Python TicTacToe 函数的时间复杂度

Question

def TicTacToe():
    board = [['S' for i in range(3)] for j in range(3)]
    BoardState(board)

    for i in range(8):
        if(i % 2 == 0):
            print("Enter the position player 1: ")
            a = int(input())
            b = int(input())
            if(board[a - 1][b - 1] == 'S'):
                board[a - 1][b - 1] = 1
            else:
                print("Invalid Input, game over")
                return
        else:
            print("Enter the position player 2: ")
            a = int(input())
            b = int(input())
            if(board[a - 1][b - 1] == 'S'):
                board[a - 1][b - 1] = 0
            else:
                print("Invalid input, game over")
                return
                
        BoardState(board)
        
        if(board[0][0] == 1 and board[1][1] == 1 and board[2][2] == 1):
            return "Player 1 wins"
        if(board[0][0] == 0 and board[1][1] == 0 and board[2][2] == 0):
            return "Player 2 wins"
        if(board[0][2] == 1 and board[1][1] == 1 and board[2][0] == 1):
            return "Player 1 wins"
        if(board[0][2] == 0 and board[1][1] == 0 and board[2][0] == 0):
            return "Player 2 wins"
        if(CheckState(board) == 0):
            return "game over"
        
    return "Draw"

def CheckState(board):        
    for x in range(3):
        if board[x][0] == board[x][1] == board[x][2] != 'S' \
        or board[0][x] == board[1][x] == board[2][x] != 'S':
            return 0
        
def BoardState(board):
    for i in range(3):
        for j in range(3):
            print(board[i][j], end = ' ')
        print("\n")    


TicTacToe();

This is a not-so-clean code I wrote for the game of tictactoe. What would be its time complexity?

The program consists of 3 functions and I wish to calculate the complexity for the same. Would it be O(1) as the input size is already fixed it doesn't vary with whatever the user inputs?

Answer 1

Would it be O(1) as the input size is already fixed it doesn't vary with whatever the user inputs?

Yes, that is exactly right. All of the loops have a fixed number of iterations.

Answer 2

I think you're actually talking about two different problems: The first is a program to act as a "referee", similar to your program above. The second is a program to play against a human player (or other program).

For complexity, think about the case of an N x N tic tac toe board. In that case, I think the complexity of the first problem is O(N), while for the second, it's exponential in N.