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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Tic-Tac-Toe
This notebook defines the game tic-tac-toe.
It is played on a $3 \times 3$ board.  There are two players, which are called X and O.  Player X starts.  Player X always puts an 'X' into an empty field on the board, while player O always puts an 'O' in an empty field of the board.  The goal of the game for player X is to get three Xs into a row, column, or diagonal line, while player O needs to get three Os into a row, column, or diagonal line.
The global variable gPlayers returns a list with the name of both players.
Step1:  In the following naive implementation, states are represented as tuples of tuples of strings.  The game starts with an empty board.  An empty field on the board is represented by a blank space ' ', while an X is represented by the string 'X' and an O is represented as the string 'O'.  The start state Start defined below represents an empty board.
We have to represent states as tuples of tuples instead of lists of lists as lists are mutable and therefore can't be stored in sets.
Step2:  The function to_list transforms a tuple of tuples into a list of lists.  As tuples are immutable, this function is needed in order to create new states from given ones.
Step3:  Conversely, the function to_tuple transforms a list of lists into a tuple of tuples.
Step4:  Given a state represented by the tuple of tuples Board, the function empty(Board) returns the list of all empty positions on the board Board, i.e. it returns the list of all pairs (row, col) such that Board[row][col] == ' ' holds.  These pairs are the coordinates of the fields on the Board that are not yet marked by either an 'X' or an 'O'.
Step5:  In the state gStart, all positions are empty.
Step6:  The function toString(State) represents the given state as a string.
Step7:  Given a State and the player whose turn it is, the function next_states(State, player) computes the list of all states that can be reached from State.
Step8:  The variable gAllLines collects the coordinates of all the fields of the three rows, the three columns, and the two diagonals.  This variable is needed to check whether the game has already terminated.
The name of the variable is prefixed with g to distinguish the variable as a global variable.
Step9:  The function utility takes one argument
Step10:  finished(State) is True if and only if the game is over.
Step11:  The function get_move asks the user to input a move in the format r,c where r is the row and the c is the column where the next symbol is to be placed. Rows and columns are counted starting from 0.  It is assumed that the user plays as 'O', i.e. the user takes the second move.
Step12:  This function informs the player, who is assumed to be 'O', about the result of the game once the game is finished.
Step13:  Drawing the Board
Step14:  This function creates the canvas for the start state.  It draws an empty board which is later used for the game.
Step15:  This function takes three arguments
Step16:  Checking the Memory Footprint
Step17:  The memory needed to store a single state is the memory needed to store a list containing three objects  plus the memory needed to store those objects.
Step18:  To compare, a single positive integer less than $1,073,741,824$ needs 28 bytes.
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Python Code:
gPlayers = [ 'X', 'O' ]
Explanation: Tic-Tac-Toe
This notebook defines the game tic-tac-toe.
It is played on a $3 \times 3$ board.  There are two players, which are called X and O.  Player X starts.  Player X always puts an 'X' into an empty field on the board, while player O always puts an 'O' in an empty field of the board.  The goal of the game for player X is to get three Xs into a row, column, or diagonal line, while player O needs to get three Os into a row, column, or diagonal line.
The global variable gPlayers returns a list with the name of both players.
End of explanation
gStart = tuple( tuple(' ' for col in range(3)) for row in range(3) )
gStart
Explanation: In the following naive implementation, states are represented as tuples of tuples of strings.  The game starts with an empty board.  An empty field on the board is represented by a blank space ' ', while an X is represented by the string 'X' and an O is represented as the string 'O'.  The start state Start defined below represents an empty board.
We have to represent states as tuples of tuples instead of lists of lists as lists are mutable and therefore can't be stored in sets.
End of explanation
def to_list(State): 
    return [list(row) for row in State]
Explanation: The function to_list transforms a tuple of tuples into a list of lists.  As tuples are immutable, this function is needed in order to create new states from given ones.
End of explanation
def to_tuple(State): 
    return tuple(tuple(row) for row in State)
Explanation: Conversely, the function to_tuple transforms a list of lists into a tuple of tuples.
End of explanation
def empty(Board):
    return [ (row, col) for row in range(3)
                        for col in range(3)
                        if  Board[row][col] == ' ' 
           ]
Explanation: Given a state represented by the tuple of tuples Board, the function empty(Board) returns the list of all empty positions on the board Board, i.e. it returns the list of all pairs (row, col) such that Board[row][col] == ' ' holds.  These pairs are the coordinates of the fields on the Board that are not yet marked by either an 'X' or an 'O'.
End of explanation
empty(gStart)
Explanation: In the state gStart, all positions are empty.
End of explanation
def toString(State):
    result = '+-+-+-+\n'
    for Row in State:
        result += '|'
        for cell in Row:
            result += cell + '|'
        result += '\n+-+-+-+\n'
    return result
print(toString(gStart))
Explanation: The function toString(State) represents the given state as a string.
