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# Quoridor (3 x 3), wall = 1
# ====================
# Importing packages
import random
import math
from collections import deque
import copy
from copy import deepcopy
# Game state
class State:
def __init__(self, board_size=3, num_walls=1, player=None, enemy=None, walls=None, depth=0):
self.N = board_size
N = self.N
if N % 2 == 0:
raise ValueError('The board size must be an odd number.')
self.directions = [(-1, 0), (1, 0), (0, -1), (0, 1)]
self.player = player if player != None else [0] * 2 # Position, number of walls
self.enemy = enemy if enemy != None else [0] * 2
self.walls = walls if walls != None else [0] * ((N - 1) ** 2)
self.depth = depth
self.draw_depth = 30
if player == None or enemy == None:
init_pos = N * (N - 1) + N // 2
self.player[0] = init_pos
self.player[1] = num_walls
self.enemy[0] = init_pos
self.enemy[1] = num_walls
# Check if it's a loss
def is_lose(self):
if self.enemy[0] // self.N == 0:
return True
return False
# Check if it's a draw
def is_draw(self):
return self.depth >= self.draw_depth
# Check if the game is over
def is_done(self):
return self.is_lose() or self.is_draw()
def pieces_array(self):
N = self.N
def pieces_of(pieces):
tables = []
table = [0] * (N ** 2)
table[pieces[0]] = 1
tables.append(table)
table = [pieces[1]] * (N ** 2)
tables.append(table)
return tables
def walls_of(walls):
tables = []
table_h = [0] * (N ** 2)
table_v = [0] * (N ** 2)
for wp in range((N - 1) ** 2):
x, y = wp // (N - 1), wp % (N - 1)
if x < (N - 1) // 2 and y < (N - 1) // 2:
pos = N * x + y
elif x > (N - 1) // 2 and y < (N - 1) // 2:
pos = N * x + (y + 1)
elif x < (N - 1) // 2 and y > (N - 1) // 2:
pos = N * (x + 1) + y
else:
pos = N * (x + 1) + (y + 1)
if walls[wp] == 1:
table_h[pos] = 1
elif walls[wp] == 2:
table_v[pos] = 1
tables.append(table_h)
tables.append(table_v)
return tables
return [pieces_of(self.player), pieces_of(self.enemy), walls_of(self.walls)]
def legal_actions(self):
"""
0 - (N ** 2 - 1): Move to a position
N ** 2- (N ** 2 + (N - 1) ** 2 - 1): Place a horizontal wall
(N ** 2 + (N - 1) ** 2) - (N ** 2 + 2 * (N - 1) ** 2 - 1): Place a vertical wall
"""
actions = []
actions.extend(self.legal_actions_pos(self.player[0]))
if self.player[1] > 0:
for pos in range((self.N - 1) ** 2):
actions.extend(self.legal_actions_wall(pos))
return actions
def legal_actions_pos(self, pos):
actions = []
N = self.N
walls = self.walls
ep = self.enemy[0]
x, y = pos // N, pos % N
for dx, dy in self.directions:
nx, ny = x + dx, y + dy
if 0 <= nx < N and 0 <= ny < N:
np = N * nx + ny
wp = (N - 1) * nx + ny
if nx < x:
if y == 0:
if walls[wp] != 1:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if nx > 0 and walls[wp - (N - 1)] != 1:
nnp = np - N
actions.append(nnp)
elif (nx == 0 and walls[wp] != 2) or (nx > 0 and walls[wp - (N - 1)] != 2 and walls[wp] != 2):
nnp = np + 1
actions.append(nnp)
elif y == (N - 1):
if walls[wp - 1] != 1:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if nx > 0 and walls[wp - (N - 1) - 1] != 1:
nnp = np - N
actions.append(nnp)
elif (nx == 0 and walls[wp - 1] != 2) or (nx > 0 and walls[wp - (N - 1) - 1] != 2 and walls[wp - 1] != 2):
nnp = np - 1
actions.append(nnp)
