我一直在尝试用python编写15个难题的求解器，但现在到了死胡同，我无法弄清楚我的代码有什么问题。它适用于简单的情况，解决难题所需的移动量很少，例如：
5 1 2 3
9 7 11 4
13 6 15 8
14 10 0 12
其中0代表空白图块。
当我使用更复杂的情况（生成here）时，该程序似乎陷入了无限循环，即使对于简单的情况，我也觉得找不到最佳解决方案。我一直在尝试找出导致问题的原因，但是在调试了多个小时之后，我什么都没找到，所有方法似乎都能正常工作。 您能告诉我这段代码有什么问题吗？ 这是求解器类：
from copy import deepcopy
class Fifteen:
heur = ''
tiles = []
undo_move = ''
h_score = 0 # calculated using heuristic
depth = 0
previous_moves = []
zero_x = 0
zero_y = 0
def __init__(self, heur, fin, parent=None):
if parent is None:
self.heur = heur
fi = open(fin, 'r', encoding='utf-8')
self.tiles = [list(map(int, line.split())) for line in fi]
self.zero_x, self.zero_y = self.find()
fi.close()
elif parent is not None:
self.heur = deepcopy(parent.heur)
self.tiles = deepcopy(parent.tiles)
self.undo_move = deepcopy(parent.undo_move)
self.depth = deepcopy(parent.depth) + 1
self.previous_moves = deepcopy(parent.previous_moves)
self.zero_x = deepcopy(parent.zero_x)
self.zero_y = deepcopy(parent.zero_y)
def find(self, tile=0):
for y in range(len(self.tiles)):
for x in range(len(self.tiles[y])):
if self.tiles[y][x] == tile:
return x, y
raise NameError
def move_tile(self, direction):
x, y = self.zero_x, self.zero_y
if direction == 'u':
self.tiles[y][x], self.tiles[y - 1][x] = self.tiles[y - 1][x], self.tiles[y][x]
self.zero_y = self.zero_y - 1
self.previous_moves.append('u')
self.undo_move = 'd'
elif direction == 'd':
self.tiles[y][x], self.tiles[y + 1][x] = self.tiles[y + 1][x], self.tiles[y][x]
self.zero_y = self.zero_y + 1
self.previous_moves.append('d')
self.undo_move = 'u'
elif direction == 'l':
self.tiles[y][x], self.tiles[y][x - 1] = self.tiles[y][x - 1], self.tiles[y][x]
self.zero_x = self.zero_x - 1
self.previous_moves.append('l')
self.undo_move = 'r'
elif direction == 'r':
self.tiles[y][x], self.tiles[y][x + 1] = self.tiles[y][x + 1], self.tiles[y][x]
self.zero_x = self.zero_x + 1
self.previous_moves.append('r')
self.undo_move = 'l'
else:
raise NameError
def generate_next_states(self):
next_states = []
x, y = self.zero_x, self.zero_y
if y != 0 and self.undo_move != 'u':
child = Fifteen(None, None, self)
child.move_tile('u')
next_states.append(child)
if y != len(self.tiles) - 1 and self.undo_move != 'd':
child = Fifteen(None, None, self)
child.move_tile('d')
next_states.append(child)
if x != 0 and self.undo_move != 'l':
child = Fifteen(None, None, self)
child.move_tile('l')
next_states.append(child)
if x != len(self.tiles[y]) - 1 and self.undo_move != 'r':
child = Fifteen(None, None, self)
child.move_tile('r')
next_states.append(child)
return next_states
def heuristic(self):
if self.heur == 'hamm':
return self.hamming()
return self.manhattan()
def hamming(self):
diff = 0
for y in range(len(self.tiles)):
for x in range(len(self.tiles[y])):
if y == len(self.tiles) - 1 and x == len(self.tiles[y]) - 1:
if self.tiles[y][x] != 0:
diff += 1
elif self.tiles[y][x] != y * len(self.tiles) + x + 1:
diff += 1
return diff
def manhattan(self):
score = 0
value = 1
for y in range(len(self.tiles)):
for x in range(len(self.tiles[y])):
if value == 16:
value = 0
x_real, y_real = self.find(value)
dx = abs(x - x_real)
dy = abs(y - y_real)
score += dx + dy
value += 1
return score
def astar(self):
queue = [self]
closed_set = {}
while len(queue) > 0:
current_state = queue.pop(0)
closed_set[repr(current_state.tiles)] = current_state
if current_state.heuristic() == 0:
print(current_state.tiles)
print(current_state.previous_moves)
print(len(current_state.previous_moves))
return
for state in current_state.generate_next_states():
if repr(state.tiles) in closed_set:
continue
state.h_score = state.heuristic()
queue.append(state)
queue.sort(key=lambda x: x.h_score, reverse=False)
print(-1)
return
这就是我的运行方式：
from fifteen import Fifteen
f = Fifteen('manh', "start.txt")
f.astar()
根据使用的启发式方法，第一个参数可以是manh或hamm，第二个参数是包含初始拼图设置的文件名。
答案 0 :(得分：0)
有多种方法可以改善您的代码，但我将解释主要问题（至少对我而言）。
1-您在对状态进行排序时未使用状态的深度值。这将防止算法找到最佳解，甚至在状态空间很大的情况下也找不到解。
2-您应该真正决定如何表示“状态”。我为我认为对这个问题正确的状态添加了一个等价重载（__eq__方法）。它比较图块，启发式分数和深度值。尽管这不是主要问题，但我认为这很重要。因为幼稚的实现可能会大大减慢算法速度，并使调试变得困难。
3-当事情不起作用时，请尝试形象化您的算法。我添加了一个PrintState函数，并试图观察解决过程中的问题。
from copy import deepcopy
class Fifteen:
heur = ''
tiles = []
undo_move = ''
