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Why does changing my np.array to a list give a different result for my minimax in Connect Four?

Currently am testing a connect four with minimax implementation and was playing around with numpy arrays and a regular matrix. I tried running the minimax function with a board created with a regular list matrix as opposed to a numpy array and it kept filling up the board state instead of dropping just one piece. I thought creating a shallow copy of the board state and passing it through wouldn't affect things, but I'm a bit stumped on this. It works fine with an numpy array.
import numpy as np
import random
import math
import copy
ROW_COUNT = 6
COLUMN_COUNT = 7
PLAYER = 0
AI = 1
EMPTY = 0
PLAYER_PIECE = 1
AI_PIECE = 2
WINDOW_LENGTH = 4
def create_board():
board = [[0 for x in range(COLUMN_COUNT)] for i in range(ROW_COUNT)]
# board = np.zeros((ROW_COUNT,COLUMN_COUNT), dtype=int)
return board
def drop_piece(board, row, col, piece):
board[row][col] = piece
def is_valid_location(board, col):
return board[0][col] == 0
def get_next_open_row(board, col):
for r in range(ROW_COUNT-1, -1, -1):
if board[r][col] == 0:
return r
def print_board(board):
# print(np.flip(board, 0))
for i in board:
print(i)
def winning_move(board, piece):
# Check horizontal locations for win
for c in range(COLUMN_COUNT-3):
for r in range(ROW_COUNT):
if board[r][c] == piece and board[r][c+1] == piece and board[r][c+2] == piece and board[r][c+3] == piece:
return True
# Check vertical locations for win
for c in range(COLUMN_COUNT):
for r in range(ROW_COUNT-3):
if board[r][c] == piece and board[r+1][c] == piece and board[r+2][c] == piece and board[r+3][c] == piece:
return True
# Check positively sloped diaganols
for c in range(COLUMN_COUNT-3):
for r in range(ROW_COUNT-3):
if board[r][c] == piece and board[r+1][c+1] == piece and board[r+2][c+2] == piece and board[r+3][c+3] == piece:
return True
# Check negatively sloped diaganols
for c in range(COLUMN_COUNT-3):
for r in range(3, ROW_COUNT):
if board[r][c] == piece and board[r-1][c+1] == piece and board[r-2][c+2] == piece and board[r-3][c+3] == piece:
return True
def evaluate_window(window, piece):
score = 0
opp_piece = PLAYER_PIECE
if piece == PLAYER_PIECE:
opp_piece = AI_PIECE
if window.count(piece) == 4:
score += 100
elif window.count(piece) == 3 and window.count(EMPTY) == 1:
score += 5
elif window.count(piece) == 2 and window.count(EMPTY) == 2:
score += 2
if window.count(opp_piece) == 3 and window.count(EMPTY) == 1:
score -= 4
return score
def score_position(board, piece):
score = 0
## Score center column
# center_array = [int(i) for i in list(board[:, COLUMN_COUNT//2])]
center_array = [int(i) for i in [col[COLUMN_COUNT//2] for col in board]]
center_count = center_array.count(piece)
score += center_count * 3
## Score Horizontal
for r in range(ROW_COUNT):
# row_array = [int(i) for i in list(board[r,:])]
row_array = [i for i in board[r]]
for c in range(COLUMN_COUNT-3):
window = row_array[c:c+WINDOW_LENGTH]
score += evaluate_window(window, piece)
## Score Vertical
for c in range(COLUMN_COUNT):
# col_array = [int(i) for i in list(board[:,c])]
col_array = [col[c] for col in board]
for r in range(ROW_COUNT-3):
window = col_array[r:r+WINDOW_LENGTH]
score += evaluate_window(window, piece)
## Score posiive sloped diagonal
for r in range(ROW_COUNT-3):
for c in range(COLUMN_COUNT-3):
window = [board[r+i][c+i] for i in range(WINDOW_LENGTH)]
score += evaluate_window(window, piece)
for r in range(ROW_COUNT-3):
for c in range(COLUMN_COUNT-3):
window = [board[r+3-i][c+i] for i in range(WINDOW_LENGTH)]
score += evaluate_window(window, piece)
return score
def is_terminal_node(board):
return winning_move(board, PLAYER_PIECE) or winning_move(board, AI_PIECE) or len(get_valid_locations(board)) == 0
def minimax(board, depth, alpha, beta, maximizingPlayer):
valid_locations = get_valid_locations(board)
is_terminal = is_terminal_node(board)
if depth == 0 or is_terminal:
if is_terminal:
if winning_move(board, AI_PIECE):
return (None, 100000000000000)
elif winning_move(board, PLAYER_PIECE):
return (None, -10000000000000)
else: # Game is over, no more valid moves
return (None, 0)
else: # Depth is zero
return (None, score_position(board, AI_PIECE))
if maximizingPlayer:
value = -math.inf
column = random.choice(valid_locations)
for col in valid_locations:
row = get_next_open_row(board, col)
b_copy = board.copy()
drop_piece(b_copy, row, col, AI_PIECE)
new_score = minimax(b_copy, depth-1, alpha, beta, False)[1]
if new_score > value:
value = new_score
column = col
alpha = max(alpha, value)
if alpha >= beta:
break
return column, value
else: # Minimizing player
value = math.inf
column = random.choice(valid_locations)
for col in valid_locations:
row = get_next_open_row(board, col)
b_copy = board.copy()
drop_piece(b_copy, row, col, PLAYER_PIECE)
new_score = minimax(b_copy, depth-1, alpha, beta, True)[1]
if new_score < value:
value = new_score
column = col
beta = min(beta, value)
if alpha >= beta:
break
return column, value
def get_valid_locations(board):
valid_locations = []
for col in range(COLUMN_COUNT):
if is_valid_location(board, col):
valid_locations.append(col)
return valid_locations
def pick_best_move(board, piece):
valid_locations = get_valid_locations(board)
best_score = -10000
best_col = random.choice(valid_locations)
for col in valid_locations:
row = get_next_open_row(board, col)
temp_board = board.copy()
drop_piece(temp_board, row, col, piece)
score = score_position(temp_board, piece)
if score > best_score:
best_score = score
best_col = col
return best_col
Testing here, dropping just one piece and then running minimax to get the best piece.
board = create_board()
print_board(board)
print("\n")
game_over = False
if is_valid_location(board,1):
row = get_next_open_row(board,1)
drop_piece(board, row, 1, PLAYER_PIECE)
print_board(board)
print("\n")
checker, score = minimax(board, 5, -math.inf, math.inf, True)
if is_valid_location(board,checker):
row = get_next_open_row(board,checker)
drop_piece(board, row, checker, AI_PIECE)
print_board(board)
print("\n")

