def minimax_max_node(board, color):
"""
Return the minimum score the MAX player can achieve
with any move starting at board.
"""
if not get_possible_moves(board, color):
return compute_utility(board, color)
alpha = -math.inf
for i, j in get_possible_moves(board, color):
new_board = play_move(board, color, i, j)
utility = minimax_min_node(new_board, color)
if utility > alpha:
alpha = utility
return alpha
def alphabeta_max_node(board, color, alpha, beta, limit, caching = 0, ordering = 0):
if caching == 1:
if board_mapping.get(board) != None:
return None, board_mapping.get(board)
myself = color
return_move = tuple()
possible_moves = get_possible_moves(board, myself)
if len(possible_moves) == 0 or limit == 0:
return None, compute_utility(board, myself)
if ordering == 1:
unsorted_score = {}
sorted_score = {}
for m in possible_moves:
new_board = play_move(board, myself, m[0], m[1])
unsorted_score.update({m:compute_utility(new_board, myself)})
sorted_score = sorted(unsorted_score.items(), key=lambda i:i[1], reverse=True)
possible_moves.clear()
for i in sorted_score:
possible_moves.append(i[0])
old_score = float('-inf')
for move in possible_moves:
new_board = play_move(board, myself, move[0], move[1])
if(alpha < beta):
score = alphabeta_min_node(new_board, myself, alpha, beta, limit-1, caching, ordering)
if score[1] > old_score:
old_score = score[1]
alpha = old_score
return_move = move
if caching == 1:
board_mapping.update({board : old_score})
return return_move, old_score
def alphabeta_max_node(board, color, beta, level, limit):
if not get_possible_moves(board, color):
return compute_utility(board, color)
alpha = -math.inf
for i, j in get_possible_moves(board, color):
new_board = play_move(board, color, i, j)
if level + 1 > limit:
continue
utility = alphabeta_min_node(new_board, color, alpha, level + 1, limit)
if utility > alpha:
alpha = utility
if alpha > beta:
return alpha
return alpha
def minmax_mode(maxi, board, color, limit, caching):
use_heuristics = False # default FALSE
# CHECK CACHE
if (caching and (board, color, maxi) in cache):
return cache[board, color, maxi]
test_color = color if maxi else next_color(color)
# DEPTH LIMIT REACHED
if limit == 0:
if use_heuristics:
return None, compute_heuristic(board, color)
else:
return None, compute_utility(board, color)
moves = get_possible_moves(board, test_color)
# TERMINAL STATE
if len(moves) == 0:
move_tup = (None, compute_utility(board, color))
if (caching):
cache[board, color, maxi] = move_tup
return move_tup
move_tups = []
for move in moves:
next_board = play_move(board, test_color, move[0], move[1])
if maxi:
move_util = minimax_min_node(next_board, color, limit - 1,
caching)[1]
else:
move_util = minimax_max_node(next_board, color, limit - 1,
caching)[1]
move_tups.append((move, move_util))
if maxi:
goal_tup = max(move_tups, key=lambda t: t[1])
else:
goal_tup = min(move_tups, key=lambda t: t[1])
if (caching):
cache[board, color, maxi] = goal_tup
return goal_tup
def minimax_max_node(board,
color,
limit,
caching=0): #returns highest possible utility
# Determine the player color
if color == 1:
oppo_color = 2
else:
oppo_color = 1
# the valid moved
valid_moves = get_possible_moves(board, color)
if (len(valid_moves) == 0):
# no move valid and board is not cached
return None, compute_utility(board, color)
elif (limit == 0):
return None, compute_utility(board, color)
else:
u_value_best = -1 * len(board) * len(
board) # set at max possible value
move_best = None
for move in valid_moves:
new_board = play_move(board, color, move[0], move[1])
# check if the new board is in the cache
if new_board in cached and caching:
new_move, u_value = cached[new_board]
else:
new_move, u_value = minimax_max_node(new_board, color,
limit - 1, caching)
if (caching):
cached[new_board] = (new_move, u_value)
# get the min value:
if (u_value > u_value_best):
u_value_best = u_value
move_best = move
return (move_best, u_value_best)
return ((0, 0), 0)
def alphabeta_max_node(board, color, alpha, beta, depth, maxdepth):
if depth > maxdepth or len(get_possible_moves(board, color)) <= 0:
if hash(board) not in seen_boards:
seen_boards.add(hash(board))
seen_boards_cost[hash(board)] = compute_utility(board, color)
