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Design Tic-Tac-Toe

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Description

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:

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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?

Solution

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class TicTacToe {
private:
    vector<vector<int>> grid;
    vector<int> rowSum;
    vector<int> rowProduct;
    vector<int> colSum;
    vector<int> colProduct;
    vector<int> diagonalSum;
    vector<int> diagonalProduct;
    int size;
    vector<int> playerProduct;
public:
    /** Initialize your data structure here. */
    TicTacToe(int n) {
        vector<vector<int>> newGrid(n, vector<int>(n, 0));
        grid = newGrid;
        
        //Target
        playerProduct.push_back(1);
        playerProduct.push_back(1 << n);
        
        //Sum
        rowSum.resize(n);
        colSum.resize(n);
        diagonalSum.resize(2);
        
        //Product
        for (int i = 0; i < n; ++i) {
            rowProduct.push_back(1);
            colProduct.push_back(1);
        }
        diagonalProduct.push_back(1);
        diagonalProduct.push_back(1);
        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) {
        grid[row][col] = player;
        
        
        rowSum[row] += player;
        rowProduct[row] *= player;
        
        colSum[col] += player;
        colProduct[col] *= player;
        
        if (int pos = diagonal(row, col)) {
            if (pos == 3) {
                diagonalSum[0] += player;
                diagonalSum[1] += player;
                diagonalProduct[0] *= player;
                diagonalProduct[1] *= player;
            }else {
                diagonalSum[pos - 1] += player; 
                diagonalProduct[pos - 1] *= player;
            }
            
            
            if ( (diagonalSum[0] == size * player 
                && diagonalProduct[0] == playerProduct[player - 1]) 
               || (diagonalSum[1] == size * player 
                && diagonalProduct[1] == playerProduct[player - 1])
               ) 
                return player;
        }
        
        if ( (rowSum[row] == size * player && rowProduct[row] == playerProduct[player - 1]) 
            || (colSum[col] == size * player && colProduct[col] == playerProduct[player - 1]) )
            return player;
        
        return 0;
    }
    
    int diagonal(int row, int col) {
        if (size % 2 && row == size / 2 && col == size / 2) return 3;
        if (row == col) return 2;
        if (row + col == size - 1) 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);
 */