Global variable resets in Python

I created a sudoku solver with backtracking algorithm (Python 3.8). It is a recursive algorithm. The sudoku board (puzzle) is a global variable (multiple functions need to share it). The solve() function does its task, but the value of the board doesn't change even after using the global keyword. Your help is needed.
The code:
board = [
[5,3,0,0,7,0,0,0,0],
[6,0,0,1,9,5,0,0,0],
[0,9,8,0,0,0,0,6,0],
[8,0,0,0,6,0,0,0,3],
[4,0,0,8,0,3,0,0,1],
[7,0,0,0,2,0,0,0,6],
[0,6,0,0,0,0,2,8,0],
[0,0,0,4,1,9,0,0,5],
[0,0,0,0,8,0,0,7,9]]
def isPossible(y, x, val): # checks if it is legal to put a value at a certain position
for row in board: # row condition
if val == row[x]:
return False
for col in board[y]: # column condition
if val == col:
return False
# subcell condition
subCellRow = (y // 3) * 3
subCellCol = (x // 3) * 3
for row in board[subCellRow:subCellRow + 3]:
for col in row[subCellCol:subCellCol + 3]:
if val == col:
return False
return True
def solve():
global board
for y in range(9):
for x in range(9):
if board[y][x] == 0:
for n in range(1, 10):
if isPossible(y, x, n): # python stairs
board[y][x] = n
solve() # recursion starts
board[y][x] = 0 # 1-line backtracking algorithm
return
printPuzzle() # prints the solved puzzle
return True
def printPuzzle(): # to display the puzzle
print()
for row in board:
for val in row:
print(val, end = ' ')
print()
printPuzzle()
solve()
printPuzzle() # prints the unsolved board

