Design Tic-Tac-Toe

Design a Tic-tac-toe game that is played between two players on a n x n grid.

You may assume the following rules:

  1. A move is guaranteed to be valid and is placed on an empty block.
  2. Once a winning condition is reached, no more moves is allowed.
  3. A player who succeeds in placing n of their marks in a horizontal, vertical, or diagonal row wins the game.

Example:

  1. Given n = 3, assume that player 1 is "X" and player 2 is "O" in the board.
  3. TicTacToe toe = new TicTacToe(3);
  5. toe.move(0, 0, 1); -> Returns 0 (no one wins)
  6. |X| | |
  7. | | | |    // Player 1 makes a move at (0, 0).
  8. | | | |
  10. toe.move(0, 2, 2); -> Returns 0 (no one wins)
  11. |X| |O|
  12. | | | |    // Player 2 makes a move at (0, 2).
  13. | | | |
  15. toe.move(2, 2, 1); -> Returns 0 (no one wins)
  16. |X| |O|
  17. | | | |    // Player 1 makes a move at (2, 2).
  18. | | |X|
  20. toe.move(1, 1, 2); -> Returns 0 (no one wins)
  21. |X| |O|
  22. | |O| |    // Player 2 makes a move at (1, 1).
  23. | | |X|
  25. toe.move(2, 0, 1); -> Returns 0 (no one wins)
  26. |X| |O|
  27. | |O| |    // Player 1 makes a move at (2, 0).
  28. |X| |X|
  30. toe.move(1, 0, 2); -> Returns 0 (no one wins)
  31. |X| |O|
  32. |O|O| |    // Player 2 makes a move at (1, 0).
  33. |X| |X|
  35. toe.move(2, 1, 1); -> Returns 1 (player 1 wins)
  36. |X| |O|
  37. |O|O| |    // Player 1 makes a move at (2, 1).
  38. |X|X|X|

Follow up:

Could you do better than O(n^2) per move() operation?

Hint:

Could you trade extra space such that move() operation can be done in O(1)?
You need two arrays: int rows[n], int cols[n], plus two variables: diagonal, anti_diagonal.