h_score = 0 # calculated using heuristic
depth = 0
previous_moves = []
zero_x = 0
zero_y = 0
def __init__(self, heur, fin, parent=None):
if parent is None:
self.heur = heur
fi = open(fin, 'r', encoding='utf-8')
self.tiles = [list(map(int, line.split())) for line in fi]
self.zero_x, self.zero_y = self.find()
fi.close()
elif parent is not None:
self.heur = deepcopy(parent.heur)
self.tiles = deepcopy(parent.tiles)
self.undo_move = deepcopy(parent.undo_move)
self.depth = deepcopy(parent.depth) + 1
self.previous_moves = deepcopy(parent.previous_moves)
self.zero_x = deepcopy(parent.zero_x)
self.zero_y = deepcopy(parent.zero_y)
def find(self, tile=0):
for y in range(len(self.tiles)):
for x in range(len(self.tiles[y])):
if self.tiles[y][x] == tile:
return x, y
raise NameError
def move_tile(self, direction):
x, y = self.zero_x, self.zero_y
if direction == 'u':
self.tiles[y][x], self.tiles[y - 1][x] = self.tiles[y - 1][x], self.tiles[y][x]
self.zero_y = self.zero_y - 1
self.previous_moves.append('u')
self.undo_move = 'd'
elif direction == 'd':
self.tiles[y][x], self.tiles[y + 1][x] = self.tiles[y + 1][x], self.tiles[y][x]
self.zero_y = self.zero_y + 1
self.previous_moves.append('d')
self.undo_move = 'u'
elif direction == 'l':
self.tiles[y][x], self.tiles[y][x - 1] = self.tiles[y][x - 1], self.tiles[y][x]
self.zero_x = self.zero_x - 1
self.previous_moves.append('l')
self.undo_move = 'r'
elif direction == 'r':
self.tiles[y][x], self.tiles[y][x + 1] = self.tiles[y][x + 1], self.tiles[y][x]
self.zero_x = self.zero_x + 1
self.previous_moves.append('r')
self.undo_move = 'l'
else:
raise NameError
def generate_next_states(self):
next_states = []
x, y = self.zero_x, self.zero_y
if y != 0 and self.undo_move != 'u':
child = Fifteen(None, None, self)
child.move_tile('u')
next_states.append(child)
if y != len(self.tiles) - 1 and self.undo_move != 'd':
child = Fifteen(None, None, self)
child.move_tile('d')
next_states.append(child)
if x != 0 and self.undo_move != 'l':
child = Fifteen(None, None, self)
child.move_tile('l')
next_states.append(child)
if x != len(self.tiles[y]) - 1 and self.undo_move != 'r':
child = Fifteen(None, None, self)
child.move_tile('r')
next_states.append(child)
return next_states
def heuristic(self):
if self.heur == 'hamm':
return self.hamming()
return self.manhattan()
def hamming(self):
diff = 0
for y in range(len(self.tiles)):
for x in range(len(self.tiles[y])):
if y == len(self.tiles) - 1 and x == len(self.tiles[y]) - 1:
if self.tiles[y][x] != 0:
diff += 1
elif self.tiles[y][x] != y * len(self.tiles) + x + 1:
diff += 1
return diff
def manhattan(self):
score = 0
value = 1
for y in range(len(self.tiles)):
for x in range(len(self.tiles[y])):
if value == 16:
value = 0
x_real, y_real = self.find(value)
dx = abs(x - x_real)
dy = abs(y - y_real)
#print("dx + dy for {}: {}".format(value, dx+dy))
score += dx + dy
value += 1
#print("Score:{}".format(score))
return score
def PrintState(self):
for y in range(len(self.tiles)):
for x in range(len(self.tiles[y])):
cellValue = self.tiles[y][x]
print(cellValue, end=" ")
print("")
def __eq__(self, other):
return (self.tiles == other.tiles
and self.h_score == other.h_score
and self.depth == other.depth)
def astar(self):
queue = [self]
closed_set = {}
while len(queue) > 0:
print("---")
print("---")
current_state = queue.pop(0)
print("current state")
#print(current_state.tiles)
#print(repr(current_state.tiles))
current_state.PrintState()
print("current scores")
print("heuristic:{}".format(current_state.heuristic()))
print("depth:{}".format(current_state.depth))
print("total:{}".format(current_state.heuristic() + current_state.depth))
closed_set[repr(current_state.tiles)] = current_state
if current_state.heuristic() == 0:
print(current_state.tiles)
print(current_state.previous_moves)
print(len(current_state.previous_moves))
return
for state in current_state.generate_next_states():
if repr(state.tiles) in closed_set:
continue
state.h_score = state.heuristic()
queue.append(state)
queue.sort(key=lambda x: (x.h_score + x.depth), reverse=False)
print(-1)
return
（可选）考虑使用基于优先级队列的实现。
更新：当心无法解决的起始位置，例如：
1 2 3 4
5 6 10 8
9 7 11 12
15 13 14 0
我在此配置上浪费了很多时间：）