348. 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:

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 trade extra space such that move() operation can be done in O(1)?

Solution:

class TicTacToe(object):
    def __init__(self, n):
        """
        Initialize your data structure here.
        :type n: int
        """
        self.size = n
        self.board = [[0] * n for _ in xrange(n)]
        self.rows = [0] * n
        self.cols = [0] * n
        self.diagonals = [0] * 2

    def move(self, row, col, player):
        """
        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.
        :type row: int
        :type col: int
        :type player: int
        :rtype: int
        """
        self.board[row][col] = player

        inc = 1 if player == 1 else -1
        full = self.size * inc

        self.rows[row] += inc
        if self.rows[row] == full:
            return player

        self.cols[col] += inc
        if self.cols[col] == full:
            return player

        if row == col:
            self.diagonals[0] += inc
            if self.diagonals[0] == full:
                return player

        if row == self.size - col - 1:
            self.diagonals[1] += inc
            if self.diagonals[1] == full:
                return player

        return 0