End of explanation
def next_states(State, player):
    Empty  = empty(State)
    Result = []
    for row, col in Empty:
        NextState           = to_list(State)
        NextState[row][col] = player
        NextState           = to_tuple(NextState)
        Result.append(NextState)
    return Result
for S in next_states(gStart, 'X'):
    print(toString(S))
Explanation: Given a State and the player whose turn it is, the function next_states(State, player) computes the list of all states that can be reached from State.
End of explanation
gAllLines = [ [ (row, col) for col in range(3) ] for row in range(3) ] \
          + [ [ (row, col) for row in range(3) ] for col in range(3) ] \
          + [ [ (0, 0), (1, 1), (2, 2) ] ]                             \
          + [ [ (0, 2), (1, 1), (2, 0) ] ]
gAllLines
Explanation: The variable gAllLines collects the coordinates of all the fields of the three rows, the three columns, and the two diagonals.  This variable is needed to check whether the game has already terminated.
The name of the variable is prefixed with g to distinguish the variable as a global variable.
End of explanation
def utility(State):
    for Line in gAllLines:
        Marks = { State[row][col] for row, col in Line }
        if len(Marks) == 1 and  Marks != { ' ' }: 
            if Marks == { 'X' }:
                return  1
            else:
                return -1
    for row in range(3):
        for col in range(3):
            if State[row][col] == ' ':
                return None  # the board is not filled  
    # at this point, the board has been filled, but there is no winner, hence it's a draw
    return 0            
print(utility(gStart))
Explanation: The function utility takes one argument:
- State is a tuple of tuples representing the board.
The function returns 1 if the player X has won the game, -1 if the game is lost for player X, 0 if it's a draw, and None if the game has not yet been decided.
End of explanation
def finished(State): 
    return utility(State) != None
finished(gStart)
Explanation: finished(State) is True if and only if the game is over.
End of explanation
def get_move(State):
    State = to_list(State)
    while True:
        try:
            row, col = input('Enter move here: ').split(',')
            row, col = int(row), int(col)
            if State[row][col] == ' ':
                State[row][col] = 'O'
                return to_tuple(State)
            print("Don't cheat! Please try again.")  
        except:
            print('Illegal input.')  
            print('row and col are numbers from the set {0,1,2}.')
Explanation: The function get_move asks the user to input a move in the format r,c where r is the row and the c is the column where the next symbol is to be placed. Rows and columns are counted starting from 0.  It is assumed that the user plays as 'O', i.e. the user takes the second move.
End of explanation
def final_msg(State):
    if finished(State):
        if utility(State) == -1:
            print('You have won!')
        elif utility(State) == 1:
            print('The computer has won!')
        else:
            print("It's a draw.")
        return True
    return False
Explanation: This function informs the player, who is assumed to be 'O', about the result of the game once the game is finished.
End of explanation
import ipycanvas as cnv
g_size = 150
Explanation: Drawing the Board
End of explanation
def create_canvas():
    n = 3
    canvas = cnv.Canvas(size=(g_size * n, g_size * n + 50))
    display(canvas)
    return canvas
Explanation: This function creates the canvas for the start state.  It draws an empty board which is later used for the game.
End of explanation
def draw(State, canvas, value):
    canvas.clear()
    n = len(State)
    canvas.font = '90px sans-serif'
    canvas.text_align    = 'center'
    canvas.text_baseline = 'middle'
    for row in range(n):
        for col in range(n):
            x = col * g_size
            y = row * g_size
            canvas.line_width = 3.0
            canvas.stroke_rect(x, y, g_size, g_size)
            symbol = State[row][col]
            if symbol != ' ':
                x += g_size // 2
                y += g_size // 2
                if symbol == 'X':
                    canvas.fill_style ='red'
                else:
                    canvas.fill_style ='blue'
                canvas.fill_text(symbol, x, y)
    canvas.font = '12px sans-serif'
    canvas.fill_style = 'green'
    for row in range(n):
        for col in range(n):
            x = col * g_size + 16
            y = row * g_size + 141
            canvas.fill_text(f'({row}, {col})', x, y)            
    canvas.font = '20px sans-serif'
    canvas.fill_style = 'black'
    x = 1.5 * g_size
    y = 3.2 * g_size
    canvas.fill_text(str(value), x, y)
State = (('O', 'X', 'O'),
         ('X', 'O', 'X'),
         ('O', 'X', 'O')
        )
         
draw(State, create_canvas(), 1)
Explanation: This function takes three arguments:
- State is the current state of the game.
- canvas is a canvas used to draw the state.
- value is the value of the game for player X.
The function draws the given State onto canvas.  Below that, the value is printed.
End of explanation
gStart
import sys
Explanation: Checking the Memory Footprint
End of explanation
sys.getsizeof(gStart) + sum([sys.getsizeof(row) for row in gStart]) + 9 * sys.getsizeof('_')
Explanation: The memory needed to store a single state is the memory needed to store a list containing three objects  plus the memory needed to store those objects.
End of explanation
sys.getsizeof(1073741823)
Explanation: To compare, a single positive integer less than $1,073,741,824$ needs 28 bytes.
End of explanation
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