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.

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|

S: O(1)

当一行，一列或一条对角线全为O或全为X时，玩家才能获胜。用1表示player1，-1表示player2只用计数即可

class TicTacToe {
public:
    /** Initialize your data structure here. */
    TicTacToe(int n) {
        r.resize(n);
        c.resize(n);
        diag1 = 0;
        diag2 = 0;
        size = n;
    }

    /** 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. */
    int move(int row, int col, int player) {
        int num = player == 1? 1 : -1;
        r[row] += num;
        c[col] += num;
        if (row == col) diag1 += num;
        if (row == size - col - 1) diag2 += num;
        if (r[row] == size || r[row] == -size || 
            c[col] == size || c[col] == -size ||
            diag1 == size || diag1 == -size || 
            diag2 == size || diag2 == -size) {
            return player;
        }
        return 0;
    }
private:
    vector<int> r; //row count
    vector<int> c; //column count
    int diag1;
    int diag2;
    int size;
};