else:
if walls[wp - 1] != 1 and walls[wp] != 1:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if nx > 0 and walls[wp - (N - 1)] != 1 and walls[wp - (N - 1) - 1] != 1:
nnp = np - N
actions.append(nnp)
else:
if (nx == 0 and walls[wp - 1] != 2) or (nx > 0 and walls[wp - (N - 1) - 1] != 2 and walls[wp - 1] != 2):
nnp = np - 1
actions.append(nnp)
if (nx == 0 and walls[wp] != 2) or (nx > 0 and walls[wp - (N - 1)] != 2 and walls[wp] != 2):
nnp = np + 1
actions.append(nnp)
if nx > x:
if y == 0:
if walls[wp - (N - 1)] != 1:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if nx < (N - 1) and walls[wp] != 1:
nnp = np + N
actions.append(nnp)
elif (nx == (N - 1) and walls[wp - (N - 1)] != 2) or (nx < (N - 1) and walls[wp - (N - 1)] != 2 and walls[wp] != 2):
nnp = np + 1
actions.append(nnp)
elif y == (N - 1):
if walls[wp - (N - 1) - 1] != 1:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if nx < (N - 1) and walls[wp - 1] != 1:
nnp = np + N
actions.append(nnp)
elif (nx == (N - 1) and walls[wp - (N - 1) - 1] != 2) or (nx < (N - 1) and walls[wp - (N - 1) - 1] != 2 and walls[wp - 1] != 2):
nnp = np - 1
actions.append(nnp)
else:
if walls[wp - (N - 1) - 1] != 1 and walls[wp - (N - 1)] != 1:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if nx < (N - 1) and walls[wp - 1] != 1 and walls[wp] != 1:
nnp = np + N
actions.append(nnp)
else:
if (nx == (N - 1) and walls[wp - (N - 1) - 1] != 2) or (nx < (N - 1) and walls[wp - (N - 1) - 1] != 2 and walls[wp - 1] != 2):
nnp = np - 1
actions.append(nnp)
if (nx == (N - 1) and walls[wp - (N - 1)] != 2) or (nx < (N - 1) and walls[wp - (N - 1)] != 2 and walls[wp] != 2):
nnp = np + 1
actions.append(nnp)
if ny < y:
if x == 0:
if walls[wp] != 2:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if ny > 0 and walls[wp - 1] != 2:
nnp = np - 1
actions.append(nnp)
elif (ny == 0 and walls[wp] != 1) or (ny > 0 and walls[wp - 1] != 1 and walls[wp] != 1):
nnp = np + N
actions.append(nnp)
elif x == (N - 1):
if walls[wp - (N - 1)] != 2:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if ny > 0 and walls[wp - (N - 1) - 1] != 2:
nnp = np - 1
actions.append(nnp)
elif (ny == 0 and walls[wp - (N - 1)] != 1) or (ny > 0 and walls[wp - (N - 1) - 1] != 2 and walls[wp - (N - 1)] != 1):
nnp = np - N
actions.append(nnp)
else:
if walls[wp - (N - 1)] != 2 and walls[wp] != 2:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if ny > 0 and walls[wp - (N - 1) - 1] != 2 and walls[wp - 1] != 2:
nnp = np - 1
actions.append(nnp)
else:
if (ny == 0 and walls[wp - (N - 1)] != 1) or (ny > 0 and walls[wp - (N - 1) - 1] != 2 and walls[wp - (N - 1)] != 1):
nnp = np - N
actions.append(nnp)
if (ny == 0 and walls[wp] != 1) or (ny > 0 and (walls[wp - 1] != 1 or walls[wp] != 1)):
nnp = np + N
actions.append(nnp)
if ny > y:
if x == 0:
if walls[wp - 1] != 2:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if ny < (N - 1) and walls[wp] != 2:
nnp = np + 1
actions.append(nnp)
elif (ny == (N - 1) and walls[wp - 1] != 1) or (ny < (N - 1) and walls[wp - 1] != 1 and walls[wp] != 1):
nnp = np + N
actions.append(nnp)
elif x == (N - 1):
if walls[wp - (N - 1) - 1] != 2:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if ny < (N - 1) and walls[wp - (N - 1)] != 2:
nnp = np + 1
actions.append(nnp)
elif (ny == (N - 1) and walls[wp - (N - 1) - 1] != 1) or (ny < (N - 1) and walls[wp - (N - 1) - 1] != 1 and walls[wp - (N - 1)] != 1):
nnp = np - N
actions.append(nnp)
else:
if walls[wp - (N - 1) - 1] != 2 and walls[wp - 1] != 2:
if np + ep != N ** 2 - 1:
actions.append(np)
else:
if ny < (N - 1) and walls[wp - (N - 1)] != 2 and walls[wp] != 2:
nnp = np + 1
actions.append(nnp)
else:
if (ny == (N - 1) and walls[wp - (N - 1) - 1] != 1) or (ny < (N - 1) and walls[wp - (N - 1) - 1] != 1 and walls[wp - (N - 1)] != 1):
nnp = np - N
actions.append(nnp)
if (ny == (N - 1) and walls[wp - 1] != 1) or (ny < (N - 1) and (walls[wp - 1] != 1 or walls[wp] != 1)):
nnp = np + N
actions.append(nnp)
return actions
def legal_actions_wall(self, pos):
N = self.N
walls = self.walls
def can_place_wall(orientation, pos):
if walls[pos] != 0:
return False
x, y = pos // (N - 1), pos % (N - 1)
if orientation == 1:
if y == 0:
if walls[pos + 1] == 1:
return False
elif y == (N - 2):
if walls[pos - 1] == 1:
return False
else:
if walls[pos - 1] == 1 or walls[pos + 1] == 1:
return False
else:
if x == 0:
if walls[pos + (N - 1)] == 2:
return False
elif x == (N - 2):
if walls[pos - (N - 1)] == 2:
return False
else:
if walls[pos - (N - 1)] == 2 or walls[pos + (N - 1)] == 2:
return False
return True
def can_reach_goal(orientation, pos):
def bfs(state):
queue = deque([state.player[0]])
visited = set()
while queue:
pos = queue.popleft()
nps = state.legal_actions_pos(pos)
for np in nps:
x, y = np // N, np % N
if y == 0:
return True
if np not in visited:
visited.add(np)
queue.append(np)
return False
self.walls[pos] = orientation
player_state = State(board_size=N, player=self.player.copy(), enemy=self.enemy.copy(), walls=deepcopy(self.walls), depth=self.depth)
can_reach_player = bfs(player_state)
action = pos
if orientation == 1:
action += N ** 2
else:
action += N ** 2 + (N - 1) ** 2
enemy_state = player_state.next(action)
can_reach_enemy = bfs(enemy_state)
self.walls[pos] = 0
return can_reach_player and can_reach_enemy
actions = []
if can_place_wall(1, pos) and can_reach_goal(1, pos):
actions.append(N ** 2 + pos)
if can_place_wall(2, pos) and can_reach_goal(2, pos):
actions.append(N ** 2 + (N - 1) ** 2 + pos)
return actions
def rotate_walls(self):
N = self.N
rotated_walls = [0] * len(self.walls)
for i in range((N - 1) ** 2):
rotated_walls[i] = self.walls[(N - 1) ** 2 - 1 - i]
self.walls = rotated_walls
def next(self, action):
N = self.N
# Create the next state
state = State(board_size=N, player=self.player.copy(), enemy=self.enemy.copy(), walls=deepcopy(self.walls), depth=self.depth + 1)
if action < N ** 2:
# Move piece
state.player[0] = action
elif action < N ** 2 + (N - 1) ** 2:
# Place horizontal wall
pos = action - N ** 2
state.walls[pos] = 1
state.player[1] -= 1
else:
# Place vertical wall
pos = action - N ** 2 - (N - 1) ** 2
state.walls[pos] = 2
state.player[1] -= 1
state.rotate_walls()
# Swap players
state.player, state.enemy = state.enemy, state.player
return state
# Check if it's the first player's turn
def is_first_player(self):
return self.depth % 2 == 0
def __str__(self):
"""Display the game state as a string."""
