348. Design Tic-Tac-Toe

348. Design Tic-Tac-Toe

Tag: Design Matrix

Difficulty: Medium

Assume the following rules are for the tic-tac-toe game on an n x n board between two players:

A move is guaranteed to be valid and is placed on an empty block. Once a winning condition is reached, no more moves are allowed. A player who succeeds in placing n of their marks in a horizontal, vertical, or diagonal row wins the game. Implement the TicTacToe class:

• TicTacToe(int n) Initializes the object the size of the board n.
• int move(int row, int col, int player) Indicates that the player with id player plays at the cell (row, col) of the board. The move is guaranteed to be a valid move, and the two players alternate in making moves. Return
  • 0 if there is no winner after the move,
  • 1 if player 1 is the winner after the move, or
  • 2 if player 2 is the winner after the move.

---

Example 1:

Input
["TicTacToe", "move", "move", "move", "move", "move", "move", "move"]
[[3], [0, 0, 1], [0, 2, 2], [2, 2, 1], [1, 1, 2], [2, 0, 1], [1, 0, 2], [2, 1, 1]]
Output
[null, 0, 0, 0, 0, 0, 0, 1]

Explanation
TicTacToe ticTacToe = new TicTacToe(3);
Assume that player 1 is "X" and player 2 is "O" in the board.
ticTacToe.move(0, 0, 1); // return 0 (no one wins)
|X| | |
| | | |    // Player 1 makes a move at (0, 0).
| | | |

ticTacToe.move(0, 2, 2); // return 0 (no one wins)
|X| |O|
| | | |    // Player 2 makes a move at (0, 2).
| | | |

ticTacToe.move(2, 2, 1); // return 0 (no one wins)
|X| |O|
| | | |    // Player 1 makes a move at (2, 2).
| | |X|

ticTacToe.move(1, 1, 2); // return 0 (no one wins)
|X| |O|
| |O| |    // Player 2 makes a move at (1, 1).
| | |X|

ticTacToe.move(2, 0, 1); // return 0 (no one wins)
|X| |O|
| |O| |    // Player 1 makes a move at (2, 0).
|X| |X|

ticTacToe.move(1, 0, 2); // return 0 (no one wins)
|X| |O|
|O|O| |    // Player 2 makes a move at (1, 0).
|X| |X|

ticTacToe.move(2, 1, 1); // return 1 (player 1 wins)
|X| |O|
|O|O| |    // Player 1 makes a move at (2, 1).
|X|X|X|

Constraints:

• 2 <= n <= 100
• player is 1 or 2.
• 0 <= row, col < n
• (row, col) are unique for each different call to move.
• At most n^2 calls will be made to move.

Follow-up: Could you do better than O(n^2) per move() operation?

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Brute Force

• Time Complexity: $O(n)$
• Space Complexity: $O(n^2)$

class TicTacToe:

    def __init__(self, n: int):
        self.board = [[None] * n for _ in range(n)]
        self.ROWS, self.COLS = n, n


    def move(self, row: int, col: int, player: int) -> int:
        if player == 1:
            self.board[row][col] = 'O'
        else:
            self.board[row][col] = 'X'

        def check_row(row, col):
            for c in range(self.COLS):
                if self.board[row][c] != self.board[row][col]:
                    return False
            return True 

        def check_col(row, col):
            for r in range(self.ROWS):
                if self.board[r][col] != self.board[row][col]:
                    return False
            return True

        def check_diagonal(row, col):
            for r in range(self.ROWS):
                if self.board[r][r] != self.board[row][col]:
                    return False
            return True

        def check_anti_diagonal(row, col):
            for r in range(self.ROWS):
                if self.board[r][self.ROWS - r - 1] != self.board[row][col]:
                    return False
            return True

        if check_row(row, col) or check_col(row, col) or check_diagonal(row, col) or check_anti_diagonal(row, col):
            return player

        return 0
        
        


# Your TicTacToe object will be instantiated and called as such:
# obj = TicTacToe(n)
# param_1 = obj.move(row,col,player)

class TicTacToe:

    def __init__(self, n: int):
        self.board = [[None] * n for _ in range(n)]
        self.ROWS, self.COLS = n, n

    def move(self, row: int, col: int, player: int) -> int:
        self.board[row][col] = player

        def check_row(row, player):
            for c in range(self.COLS):
                if self.board[row][c] != player:
                    return False
            return True 

        def check_col(col, player):
            for r in range(self.ROWS):
                if self.board[r][col] != player:
                    return False
            return True

        def check_diagonal(player):
            for r in range(self.ROWS):
                if self.board[r][r] != player:
                    return False
            return True

        def check_anti_diagonal(player):
            for r in range(self.ROWS):
                if self.board[r][self.ROWS - r - 1] != player:
                    return False
            return True

        if check_row(row, player) or check_col(col, player) or check_diagonal(player) or check_anti_diagonal(player):
            return player

        return 0


# Your TicTacToe object will be instantiated and called as such:
# obj = TicTacToe(n)
# param_1 = obj.move(row,col,player)

Optimized Brute Force

• Time Complexity: $O(1)$
• Space Complexity: $O(n)$

class TicTacToe:

    def __init__(self, n: int):
        self.player1 = {'row': collections.defaultdict(int), 'col':collections.defaultdict(int), 'diagonal':0, 'anti_diagonal':0}
        self.player2 = {'row': collections.defaultdict(int), 'col':collections.defaultdict(int), 'diagonal':0, 'anti_diagonal':0}
        self.size = n


    def move(self, row: int, col: int, player: int) -> int:
        if player == 1:
            current = self.player1
        else:
            current = self.player2
        
        current['row'][row] += 1
        current['col'][col] += 1

        if row == col:
            current['diagonal'] += 1
        if row + col == self.size - 1:
            current['anti_diagonal'] += 1
        
        if current['row'][row] == self.size or current['col'][col] == self.size or current['diagonal'] == self.size or current['anti_diagonal'] == self.size:
            return player
        
        return 0


# Your TicTacToe object will be instantiated and called as such:
# obj = TicTacToe(n)
# param_1 = obj.move(row,col,player)

class TicTacToe:

    def __init__(self, n: int):
        self.size = n
        self.horizontal = [0] * n
        self.vertical = [0] * n
        self.diagonal = 0
        self.anti_diagonal = 0

    def move(self, row: int, col: int, player: int) -> int:
        if player == 1:
            move = 1
        else:
            move = -1
        
        self.horizontal[col] += move
        self.vertical[row] += move

        if row == col:
            self.diagonal += move
        if row + col == self.size - 1:
            self.anti_diagonal += move
        
        if abs(self.horizontal[col]) == self.size or abs(self.vertical[row]) == self.size or abs(self.diagonal) == self.size or abs(self.anti_diagonal) == self.size:
            return player
        
        return 0


# Your TicTacToe object will be instantiated and called as such:
# obj = TicTacToe(n)
# param_1 = obj.move(row,col,player)