⭕❌⭕ The Tic Tac Toe Referee (Solution)¶

Scenario:

You're a famous Tic Tac Toe referee, and you've been called in to resolve a dispute between two players. Multiple games have been played but no one can remember exactly how they played out, and checking all the games by hand would take a lot of time.

Exercise:

You've been given the moves for each game, and you need to figure out the winner of each game where 1 represents player 1, 2 represents player 2, and 0 represents an empty space.

In [1]:

import numpy as np

# Initialize an array of zeros with the dimensions of your games
num_games = 1000
games = np.zeros((num_games, 3, 3), dtype=int)

# Fill the array with random moves
for game in games:
    # Randomly choose your moves
    num_your_moves = np.random.randint(1, 5)
    your_moves = np.random.choice(9, num_your_moves, replace=False)
    np.put(game, your_moves, 1)  # Fill your moves into the game grid

    # Randomly choose the opponent's moves
    num_opponent_moves = np.random.randint(1, 9 - num_your_moves)
    opponent_moves = np.random.choice(list(set(range(9)) - set(your_moves)), num_opponent_moves, replace=False)
    np.put(game, opponent_moves, 2)

import numpy as np # Initialize an array of zeros with the dimensions of your games num_games = 1000 games = np.zeros((num_games, 3, 3), dtype=int) # Fill the array with random moves for game in games: # Randomly choose your moves num_your_moves = np.random.randint(1, 5) your_moves = np.random.choice(9, num_your_moves, replace=False) np.put(game, your_moves, 1) # Fill your moves into the game grid # Randomly choose the opponent's moves num_opponent_moves = np.random.randint(1, 9 - num_your_moves) opponent_moves = np.random.choice(list(set(range(9)) - set(your_moves)), num_opponent_moves, replace=False) np.put(game, opponent_moves, 2)

Your Tasks:

1. Create a function that checks if a player has won a game along the rows.

In [2]:

def check_row(row: np.ndarray) -> int:
    """Check if a row is a winning row.

    Args:
        row (np.ndarray): A row of a tic-tac-toe game. Shape (3,).

    Returns:
        int: 1 if the row is a winning row for the player 1, 
            2 if the row is a winning row for the player 2, 
            0 otherwise.
    """
    if np.all(row == 1):
        return 1
    elif np.all(row == 2):
        return 2
    else:
        return 0

def check_row(row: np.ndarray) -> int: """Check if a row is a winning row. Args: row (np.ndarray): A row of a tic-tac-toe game. Shape (3,). Returns: int: 1 if the row is a winning row for the player 1, 2 if the row is a winning row for the player 2, 0 otherwise. """ if np.all(row == 1): return 1 elif np.all(row == 2): return 2 else: return 0

1. Create a function that checks if a player has won a game along the rows using the previous function.

In [3]:

def check_rows(grid: np.ndarray) -> int:
    """Check if any row is a winning row.

    Args:
        grid (np.ndarray): A tic-tac-toe game. Shape (3, 3).

    Returns:
        int: 1 if the row is a winning row for the player 1, 
            2 if the row is a winning row for the player 2, 
            0 otherwise.
    """
    for row in grid:
        result = check_row(row)
        if result != 0:
            return result
    return 0

def check_rows(grid: np.ndarray) -> int: """Check if any row is a winning row. Args: grid (np.ndarray): A tic-tac-toe game. Shape (3, 3). Returns: int: 1 if the row is a winning row for the player 1, 2 if the row is a winning row for the player 2, 0 otherwise. """ for row in grid: result = check_row(row) if result != 0: return result return 0

1. Create a function that checks if a player has won a game along the columns.

In [4]:

def check_columns(grid: np.ndarray) -> int:
    """Check if any column is a winning column.

    Args:
        grid (np.ndarray): A tic-tac-toe game. Shape (3, 3).

