My first instinct was to just scan the whole board after every move, which is obviously wrong for a senior-level question.
Start by clarifying the game rules and constraints, then propose a board representation (e.g., 2D array with column heights) and a move function that places the piece and checks only the lines through the new piece. Explain the O(1) per-move time complexity by leveraging the fact that only the newly placed piece can create a winning line, and detail the directional checks.
Pro tip: Mention that you can optimize the win check by only examining the four lines (horizontal, vertical, and two diagonals) that pass through the newly placed piece, rather than scanning the entire board. This demonstrates awareness of efficiency and shows you understand the game's mechanics.
Ask about board dimensions, N value, number of players, and whether moves are always valid. Confirm that the board is fixed-size and pieces fall to the lowest empty cell.
Propose a 2D array (or list of lists) to represent the board, and an array of column heights to track the next available row in each column. This allows O(1) placement.
Place the piece at the next available row in the given column, update the column height, then check for a win by counting consecutive pieces in all four directions from the new piece.
Explain that each move is O(1) because the win check examines at most 4 directions × 2 sides × (N-1) cells, which is constant for fixed N. Also note that board size does not affect per-move time.
Mention handling of full columns, invalid moves, and potential optimizations like bitboards for small boards. Discuss space complexity O(rows × cols).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.