_value * 12^position, where position is 0 to 15.
Iterate over the 16 cells, map each tile to its 0-11 code, and accumulate the result using multiplication by 12 or bit shifts (since 12 is not a power of two, use multiplication). Ensure the final value fits in a 64-bit unsigned integer.
Extract each cell by repeatedly taking modulo 12 and integer division by 12 (or using precomputed powers). Map the 0-11 code back to the tile value (0 -> empty, 1 -> 2, etc.) and reconstruct the board.
Check that the encoded value is within range and that decoding recovers the original board. Discuss handling of invalid tiles (e.g., >2048) and whether to use a sentinel or throw an error.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.