return seen_boards_cost[hash(board)]
else:
nowAlpha = alpha
bestVal = -3000000000
bestCheck = []
for x in get_possible_moves(board, color):
playedBoard = play_move(board, color, x[0], x[1])
if playedBoard not in seen_boards_heuristic:
seen_boards_heuristic.add(playedBoard)
seen_boards_heuristic_cost[playedBoard] = get_heuristic(
playedBoard, color)
#toCheck = alphabeta_max_node(playedBoard, color, switch_color(currentColor), alpha, nowBeta, depth + 1, maxdepth )
bestCheck.append(
(seen_boards_heuristic_cost[playedBoard], playedBoard))
bestCheck.sort()
bestCheck.reverse()
for x, playedBoard in bestCheck:
#playedBoard = play_move(board, currentColor, x[0], x[1])
#toCheck = alphabeta_min_node(playedBoard, color, switch_color(currentColor), nowAlpha, beta, depth + 1, maxdepth )
toCheck = 0
if playedBoard not in seen_boards_min:
seen_boards_min.add(playedBoard)
seen_boards_min_cost[playedBoard] = alphabeta_min_node(
playedBoard, color, nowAlpha, beta, depth + 1, maxdepth)
toCheck = seen_boards_min_cost[playedBoard]
toCheck += random.randint(-volatile_level, volatile_level)
if toCheck > bestVal:
bestVal = toCheck
if bestVal > nowAlpha:
nowAlpha = bestVal
if nowAlpha >= beta:
break
#return max(childrenNodes)
return bestVal
def minimax_min_node(board, color):
#function MIN-VALUE(state) returns a utility value
#if TERMINAL-TEST(state) then return UTILITY(state) v←∞
#for each a in ACTIONS(state) do
#v ← MIN(v, MAX-VALUE(RESULT(s, a))) return v
moves = get_possible_moves(board, color)
move = min(moves)
#(col,row) tuples representing legal moves for player color
results = play_move(board, color, move)
#computes successor board state that results from player color playing move (a(col,row)tuple)
if color.status == "FINAL":
return color.compute_utility(board, color)
v = inf
for (a, s) in color.results(board):
v = min(v, minimax_max_node(board, color))
return v
def select_move_alphabeta(board, color):
moves = get_possible_moves(board, color)
max_score = float("-inf")
best_move = [0, 0]
alpha = float("-inf")
beta = float("inf")
for move in moves:
new_board = play_move(board, color, move[0], move[1])
score = alphabeta_min_node(new_board, color, alpha, beta, 1, limit)
if score > max_score:
max_score = score
best_move[0] = move[0]
best_move[1] = move[1]
alpha = max(alpha, max_score)
return best_move[0], best_move[1]
def select_move_alphabeta(board, color):
max_utility = float("-inf")
best_move = None
for move in get_possible_moves(board, color):
i,j = move
new_board = play_move(board, color, i,j)
utility = alphabeta_min_node(new_board, color, 0, float("-inf"), float("inf"), 24)
# select the move that gives the highest utility
if utility > max_utility:
max_utility = utility
best_move = (i, j)
return best_move
def minimax_max_node(board, color):
if board in move_dictionary:
return move_dictionary[board]
else:
max_next_nodes = get_possible_moves(board, color)
utility_list = []
if (len(max_next_nodes) == 0):
return compute_utility(board, color)
for items in max_next_nodes:
successor_board = play_move(board, color, items[0], items[1])
curr_utility = minimax_min_node(successor_board, color)
utility_list.append(curr_utility)
move_dictionary.update({board: min(utility_list)})
return max(utility_list)
def ordered_moves(board, moves, color, current_player):
'''This is for ordering possible moves'''
dic = dict()
result = []
for move in moves:
(column, row) = move
new_board = play_move(board, current_player, column, row)
successor_utility = compute_utility(new_board, color)
if successor_utility in dic and dic[successor_utility] != [move]:
dic[successor_utility].append(move)
else:
dic[successor_utility] = [move]
ordered_utility = sorted(list(dic.keys()), reverse=True)
for utility in ordered_utility:
result += dic[utility]
return result
def minimax_min_node(board, color):
anti_color = 3 - color
moves = get_possible_moves(board, anti_color)
if not moves:
return compute_utility(board, color)
mini_score = float("inf")
for move in moves:
new_board = play_move(board, anti_color, move[0], move[1])
score = minimax_max_node(new_board, color)
if score < mini_score:
mini_score = score
return mini_score
def minimax_min_node(board, color, depth, end_time):
