Đề bài
Minimax is how game-playing programs choose moves: assume both players play perfectly, score every finished game, and back the scores up the game tree. The player to move picks the child with the highest score for itself.
The board is a 9-character string read row by row (indices 0-8), with "X", "O" or "." for an empty cell. X always moves first, so it is X's turn when both have the same number of marks and O's turn otherwise.
Score a finished game from the point of view of the player to move: +1 for a win, 0 for a draw, -1 for a loss. Return the empty cell whose move has the best minimax score; if several are equally good, return the lowest index.
Implement best_move(board).
Input
board: A valid position where nobody has won yet and at least one cell is empty.
Output
Return the index (0-8) of the best move.
Ràng buộc
board has exactly 9 characters, each X, O or .
The position is reachable in a real game, nobody has won, and at least one cell is empty
Ví dụ
Đầu vào:
board = "XX.OO...."
Kết quả mong đợi:
expected = 2Đầu vào:
std::string board = "XX.OO....";
Kết quả mong đợi:
long long expected = 2;Đầu vào:
string board = "XX.OO....";
Kết quả mong đợi:
long expected = 2;Giải thích
X and O have two marks each, so X moves. Playing 2 completes the top row and wins at once (+1).
Đầu vào:
board = "X..OO...X"
Kết quả mong đợi:
expected = 5Đầu vào:
std::string board = "X..OO...X";
Kết quả mong đợi:
long long expected = 5;Đầu vào:
string board = "X..OO...X";
Kết quả mong đợi:
long expected = 5;Giải thích
X moves. O threatens to complete the middle row at 5. Every other move lets O win (-1), while blocking at 5 leads to a draw (0), so the answer is 5.
Hướng tiếp cận
Hãy tự thử trước, sau đó mở từng gợi ý một.
Gợi ý 1
Determine whose turn it is from the counts of X and O, then evaluate every legal move recursively.
Gợi ý 2
Score terminal boards from the current player’s perspective, and choose the move that maximizes that value.
Gợi ý 3
If multiple moves tie, keep the earliest empty cell index, and ensure wins are detected before considering further moves.
Độ phức tạp mong đợi
O(9!) time, O(9) extra space
Tham khảo
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