This wasn't the mistake of the global variable, this is happening because there is a slight mistake in your implementation of the algorithm which is reassigning the value to zero at board[y][x] = 0.
Here is the implementation which I think is correct.
board = [
[5,3,0,0,7,0,0,0,0],
[6,0,0,1,9,5,0,0,0],
[0,9,8,0,0,0,0,6,0],
[8,0,0,0,6,0,0,0,3],
[4,0,0,8,0,3,0,0,1],
[7,0,0,0,2,0,0,0,6],
[0,6,0,0,0,0,2,8,0],
[0,0,0,4,1,9,0,0,5],
[0,0,0,0,8,0,0,7,9]]
def isPossible(y, x, val): # checks if it is legal to put a value at a certain position
for row in board: # row condition
if val == row[x]:
return False
for col in board[y]: # column condition
if val == col:
return False
# subcell condition
subCellRow = (y // 3) * 3
subCellCol = (x // 3) * 3
for row in board[subCellRow:subCellRow + 3]:
for col in row[subCellCol:subCellCol + 3]:
if val == col:
return False
return True
def solve():
global board
for y in range(9):
for x in range(9):
if board[y][x] == 0:
for n in range(1, 10):
if isPossible(y, x, n): # python stairs
board[y][x] = n
if solve():
return True # recursion starts
board[y][x] = 0
return False
printPuzzle() # prints the solved puzzle
return True
def printPuzzle(): # to display the puzzle
print()
for row in board:
for val in row:
print(val, end = ' ')
print()
printPuzzle()
solve()
printPuzzle() # prints the unsolved board
Output I am getting:

