I started with the classic 3x3 mental model and had to consciously reset when I realized n could be huge.
Start by clarifying requirements and edge cases (e.g., k players, n x n board, win condition of 3 consecutive marks, invalid moves). Then outline a class design with methods for move, status check, and win detection, focusing on efficient win checking by scanning only around the last move. Finally, analyze time and space complexity and discuss potential optimizations or trade-offs.
Pro tip: Demonstrate awareness of real-world constraints: mention that checking only the last move's row, column, and diagonals reduces win detection from O(n^2) to O(1) per move, and discuss how to handle invalid moves gracefully with exceptions or error returns.
Ask clarifying questions about k (number of players), n (board size), win condition (exactly 3 or at least 3?), and how invalid moves should be handled. Confirm that the game ends when a player wins or the board is full.
Propose a class with an n x n board (e.g., 2D array or 1D array), a list of players, and methods like move(player, row, col) and getStatus(). Define how to track the current player and game state.
For each move, validate that the cell is empty and the player is correct. After placing the mark, check for a win by scanning only the row, column, and two diagonals passing through the last move for 3 consecutive marks of that player.
Explain that move validation is O(1), win detection is O(1) (since only constant number of cells checked), and space is O(n^2). Discuss alternative approaches like precomputing counts or using bitboards for larger n.
Walk through a few moves, including invalid ones, and show how the status updates. Test edge cases like a win on the last move, a draw, and multiple players.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.