The Chessboard virus problem is similar to Conway's "Game of Life". The rule is that any two squares with infected neighbours will become infected.
I have tried to implement the simulation in Python, but there is a logic error. I think what is happening is that the board is being updated within a single round, so intermediate steps are missed. For example, with
grid = [
[0, 1, 0, 1],
[1, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]
]
I get following output:
Initial State of board:
0 1 0 1
1 0 0 0
0 0 0 0
0 0 0 0
State 2 of board:
1 1 1 1
1 1 1 1
0 0 0 0
0 0 0 0
Infinite loop entered.
The first round should only show
1 1 1 1
1 1 0 0
0 0 0 0
0 0 0 0
Unless I am mistaken.
Can anyone help me to fix the logic error please?
grid = [
[0, 1, 0, 1],
[1, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]
]
def write(grid):
"""
Writes the lists of lists of booleans
in grid using 0 for False and 1 for True.
"""
for row in grid:
for item in row:
print(f" {item}", end="")
print()
def neighbors(grid, i, j):
"""
Returns the number of live cells
next to grid[i][j]. Does not include diagonals.
"""
num_neighbours = 0
if i > 0:
if grid[i - 1][j]:
num_neighbours = num_neighbours + 1
if i < len(grid) - 1:
if grid[i + 1][j]:
num_neighbours = num_neighbours + 1
if j > 0:
if grid[i][j - 1]:
num_neighbours = num_neighbours + 1
if j < len(grid[i]) - 1:
if grid[i][j + 1]:
num_neighbours = num_neighbours + 1
print(num_neighbours)
return num_neighbours
def update(grid):
"""
Applies the rule of the chessboard virus to grid
and returns a new grid.
"""
new_board = grid[:]
for i in range(len(grid)):
for j in range(len(grid[i])):
num_neighbours = neighbors(grid, i, j)
if num_neighbours >= 2:
new_board[i][j] = 1
return new_board
def check_all_ones(a):
return not any(c != 1 for r in a for c in r)
def main():
"""
Runs the simulation.
"""
global grid
grid = grid
print("Initial State of board:")
print()
write(grid)
state_num = 1
while True:
last_grid = grid[:] # Clone grid.
grid = update(grid)
state_num = state_num + 1
print()
print(f"State {state_num} of board:")
print()
write(grid)
if check_all_ones(grid):
print()
print("Virus has spread to whole board.")
break
if grid == last_grid:
print()
print("Infinite loop entered.")
break
if __name__ == "__main__":
main()
I believe the problem is that new_board = grid[:] is not a 'deep' copy - the individual row lists are the original list objects from grid, so the update steps set + find all the newly filled neighbours in the first sweep.
It appears to work with a deep copy, e.g., using new_board = [r.copy() for r in grid] or new_board = copy.deepcopy(grid) (thnx @Demi-Lune).
As noted in the comment by @Ramirez below, the same applies to the clone in the main loop.