def maximize(grid, depth=DEPTH, alpha=MIN_VALUE, beta=MAX_VALUE):
"""
Maximize function for the max (AI) of the MiniMax Algorithm
If you want to change the depth of the search tree, try to
implement some conditions for the "early stopping" at minimize
or set up your own limit constant.
"""
# TODO: Replace the value of the best_score
# If you are not sure, check the implementation we talked about in week 2
empty_cells = free_cells(grid)
if depth == 0:
return 0, heuristics(grid, len(empty_cells))
best_score = MIN_VALUE
best_move = None
for i in range(4):
moved_grid = deepcopy(grid)
_, num, _ = move(moved_grid, i)
if num != 0:
new_score = minimize(moved_grid, depth - 1, alpha, beta)
if best_score < new_score:
best_move = i
best_score = new_score
# alpha = max(alpha, best_score)
#
# if beta <= alpha:
# break
return best_move, best_score
def maximize(grid, depth=0, alpha=float("-inf"), beta=float("inf")):
'''
Maximize function for the max (AI) of the MiniMax Algorithm
If you want to change the depth of the search tree, try to
implement some conditions for the "early stopping" at minimize
or set up your own limit constant.
'''
empty_cells = free_cells(grid)
num_empty = len(empty_cells)
if depth > DEPTH:
return None, heuristics(grid, num_empty)
# TODO: Replace the value of the best_score
# If you are not sure, check the implementation we talked about in week 2
best_score = float('-inf')
best_move = None
# TODO: Implement maximize function here
for i in range(4):
new_grid = deepcopy(grid)
move(new_grid, i)
if (not same(grid, new_grid)):
sum_score = minimize(new_grid, depth + 1)
if sum_score > best_score:
best_score = sum_score
best_move = i
alpha = max(alpha, best_score)
if beta <= alpha:
break
return best_move, best_score
def minimize(grid, depth=DEPTH, alpha=MIN_VALUE, beta=MAX_VALUE):
"""
Minimize function for the min (Computer) of the Minimax Algorithm
Computer put new 2 tile (with 90% probability) or
4 tile (with 10% probability) at one of empty spaces
"""
empty_cells = free_cells(grid)
num_empty = len(empty_cells)
if depth == 0:
return heuristics(grid, num_empty)
if num_empty == 0:
# return heuristics(grid, num_empty)
_, new_score = maximize(grid, depth - 1, alpha, beta)
return new_score
# TODO: (Optional) Implement conditions to stop the searching earlier
# Would implement it after finish implementing Heuristics and MiniMax
# ex) If there are enough empty spaces, we will proceed by skipping last two nodes
if num_empty >= 6 and depth >= 3:
return heuristics(grid, num_empty)
sum_score = 0
for c, r in empty_cells:
for v in [2, 4]:
new_grid = deepcopy(grid)
new_grid[c][r] = v
_, new_score = maximize(new_grid, depth - 1, alpha, beta)
# beta = new_score
# beta = min(beta, new_score)
# if beta <= alpha:
# break
if v == 2:
new_score *= (0.9 / num_empty) # Probability of 2 tile being placed
else:
new_score *= (0.1 / num_empty) # Probability of 4 tile being placed
sum_score += new_score
return sum_score
def minimize(grid, depth=0, alpha=float("-inf"), beta=float("inf")):
'''
Minimize function for the min (Computer) of the Minimax Algorithm
Computer put new 2 tile (with 90% probability) or
4 tile (with 10% probability) at one of empty spaces
'''
empty_cells = free_cells(grid)
num_empty = len(empty_cells)
if num_empty >= 6 and depth >= 3:
return heuristics(grid, num_empty)
if depth > DEPTH:
return heuristics(grid, num_empty)
if num_empty == 0:
_, new_score = maximize(grid, depth + 1)
return new_score
# TODO: (Optional) Implement conditions to stop the searching earlier
# Would implement it after finish implementing Heuristics and MiniMax
# ex) If there are enough empty spaces, we will proceed by skipping last two nodes
# if num_empty >= 6 and depth >= 3:
# return heuristics(grid, num_empty)
sum_score = 0
for r, c in empty_cells: #random.sample(range(len(empty_cells)), min(len(empty_cells),4)):
#r,c = empty_cells[i]
for v in [2, 4]:
new_grid = deepcopy(grid)
new_grid[c][r] = v
_, new_score = maximize(new_grid, depth + 1, alpha, beta)
if v == 2:
new_score *= (0.9 / num_empty)
else:
new_score *= (0.1 / num_empty)
sum_score += new_score
beta = min(beta, new_score)
if beta <= alpha:
break
return sum_score