    Returns:
        int: 1 if the row is a winning row for the player 1, 
            2 if the row is a winning row for the player 2, 
            0 otherwise.
    """
    return check_rows(grid.T)  # Transpose the grid to check the columns

def check_columns(grid: np.ndarray) -> int: """Check if any column is a winning column. Args: grid (np.ndarray): A tic-tac-toe game. Shape (3, 3). Returns: int: 1 if the row is a winning row for the player 1, 2 if the row is a winning row for the player 2, 0 otherwise. """ return check_rows(grid.T) # Transpose the grid to check the columns

1. Create a function that checks if a player has won a game along the diagonals.

In [5]:

def check_diagonals(grid: np.ndarray) -> int:
    """Check if any diagonal is a winning diagonal.

    Args:
        grid (np.ndarray): A tic-tac-toe game. Shape (3, 3).

    Returns:
        int: 1 if the row is a winning row for the player 1, 
            2 if the row is a winning row for the player 2, 
            0 otherwise.
    """
    diagonal_0 = np.diag(grid)
    diagonal_1 = np.diag(np.fliplr(grid))
    diagonals = np.array([diagonal_0, diagonal_1], dtype=int) # Combine the diagonals
    return check_rows(diagonals)

def check_diagonals(grid: np.ndarray) -> int: """Check if any diagonal is a winning diagonal. Args: grid (np.ndarray): A tic-tac-toe game. Shape (3, 3). Returns: int: 1 if the row is a winning row for the player 1, 2 if the row is a winning row for the player 2, 0 otherwise. """ diagonal_0 = np.diag(grid) diagonal_1 = np.diag(np.fliplr(grid)) diagonals = np.array([diagonal_0, diagonal_1], dtype=int) # Combine the diagonals return check_rows(diagonals)

1. Create a function that checks if a player has won a game using the previous three functions.

In [6]:

def check_win(grid: np.ndarray) -> int:
    """Check if any row, column, or diagonal is a winning row, column, or
    diagonal.

    Args:
        grid (np.ndarray): A tic-tac-toe game. Shape (3, 3).

    Returns:
        int: 1 if a row, column, or diagonal is a winning row, column, or
            diagonal for the player 1, 2 if it is a winning row, column, or
            diagonal for the player 2, 0 otherwise.
    """
    # check rows
    result = check_rows(grid)
    if result != 0:
        return result
    # check columns
    result = check_columns(grid)
    if result != 0:
        return result
    # check diagonals
    result = check_diagonals(grid)
    if result != 0:
        return result
    # no win
    return 0

def check_win(grid: np.ndarray) -> int: """Check if any row, column, or diagonal is a winning row, column, or diagonal. Args: grid (np.ndarray): A tic-tac-toe game. Shape (3, 3). Returns: int: 1 if a row, column, or diagonal is a winning row, column, or diagonal for the player 1, 2 if it is a winning row, column, or diagonal for the player 2, 0 otherwise. """ # check rows result = check_rows(grid) if result != 0: return result # check columns result = check_columns(grid) if result != 0: return result # check diagonals result = check_diagonals(grid) if result != 0: return result # no win return 0

1. Compute how many games you've won/lost/drawn in the dataset.

In [7]:

player_1, player_2, draws = 0, 0, 0
for game in games:
    result = check_win(game)
    if result == 1:
        player_1 += 1
    elif result == 2:
        player_2 += 1
    else:
        draws += 1

print(f"Player 1 wins: {player_1}")
print(f"Player 2 wins: {player_2}")
print(f"Draws: {draws}")

player_1, player_2, draws = 0, 0, 0 for game in games: result = check_win(game) if result == 1: player_1 += 1 elif result == 2: player_2 += 1 else: draws += 1 print(f"Player 1 wins: {player_1}") print(f"Player 2 wins: {player_2}") print(f"Draws: {draws}")

Player 1 wins: 117
Player 2 wins: 309
Draws: 574

🎉 Congratulations! You've just created a Tic Tac Toe referee that can check the winner of any game! 🎉