possible_moves = get_possible_moves(board, color)
current_time = datetime.now()
if possible_moves == [] or depth == 0 or current_time >= end_time:
score = get_score_weighted(board) # get_score(board)
return score[color%2] - score[(color+1)%2]
else:
next_color = color % 2 + 1
best_min_score = 1000000
for move in possible_moves:
new_board = play_move(board, color, move[0], move[1])
move_score = minimax_max_node(new_board, next_color, depth - 1, end_time)
if move_score < best_min_score:
best_min_score = move_score
return best_min_score
return None
def select_move_alphabeta(board, color):
moves = get_possible_moves(board, color)
best_move = None
alpha = -math.inf
for move in moves:
if move == (0, 0) or move == (0, 7) or move == (7, 0) or move == (7,
7):
return move
i, j = move
new_board = play_move(board, color, i, j)
score = alphabeta_min_node(new_board, color, alpha, 0, 4)
if score > alpha:
best_move = move
alpha = score
return best_move
def alphabeta_min_node(board, color, alpha, beta, limit, caching = 0, ordering = 0):
if caching:
global cache
if board in cache.keys():
return cache[(board,color)]
opponent_col = None
if color == 1:
opponent_col = 2
else:
opponent_col = 1
list_of_moves = get_possible_moves(board, opponent_col)
if list_of_moves == [] or limit == 0:
return (None, compute_utility(board,color))
children = []
for move in list_of_moves:
children.append(play_move(board, opponent_col, move[0], move[1]))
if ordering:
utilities = []
for c in children:
utilities.append(compute_utility(c, color))
zipped = list(zip(utilities, children, list_of_moves))
zipped.sort(key = lambda x: x[0])
children = []
list_of_moves = []
for x, y, z in zipped:
children.append(y)
list_of_moves.append(z)
ut_val = float("inf")
values = []
for c in children:
ut_val = min(ut_val, alphabeta_max_node(c,color, alpha, beta, limit-1)[1])
values.append(ut_val)
beta = min(beta, ut_val)
if beta <= alpha:
return (None, ut_val)
move = list_of_moves[values.index(ut_val)]
if caching:
cache[(board,color)] = (move, ut_val)
return (move, ut_val)
def alphabeta_max_node(board,
color,
alpha,
beta,
limit,
caching=0,
ordering=0):
moves = get_possible_moves(board, color)
if moves == [] or limit == 0:
return (-1, -1), compute_utility(board, color)
max_utility = -float('inf')
successors = []
for i in range(len(moves)):
temp_board = play_move(board, color, moves[i][0], moves[i][1])
successors.append((temp_board, compute_utility(temp_board, color)))
if ordering == 1:
successors.sort(key=takeSecond, reverse=True)
for i in range(len(successors)):
if caching == 1:
if successors[i][0] in cached:
temp_utility = cached[successors[i][0]]
else:
temp_move, temp_utility = alphabeta_min_node(
successors[i][0], color, alpha, beta, limit - 1, caching,
ordering)
cached[successors[i][0]] = temp_utility
else:
temp_move, temp_utility = alphabeta_min_node(
successors[i][0], color, alpha, beta, limit - 1, caching,
ordering)
if temp_utility > max_utility:
max_utility = temp_utility
max_move = moves[i]
if alpha < max_utility:
alpha = max_utility
if beta <= alpha:
break
return max_move, max_utility
def alphabeta_max_node(board,
color,
alpha,
beta,
limit,
caching=0,
ordering=0):
#IMPLEMENT (and replace the line below)
# Check cache
if caching and (board, color) in cache:
return cache[(board, color)]
best_move = None
max_utility = float('-inf')
possible_moves = get_possible_moves(board, color)
# Check if limit reached or end of game
if limit == 0 or len(possible_moves) == 0:
return None, compute_utility(board, color)
# Order (move, board) tuples according to the utility successor states
move_and_board = []
for move in possible_moves:
nxt_board = play_move(board, color, move[0], move[1])
move_and_board.append((move, nxt_board))
if ordering:
move_and_board.sort(key=lambda move_and_board: compute_utility(
move_and_board[1], color),
reverse=True)
for (move, nxt_board) in move_and_board:
# Compute next utility
_, nxt_utility = alphabeta_min_node(nxt_board, color, alpha, beta,
limit - 1, caching, ordering)
if max_utility < nxt_utility:
best_move = move
max_utility = nxt_utility
# Prune
alpha = max(alpha, max_utility)
if alpha >= beta:
break
# Cache the board
if caching:
