348. Design Tic-Tac-Toe¶

Problem:¶

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

You may assume the following rules:

A move is guaranteed to be valid and is placed on an empty block.
Once a winning condition is reached, no more moves is allowed.
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() 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.

Solutions:¶

```java public class TicTacToe { private int[][] board; private int n; private int rowSum[]; private int colSum[]; private int diag; private int antiDiag; /** Initialize your data structure here. */ public TicTacToe(int n) { board = new int[n][n]; this.n = n; rowSum = new int[n]; colSum = new int[n]; diag = 0; antiDiag = 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) {
    int add = 1;
    if (player == 1) {
        add = -1;
    }
    rowSum[row] += add;
    colSum[col] += add;
    if (row == col) {
        diag += add;
    }
    if (row + col == n - 1) {
        antiDiag += add;
    }
    if (rowSum[row] == n || colSum[col] == n || diag == n || antiDiag == n) {
        return 2;
    }
    if (rowSum[row] == -n || colSum[col] == -n || diag == -n || antiDiag == -n) {
        return 1;
    }
    return 0;
}

}

/** * Your TicTacToe object will be instantiated and called as such: * TicTacToe obj = new TicTacToe(n); * int param_1 = obj.move(row,col,player); */ ```