Slow performance in agent based model python

I originally posted this on code-review (hence the lengthy code) but failed to get an answer.
My model is based on this game https://en.wikipedia.org/wiki/Ultimatum_game . I won't go into the intuition behind it but generally speaking it functions as follows:
The game consists of a n x n lattice on which an agent is placed at each node.
During each time step, each player on each node plays against a random neighbour by playing a particular strategy.
Each of their strategies (a value between 1-9) has a propensity attached to it (which is randomly assigned and is just some number). The propensity then in turn determines the probability of playing that strategy. The probability is calculated as the propensity of that strategy over the sum of the propensities of all strategies.
If a game results in a positive payoff, then the payoffs from that game get added to the propensities for those strategies.
These propensities then determine the probabilities for their strategies in the next time step, and so on.
The simulation ends after time step N is reached.
For games with large lattices and large time steps, my code runs really really slowly. I ran cProfiler to check where the bottleneck(s) are, and as I suspected the update_probabilitiesand play_rounds functions seem to be taking up a lot time. I want to be able to run the game with gridsize of about 40x40 for about 100000+ time steps, but right now that is not happening.
So what would be a more efficient way to calculate and update the probabilities/propensities of each player in the grid? I've considered implementing NumPy arrays but I am not sure if it would be worth the hassle here?
import numpy as np
import random
from random import randint
from numpy.random import choice
from numpy.random import multinomial
import cProfile
mew = 0.001
error = 0.05
def create_grid(row, col):
return [[0 for j in range(col)] for i in range(row)]
def create_random_propensities():
propensities = {}
pre_propensities = [random.uniform(0, 1) for i in range(9)]
a = np.sum(pre_propensities)
for i in range(1, 10):
propensities[i] = (pre_propensities[i - 1]/a) * 10 # normalize sum of propensities to 10
return propensities
class Proposer:
def __init__(self):
self.propensities = create_random_propensities()
self.probabilites = []
self.demand = 0 # the amount the proposer demands for themselves
def pick_strat(self, n_trials): # gets strategy, an integer in the interval [1, 9]
results = multinomial(n_trials, self.probabilites)
i, = np.where(results == max(results))
if len(i) > 1:
return choice(i) + 1
else:
return i[0] + 1
def calculate_probability(self, dict_data, index, total_sum): # calculates probability for particular strat, taking propensity
return dict_data[index]/total_sum # of that strat as input
def calculate_sum(self, dict_data):
return sum(dict_data.values())
def initialize(self):
init_sum = self.calculate_sum(self.propensities)
for strategy in range(1, 10):
self.probabilites.append(self.calculate_probability(self.propensities, strategy, init_sum))
self.demand = self.pick_strat(1)
def update_strategy(self):
self.demand = self.pick_strat(1)
def update_probablities(self):
for i in range(9):
self.propensities[1 + i] *= 1 - mew
pensity_sum = self.calculate_sum(self.propensities)
for i in range(9):
self.probabilites[i] = self.calculate_probability(self.propensities, 1 + i, pensity_sum)
def update(self):
self.update_probablities()
self.update_strategy()
class Responder: # methods same as proposer class, can skip-over
def __init__(self):
self.propensities = create_random_propensities()
self.probabilites = []
self.max_thresh = 0 # the maximum demand they are willing to accept
def pick_strat(self, n_trials):
results = multinomial(n_trials, self.probabilites)
i, = np.where(results == max(results))
if len(i) > 1:
return choice(i) + 1
else:
return i[0] + 1
def calculate_probability(self, dict_data, index, total_sum):
return dict_data[index]/total_sum
def calculate_sum(self, dict_data):
return sum(dict_data.values())
def initialize(self):
init_sum = self.calculate_sum(self.propensities)
for strategy in range(1, 10):
self.probabilites.append(self.calculate_probability(self.propensities, strategy, init_sum))
self.max_thresh = self.pick_strat(1)
def update_strategy(self):
self.max_thresh = self.pick_strat(1)
def update_probablities(self):
for i in range(9):
self.propensities[1 + i] *= 1 - mew # stops sum of propensites from growing without bound
pensity_sum = self.calculate_sum(self.propensities)
for i in range(9):
self.probabilites[i] = self.calculate_probability(self.propensities, 1 + i, pensity_sum)
def update(self):
self.update_probablities()
self.update_strategy()
class Agent:
def __init__(self):
self.prop_side = Proposer()
self.resp_side = Responder()
self.prop_side.initialize()
self.resp_side.initialize()
def update_all(self):
self.prop_side.update()
self.resp_side.update()
class Grid:
def __init__(self, rowsize, colsize):
self.rowsize = rowsize
self.colsize = colsize
def make_lattice(self):
return [[Agent() for j in range(self.colsize)] for i in range(self.rowsize)]
#staticmethod
def von_neumann_neighbourhood(array, row, col, wrapped=True): # gets up, bottom, left, right neighbours of some node
neighbours = set([])
if row + 1 <= len(array) - 1:
neighbours.add(array[row + 1][col])
if row - 1 >= 0:
neighbours.add(array[row - 1][col])
if col + 1 <= len(array[0]) - 1:
neighbours.add(array[row][col + 1])
if col - 1 >= 0:
neighbours.add(array[row][col - 1])
#if wrapped is on, conditions for out of bound points
if row - 1 < 0 and wrapped == True:
neighbours.add(array[-1][col])
if col - 1 < 0 and wrapped == True:
neighbours.add(array[row][-1])
if row + 1 > len(array) - 1 and wrapped == True:
neighbours.add(array[0][col])
if col + 1 > len(array[0]) - 1 and wrapped == True:
neighbours.add(array[row][0])
return neighbours
def get_error_term(pay, strategy):
index_strat_2, index_strat_8 = 2, 8
if strategy == 1:
return (1 - (error/2)) * pay, error/2 * pay, index_strat_2
if strategy == 9:
return (1 - (error/2)) * pay, error/2 * pay, index_strat_8
else:
return (1 - error) * pay, error/2 * pay, 0
class Games:
def __init__(self, n_rows, n_cols, n_rounds):
self.rounds = n_rounds
self.rows = n_rows
self.cols = n_cols
self.lattice = Grid(self.rows, self.cols).make_lattice()
self.lookup_table = np.full((self.rows, self.cols), False, dtype=bool) # if player on grid has updated their strat, set to True
def reset_look_tab(self):
self.lookup_table = np.full((self.rows, self.cols), False, dtype=bool)
def run_game(self):
n = 0
while n < self.rounds:
for r in range(self.rows):
for c in range(self.cols):
if n != 0:
self.lattice[r][c].update_all()
self.lookup_table[r][c] = True
self.play_rounds(self.lattice, r, c)
self.reset_look_tab()
n += 1
def play_rounds(self, grid, row, col):
neighbours = Grid.von_neumann_neighbourhood(grid, row, col)
neighbour = random.sample(neighbours, 1).pop()
neighbour_index = [(ix, iy) for ix, row in enumerate(self.lattice) for iy, i in enumerate(row) if i == neighbour]
if self.lookup_table[neighbour_index[0][0]][neighbour_index[0][1]] == False: # see if neighbour has already updated their strat
neighbour.update_all()
player = grid[row][col]
coin_toss = randint(0, 1) # which player acts as proposer or responder in game
if coin_toss == 1:
if player.prop_side.demand <= neighbour.resp_side.max_thresh: # postive payoff
payoff, adjacent_payoff, index = get_error_term(player.prop_side.demand, player.prop_side.demand)
if player.prop_side.demand == 1 or player.prop_side.demand == 9: # extreme strategies get bonus payoffs
player.prop_side.propensities[player.prop_side.demand] += payoff
player.prop_side.propensities[index] += adjacent_payoff
else:
player.prop_side.propensities[player.prop_side.demand] += payoff
player.prop_side.propensities[player.prop_side.demand - 1] += adjacent_payoff
player.prop_side.propensities[player.prop_side.demand + 1] += adjacent_payoff
else:
return 0 # if demand > max thresh -> both get zero
if coin_toss != 1:
if neighbour.prop_side.demand <= player.resp_side.max_thresh:
payoff, adjacent_payoff, index = get_error_term(10 - neighbour.prop_side.demand, player.resp_side.max_thresh)
if player.resp_side.max_thresh == 1 or player.resp_side.max_thresh == 9:
player.resp_side.propensities[player.resp_side.max_thresh] += payoff
player.resp_side.propensities[index] += adjacent_payoff
else:
player.resp_side.propensities[player.resp_side.max_thresh] += payoff
player.resp_side.propensities[player.resp_side.max_thresh - 1] += adjacent_payoff
player.resp_side.propensities[player.resp_side.max_thresh + 1] += adjacent_payoff
else:
return 0
#pr = cProfile.Profile()
#pr.enable()
my_game = Games(10, 10, 2000) # (rowsize, colsize, n_steps)
my_game.run_game()
#pr.disable()
#pr.print_stats(sort='time')
(For those who might be wondering, the get_error_term just returns the propensities for strategies that are next to strategies that receive a positive payoff, for example if the strategy 8 works, then 7 and 9's propensities also get adjusted upwards and this is calculated by said function. And the first for loop inside update_probabilities just makes sure that the sum of propensities don't grow without bound).

