请给出一个python语言写的,A*算法求解八数码问题的可运行的代码,并且要能输出初始状态、目标状态、完整的最优解、扩展节点数和生成节点数,要求时间复杂度不是太大,不能陷入较长的等待运行结果。并且,不能出现unhashable的错误,以及其他语法错误
时间: 2023-06-01 17:01:44 浏览: 66
由于A*算法是一种启发式搜索算法,其时间复杂度与启发函数的选择有关,因此无法保证时间复杂度不会太大,但我们可以优化算法以尽可能减少运行时间。以下是一个可能的Python代码实现:
```python
from queue import PriorityQueue
# 定义目标状态
goal_state = [[1, 2, 3], [4, 5, 6], [7, 8, 0]]
# 定义启发函数,这里采用曼哈顿距离
def heuristic(state):
distance = 0
for i in range(3):
for j in range(3):
if state[i][j] != 0:
distance += abs(i - (state[i][j]-1)//3) + abs(j - (state[i][j]-1)%3)
return distance
# 定义状态类
class State:
def __init__(self, state, g, parent=None):
self.state = state
self.g = g
self.h = heuristic(state)
self.parent = parent
def __lt__(self, other):
return self.g + self.h < other.g + other.h
def __eq__(self, other):
return self.state == other.state
def __hash__(self):
return hash(str(self.state))
def get_children(self):
children = []
i, j = self.get_blank_position()
if i > 0:
child_state = self.get_copy()
child_state[i][j], child_state[i-1][j] = child_state[i-1][j], child_state[i][j]
children.append(State(child_state, self.g+1, self))
if i < 2:
child_state = self.get_copy()
child_state[i][j], child_state[i+1][j] = child_state[i+1][j], child_state[i][j]
children.append(State(child_state, self.g+1, self))
if j > 0:
child_state = self.get_copy()
child_state[i][j], child_state[i][j-1] = child_state[i][j-1], child_state[i][j]
children.append(State(child_state, self.g+1, self))
if j < 2:
child_state = self.get_copy()
child_state[i][j], child_state[i][j+1] = child_state[i][j+1], child_state[i][j]
children.append(State(child_state, self.g+1, self))
return children
def get_blank_position(self):
for i in range(3):
for j in range(3):
if self.state[i][j] == 0:
return i, j
def get_copy(self):
return [row[:] for row in self.state]
# 定义A*算法
def astar(start_state):
start = State(start_state, 0)
queue = PriorityQueue()
queue.put(start)
closed_set = set()
generated_count = 0
while not queue.empty():
current = queue.get()
if current.state == goal_state:
path = []
while current is not None:
path.append(current.state)
current = current.parent
path.reverse()
return path, generated_count, len(closed_set)
closed_set.add(current)
for child in current.get_children():
generated_count += 1
if child in closed_set:
continue
queue.put(child)
return None, generated_count, len(closed_set)
# 测试代码
start_state = [[2, 8, 3], [1, 6, 4], [7, 0, 5]]
path, generated_count, closed_count = astar(start_state)
if path is not None:
print("Initial state:")
print(start_state)
print("Goal state:")
print(goal_state)
print("Path:")
for state in path:
print(state)
print("Total steps:", len(path)-1)
print("Generated nodes:", generated_count)
print("Closed nodes:", closed_count)
else:
print("Failed to find a solution.")
```
在上述代码中,我们首先定义了目标状态和启发函数,然后定义了状态类,其中包含了状态、g值、h值和父节点等信息。我们重载了状态类的一些方法,如小于运算符、等于运算符和哈希函数等,以便于后续的比较和存储。同时,我们还定义了一个方法用于获取状态的所有子节点,这里采用了四联通的移动方式,即上下左右四个方向。
在A*算法的实现中,我们使用了优先队列来存储待扩展的节点,每次取出h+g值最小的节点进行扩展。同时,我们维护了一个closed集合,用于存储已经扩展过的节点。由于我们采用了哈希函数来对状态进行哈希,因此不会出现unhashable的错误。在算法结束后,我们可以根据父节点指针,从最终状态一直回溯到初始状态,得到完整的最优解,并输出相关信息。