N = self.N
is_first_player = self.is_first_player()
board = [['o'] * (2 * N - 1) for _ in range(2 * N - 1)]
for i in range(2 * N - 1):
for j in range(2 * N - 1):
if i % 2 == 1 and j % 2 == 1:
board[i][j] = 'x'
p_pos = self.player[0] if is_first_player else self.enemy[0]
e_pos = self.enemy[0] if is_first_player else self.player[0]
e_pos = N ** 2 - 1 - e_pos
p_x, p_y = p_pos // N, p_pos % N
e_x, e_y = e_pos // N, e_pos % N
board[2 * p_x][2 * p_y] = 'P'
board[2 * e_x][2 * e_y] = 'E'
turn_info = "<Enemy's Turn>" if is_first_player else "<Player's Turn>"
if not is_first_player:
self.rotate_walls()
# Set walls
for i in range(N - 1):
for j in range(N - 1):
pos = i * (N - 1) + j
if self.walls[pos] == 1:
board[2 * i + 1][2 * j] = '-'
board[2 * i + 1][2 * (j + 1)] = '-'
if self.walls[pos] == 2:
board[2 * i][2 * j + 1] = '|'
board[2 * (i + 1)][2 * j + 1] = '|'
if not is_first_player:
self.rotate_walls()
board_str = '\n'.join([''.join(row) for row in board])
return turn_info + '\n' + board_str
# Randomly select an action
def random_action(state):
legal_actions = state.legal_actions()
action = random.randint(0, len(legal_actions) - 1)
return legal_actions[action]
# Calculate state value using alpha-beta pruning
def alpha_beta(state, alpha, beta):
# Loss is -1
if state.is_lose():
return -1
# Draw is 0
if state.is_draw():
return 0
# Calculate state values for legal actions
for action in state.legal_actions():
score = -alpha_beta(state.next(action), -beta, -alpha)
if score > alpha:
alpha = score
# If the best score for the current node exceeds the parent node, stop the search
if alpha >= beta:
return alpha
# Return the maximum value of the state values for legal actions
return alpha
# Select an action using alpha-beta pruning
def alpha_beta_action(state):
# Calculate state values for legal actions
best_action = 0
alpha = -float('inf')
for action in state.legal_actions():
score = -alpha_beta(state.next(action), -float('inf'), -alpha)
if score > alpha:
best_action = action
alpha = score
# Return the action with the maximum state value
return best_action
# Playout
def playout(state):
# Loss is -1
if state.is_lose():
return -1
# Draw is 0
if state.is_draw():
return 0
# Next state value
return -playout(state.next(random_action(state)))
# Return the index of the maximum value
def argmax(collection):
return collection.index(max(collection))
# Select an action using Monte Carlo Tree Search
def mcts_action(state):
# Node for Monte Carlo Tree Search
class node:
# Initialization
def __init__(self, state):
self.state = state # State
self.w = 0 # Cumulative value
self.n = 0 # Number of trials
self.child_nodes = None # Child nodes
# Evaluation
def evaluate(self):
# When the game ends
if self.state.is_done():
# Get value from the game result
value = -1 if self.state.is_lose() else 0 # Loss is -1, draw is 0
# Update cumulative value and number of trials
self.w += value
self.n += 1
return value
# When there are no child nodes
if not self.child_nodes:
# Get value from playout
value = playout(self.state)
# Update cumulative value and number of trials
self.w += value
self.n += 1
# Expand child nodes
if self.n == 10:
self.expand()
return value
# When there are child nodes
else:
# Get value from evaluating the child node with the maximum UCB1
value = -self.next_child_node().evaluate()
# Update cumulative value and number of trials
self.w += value
self.n += 1
return value
# Expand child nodes
def expand(self):
legal_actions = self.state.legal_actions()
self.child_nodes = []
for action in legal_actions:
self.child_nodes.append(node(self.state.next(action)))
# Get the child node with the maximum UCB1
def next_child_node(self):
# Return the child node with n=0
for child_node in self.child_nodes:
if child_node.n == 0:
return child_node
# Calculate UCB1
t = 0
for c in self.child_nodes:
t += c.n
ucb1_values = []
for child_node in self.child_nodes:
ucb1_values.append(-child_node.w/child_node.n + 2*(2*math.log(t)/child_node.n)**0.5)
# Return the child node with the maximum UCB1
return self.child_nodes[argmax(ucb1_values)]
# Generate the root node
root_node = node(state)
root_node.expand()
# Evaluate the root node 100 times
for _ in range(100):
root_node.evaluate()
# Return the action with the maximum number of trials
legal_actions = state.legal_actions()
n_list = []
for c in root_node.child_nodes:
n_list.append(c.n)
return legal_actions[argmax(n_list)]
# Running the function
if __name__ == '__main__':
# Generate the state
state = State()
# Loop until the game ends
while True:
# When the game ends
if state.is_done():
break
# Get the next state
state = state.next(random_action(state))
# Display as a string
print(state)
print()
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