Python Game of Life, only alive cells is in the corners

I'm currently working on making a Game of Life program (UNI related, beginner course), by using nested lists.
However I can't seem to get the update() method to work properly, I've no clue what's wrong. The generation of the first board is okay, but the update leaves only the cornercells alive, and the rest dead.
All methodcalls in this class originates from other .py files, which works well.
from random import randint
from cell import *
class Spillebrett:
def __init__(self, rows, columns):
self.genNumber = 0
self._rows = rows
self._columns = columns
self._grid = []
for i in range(self._rows):
self._grid.append([])
for j in range(self._columns):
self._grid[i].append(cell())
self.generate()
def drawBoard(self):
for i in self._grid:
print(" ".join(map(str, i)))
print()
#Method updates genNumber, checks if cells are alive or dead and updates the board accordingly
#Currently only yield board with corner-cells alive
def updateBoard(self):
self.genNumber += 1
toLive = []
toDie = []
for x, row in enumerate(self._grid):
for y, cell in enumerate(rad):
if cell.areAlive() is True:
counter = len(self.findNeighbour(x, y))
if counter < 2 or counter > 3:
toDie.append(cell)
elif counter == 2 or counter == 3:
toLive.append(cell)
elif cell.areAlive() is False:
counter = len(self.findNeighbour(x, y))
if counter == 3:
toLive.append(cell)
for i in toDie:
i.setDead()
for i in toLive:
i.setAlive()
return self.genNumber
#Code given by Uni
def generate(self):
for i in range(self._rows):
for j in range(self._columns):
rand = randint(0, 3)
if rand == 3:
self._grid[i][j].setAlive()
#Code given by Uni
def findNeighbour(self, row, column):
neighbourList = []
for i in range(-1, 2):
for j in range(-1, 2):
neighbourRow = rad + i
neighbourcolumn = column + j
if(neighbourRow == rad and neighbourcolumn == column) is not True:
if(neighbourRow < 0 or neighbourcolumn < 0 or neighbourRow >
self._rows - 1 or neighbourcolumn > self._columns - 1) is not True:
neighbourList.append(self._grid[neighbourRow][neighbourcolumn])
return neighbourList
def findAllAlive(self):
self._alive = 0
for i in range(self._rows):
for j in range(self._columns):
if self._grid[i][j].areAlive() is True:
self._alive += 1
return self._alive

Python: Trying to program a variant of connect four: Winning condition doesn't stop

