← Microsoft Interview Insights
My first instinct was to just scan the whole row and column after each move, which works but falls apart at n=10^4.
Start by clarifying the requirements and constraints, then propose a solution using row, column, and diagonal counters to track each player's progress. Explain how each move updates these counters in O(1) time and how a win is detected by checking if any counter reaches n or -n.
Pro tip: Mention that you would use separate arrays for each player or a single array with signed values to distinguish players, and emphasize that this approach avoids scanning the board, achieving true O(1) per move.
Confirm the board size n, the player numbers (e.g., 1 and 2), and the win condition (n in a row, column, or diagonal). Ask if moves are guaranteed to be valid.
Propose maintaining arrays for row counts, column counts, and two diagonal counts. Use signed integers to represent each player's progress, or separate arrays per player.
For each move, update the corresponding row, column, and diagonal counters (if applicable) by adding +1 for player 1 and -1 for player 2. Then check if any updated counter equals n or -n.
Explain that each move updates a constant number of counters and performs constant-time checks, achieving O(1) time per move. Space is O(n) due to the arrays of size n.
Address invalid moves, multiple wins, and the possibility of a draw. Mention that this approach assumes valid moves and does not track the board state, which is acceptable for the given requirements.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.