cache[(board, color)] = (best_move, max_utility)
return best_move, max_utility
def minimax_min_node(board, color):
if color == 2:
opp_color = 1
elif color == 1:
opp_color = 2
if not get_possible_moves(board, opp_color):
return compute_utility(board, color)
beta = math.inf
for i, j in get_possible_moves(board, opp_color):
new_board = play_move(board, opp_color, i, j)
utility = minimax_max_node(new_board, color)
if utility < beta:
beta = utility
return beta
def minimax_max_node(board, color):
possibleMoves = get_possible_moves(board, color)
if not possibleMoves:
return compute_utility(board, color)
bestMove = None
bestScore = -math.inf
for y in possibleMoves:
newBoard = play_move(board, color, y[0], y[1])
score = minimax_min_node(newBoard, oppColor)
if score > bestScore:
bestMove = move
bestScore = score
return bestScore
def minimax_max_node(board, color):
if board in minimax_cache.keys():
return minimax_cache[board]
opponent_color = 0
if color == 1:
opponent_color = 2
else:
opponent_color = 1
possible_moves = get_possible_moves(board, color)
if not possible_moves:
return compute_utility(board, color)
v = float("-inf")
for move in possible_moves:
new_board = play_move(board, color, move[0], move[1])
v = max(v, minimax_min_node(new_board, opponent_color))
minimax_cache[new_board] = v
return v
def select_move_minimax(board, color):
"""
Given a board and a player color, decide on a move.
The return value is a tuple of integers (i,j), where
i is the column and j is the row on the board.
"""
moves = get_possible_moves(board, color)
bestMoveScore = -math.inf
bestMove = (1, 1)
for i in moves:
newBoard = play_move(board, color, i[0], i[1])
score = minimax_min_node(newBoard, color)
if score > bestMoveScore:
bestMoveScore = score
bestMove = i
return bestMove
def select_move_minimax(board, color):
"""
Given a board and a player color, decide on a move.
The return value is a tuple of integers (i,j), where
i is the column and j is the row on the board.
"""
best_value = 0
for (i, j) in get_possible_moves(board, color):
next_board = play_move(board, color, i, j)
value = minimax_min_node(next_board, color)
if value > best_value:
best_value = value
x = i
y = j
return x, y
def move_mobility_heuristic(board,color):
'''
A secondary heuristic to maximize the number of plays the AI can do. Intended to synergize with sweet 16.
'''
if color == 1:
opposing_color = 2
else:
opposing_color = 1
opposing_possible_moves = 0
moves = get_possible_moves(board,color)
for (column,row) in moves:
new_board = play_move(board,color,column,row)
if len(get_possible_moves(new_board,opposing_color)) > opposing_possible_moves:
opposing_possible_moves = len(get_possible_moves(new_board,opposing_color))
#sys.stderr.write('Move mobility: {}\n'.format(len(moves) - opposing_possible_moves))
return len(moves) - opposing_possible_moves + random.randint(0,9)
def select_move_alphabeta(board, color):
dic = {}
if color == 1:
opponent_color = 2
else:
opponent_color = 1
v = -inf
#v = alphabeta_max_node(board, color, -inf, inf)
for successor in get_possible_moves(board, color):
new_board = play_move(board, color, successor[0], successor[1])
v = max(v,
alphabeta_min_node(new_board, opponent_color, -inf, inf, 1, 5))
if v not in dic:
dic.update({v: successor})
return dic[v]
def minimax_max_node(board, color, limit, caching = 0): #returns highest possible utility
#IMPLEMENT (and replace the line belowS
global cache
if color==1: other_color=2
else: other_color=1
limit-=1
if caching==1:
if board in cache:
return cache[board]
#iniitlazing a very low value for the node
best_node = float("-Inf")
#checking if we are at the end leaf
if not get_possible_moves(board,color) or limit==0:
return compute_utility(board,color)
for move in get_possible_moves(board,color):
best_node= max(best_node,minimax_min_node(play_move(board,color,move[0],move[1]),opponent,lim))
return best_node
def alphabeta_max_node(board, color, beta, level, limit):
level += 1
if level >= limit:
return heuristic_evaluation(board, color)
opp_color = 1 if color == 2 else 2
moves = get_possible_moves(board, color)
if not moves:
return compute_utility(board, color)
alpha = -math.inf
for x in moves:
one, two = x
testBoard = play_move(board, color, one, two)