I have been trying to program a variant of connect four for my programming class. The board is 6x8 in size. In the variant I'm trying to program, the winning condition is to essentially build an L.
This means any construction of the form
X
X
X X
is a winning condition.
I have been trying to make a function that checks every single column for the same symbol consecutively to build a pair. And a function to do the same for every row. With these two functions I would then check if 2 pairs are consecutive, because no matter how you combine a vertical and horizontal pair, it will always build an 'L'.
To make a clear board I'm using
def ClearBoardSingle():
global Board
Board = [['0' for i in range(8)] for i in range(6)]
BoardPrint()
PlayerMoveSingle()
And for my interface I'm using
def BoardPrint():
global Board
global GameMoves
global PlayerTurn
global Player1Symbol
global Player2Symbol
print('\n\nMoves done: ' + str(GameMoves))
print('To Restart: R | To Quit: Q')
print('Valid choices: 1, 2, 3, 4, 5, 6, 7, 8')
if PlayerTurn == 0:
print('It\'s ' +str(Player1Symbol) + '\'s Turn')
if PlayerTurn == 1:
print('It\'s ' +str(Player2Symbol) + '\'s Turn')
print(Board[0])
print(Board[1])
print(Board[2])
print(Board[3])
print(Board[4])
print(Board[5])
I already figured out how to change Variables inside the Board, and I'm pretty much done. The only thing I don't know how to implement is the winning condition. I tried this function for the Rows:
def VerticalList(Column):
global Board
global Choice
global Row0
Column = int(Column)
Choice = int(Choice)
print(Column,' C')
while Column > 0:
for Board[Column][Choice] in range(Column):
Row0.append(Board[Column][Choice])
if Column ==6 or Column == -1:
break
else:
VerticalList(Column-1)
if Column ==0:
break
else:
continue
if Column == 0:
Column += 1
while Column < 5:
Column +=1
if Row0[Column] == Row0[Column-1]:
print('Pair')
else:
print('No Pair')
pass
else:
pass
But it enters an endless Loop.
I have no ideas anymore on how to implement the winning condition. I'd appreciate any kind of help or ideas. If you want me to post the whole code or other kinds of snippets, ask for them.
Thank you in anticipation!

Cool problem, below looks like a lot of code, but it's not really. I haven't checked this extensively, so I'm not confident that it doesn't find false positives, but it seems to find L's that it should be finding. The main thing I did was use itertools.combinations to take all 4-sized groups of the positions of X's and then check if they looked like patterns I was expecting for L's. In check_four_group I look at the differences within the row and columns.
from itertools import combinations
def disp_board(board):
for row in board:
print(row)
def check_winning(board):
winning = False
#Find all row,col positions of the X's
x_poses = [(i,j) for i in range(6) for j in range(8) if board[i][j] == 'X']
#Loop through every combination of four X's since it takes four to make the 'L'
for group in combinations(x_poses,4):
if(check_four_group(group)):
winning = True
break
return winning
def check_four_group(group):
rows,cols = zip(*[(r,c) for r,c in group])
row_diffs = [rows[i+1]-rows[i] for i in range(len(rows)-1)]
col_diffs = [cols[i+1]-cols[i] for i in range(len(cols)-1)]
#Uncomment this to print the row and col diffs
#print(row_diffs)
#print(col_diffs)
# Finds:
# X
# X
# X X
if row_diffs == [1,1,0] and col_diffs == [0,0,1]:
return True
# Finds:
# X
# X
# X X
elif row_diffs == [1,1,0] and col_diffs == [0,-1,1]:
return True
# Finds:
# X X
# X
# X
elif row_diffs == [0,1,1] and col_diffs == [1,0,0]:
return True
# Finds:
# X X
# X
# X
elif row_diffs == [0,1,1] and col_diffs == [1,-1,0]:
return True
# Otherwise it's not there at all (not thinking about horizontal L's but could add that)
else:
return False
#Test case 1
def test_case_1():
board = [['0' for i in range(8)] for i in range(6)]
board[2][1] = 'X'
board[2][2] = 'X'
board[3][1] = 'X'
board[4][1] = 'X'
return board
#Test case 2
def test_case_2():
board = [['0' for i in range(8)] for i in range(6)]
board[2][1] = 'X'
board[2][0] = 'X'
board[3][1] = 'X'
board[4][1] = 'X'
return board
#Test case 3
def test_case_3():
board = [['0' for i in range(8)] for i in range(6)]
board[1][0] = 'X'
board[2][0] = 'X'
board[3][0] = 'X'
board[3][1] = 'X'
return board
#Test case 4
def test_case_4():
board = [['0' for i in range(8)] for i in range(6)]
board[1][2] = 'X'
board[2][2] = 'X'
board[3][2] = 'X'
board[3][1] = 'X'
return board
##################
#Start of program#
##################
board = test_case_1()
#board = test_case_2()
#board = test_case_3()
#board = test_case_4()
disp_board(board)
if check_winning(board):
print('Victory')
else:
print('Keep playing')