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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:

Given n = 3, assume that player 1 is "X" and player 2 is "O" in the board.

TicTacToe toe = new TicTacToe(3);

toe.move(0, 0, 1); -> Returns 0 (no one wins)
|X| | |
| | | | // Player 1 makes a move at (0, 0).
| | | |

toe.move(0, 2, 2); -> Returns 0 (no one wins)
|X| |O|
| | | | // Player 2 makes a move at (0, 2).
| | | |

toe.move(2, 2, 1); -> Returns 0 (no one wins)
|X| |O|
| | | | // Player 1 makes a move at (2, 2).
| | |X|

toe.move(1, 1, 2); -> Returns 0 (no one wins)
|X| |O|
| |O| | // Player 2 makes a move at (1, 1).
| | |X|

toe.move(2, 0, 1); -> Returns 0 (no one wins)
|X| |O|
| |O| | // Player 1 makes a move at (2, 0).
|X| |X|

toe.move(1, 0, 2); -> Returns 0 (no one wins)
|X| |O|
|O|O| | // Player 2 makes a move at (1, 0).
|X| |X|

toe.move(2, 1, 1); -> Returns 1 (player 1 wins)
|X| |O|
|O|O| | // Player 1 makes a move at (2, 1).
|X|X|X|

Follow up:
Could you do better than O(n2) per move()

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.

解法：

public class TicTacToe {
    int n;
    int[] rows;
    int[] cols;
    int diagonal;
    int anti_diagonal;
    int wins;

    /**
     * Initialize your data structure here.
     */
    public TicTacToe(int n) {
        this.n = n;
        rows = new int[n];
        cols = new int[n];
        diagonal = 0;
        anti_diagonal = 0;
        wins = 0;
    }

    /**
     * Player {player} makes a move at ({row}, {col}).
     *
     * @param row    The row of the board.
     * @param col    The column of the board.
     * @param player The player, can be either 1 or 2.
     * @return The current winning condition, can be either:
     * 0: No one wins.
     * 1: Player 1 wins.
     * 2: Player 2 wins.
     */
    public int move(int row, int col, int player) {
        if (player == 1) {
            rows[row]++;
            cols[col]++;
            if (row == col)
                diagonal++;
            if (row + col == n - 1)
                anti_diagonal++;
        } else if (player == 2) {
            rows[row]--;
            cols[col]--;
            if (row == col)
                diagonal--;
            if (row + col == n - 1)
                anti_diagonal--;
        }
        if (rows[row] == n || cols[col] == n || diagonal == n || anti_diagonal == n)
            wins = 1;
        else if (rows[row] == -n || cols[col] == -n || diagonal == -n || anti_diagonal == -n)
            wins = 2;
        return wins;
    }
}