minNode = alphabeta_min_node(testBoard, opp_color, alpha, level, limit)
if minNode >= beta:
return minNode
alpha = max(alpha, minNode)
return alpha
def minimax_min_node(board, color, depth, temp_max_depth=max_depth):
if depth >= max_depth:
return compute_utility(board, color)
moves = get_possible_moves(board, color)
move_utility = {}
if len(moves) != 0:
for (column, row) in moves:
new_board = play_move(board, color, column, row)
#sys.stderr.write(str(new_board) + '\n')
if not new_board in move_utility.values():
utility = minimax_max_node(new_board, color, depth + 1)
move_utility[utility] = new_board
else:
return compute_utility(new_board, color)
return min(move_utility.keys())
return compute_utility(board, color)
def minimax_min_node(board, color, limit, caching=0):
# Determine the player color
if color == 1:
oppo_color = 2
else:
oppo_color = 1
# the valid moved
valid_moves = get_possible_moves(board, oppo_color)
if (len(valid_moves) == 0):
# no move valid and board is not cached
return None, compute_utility(board, color)
elif (limit == 0):
# reach search limit
return None, compute_utility(board, color)
else:
u_value_best = float("Inf") # inf as looking for small number
move_best = None
for move in valid_moves:
new_board = play_move(board, oppo_color, move[0], move[1])
# check if the new board is in the cache
if new_board in cached and caching:
new_move, u_value = cached[new_board]
else:
new_move, u_value = minimax_max_node(new_board, color,
limit - 1, caching)
if (caching):
cached[new_board] = (new_move, u_value)
# get the min value:
if (u_value < u_value_best):
u_value_best = u_value
move_best = move
return (move_best, u_value_best)
return ((0, 0), 0)
def minimax_min_node(board, color):
# Get the color of the next player
if color == 1:
other_color = 2
else:
other_color = 1
# Get the allowed moves
all_moves = get_possible_moves(board, other_color)
# If there are no moves left, return the utility
if len(all_moves) == 0:
return None, compute_utility(board, color)
# Else if there are moves, get their utility and return the min
else:
# Get the maximum utility possible to use as a starting point for min
min_utility = len(board) * len(board)
min_move = None
# For each possible move, get the max utiltiy
for each in all_moves:
# Get the next board from that move
next_board = play_move(board, other_color, each[0], each[1])
# First check the cache for the board
if next_board in board_utilities:
move, new_utiltiy = board_utilities[next_board]
else:
# If the new utility is less than the current min, update min_utiltiy
move, new_utiltiy = minimax_max_node(next_board, color)
board_utilities[next_board] = (move, new_utiltiy)
if new_utiltiy < min_utility:
min_utility = new_utiltiy
min_move = each
# After checking every move, return the minimum utility
return min_move, min_utility
# Default return - should never be called
return None, None
def select_move_alphabeta(board, color):
best_utility = -math.inf
beta = math.inf
best_move = 0, 0
new_color = 1 if color == 2 else 2
# caching_states = get_cached_states(color)
possible_moves = get_possible_moves(board, color)
level = 0
limit = 5
if len(possible_moves) > 0:
sorted_states_list = []
for move in possible_moves:
new_board = play_move(board, color, move[0], move[1])
sort_utility = compute_utility(new_board, new_color)
heappush(sorted_states_list, (sort_utility, new_board, move))
sorted_states = [x[1] for x in sorted_states_list]
moves = [x[2] for x in sorted_states_list]
index = 0
for board_state in sorted_states:
if board_state in caching_states:
utility = caching_states[board_state]
else:
utility = alphabeta_min_node(board_state, new_color,
best_utility, beta, level + 1,
limit)
caching_states[board_state] = utility
if utility > best_utility:
best_utility = utility
best_move = moves[index]
index += 1
"""
for move in possible_moves:
new_board = play_move(board, color, move[0], move[1])
if new_board in caching_states:
utility = caching_states[new_board]
else:
utility = alphabeta_min_node(new_board, new_color, best_utility, beta, level + 1, limit)
caching_states[new_board] = utility
if utility > best_utility:
best_utility = utility
best_move = move
"""
return best_move