a*算法八数码问题python

A*算法是一种启发式搜索算法，常用于解决路径规划问题。八数码问题是其中一种经典的路径规划问题，也可以使用A*算法来求解。

下面是使用Python实现A*算法解决八数码问题的代码：

import heapq

# 定义八数码问题的状态类
class EightPuzzleState:
    def __init__(self, state, parent=None, action=None, depth=0, heuristic=0):
        self.state = state
        self.parent = parent
        self.action = action
        self.depth = depth
        self.heuristic = heuristic

    def __lt__(self, other):
        return self.depth + self.heuristic < other.depth + other.heuristic

    def __eq__(self, other):
        return self.state == other.state

    def __hash__(self):
        return hash(str(self.state))

    def __repr__(self):
        return str(self.state)

    # 获取当前状态的子状态
    def get_successors(self):
        successors = []
        zero_index = self.state.index(0)
        if zero_index >= 3:
            new_state = self.state[:]
            new_state[zero_index], new_state[zero_index - 3] = new_state[zero_index - 3], new_state[zero_index]
            successors.append(EightPuzzleState(new_state, parent=self, action='up', depth=self.depth + 1, heuristic=self.get_heuristic(new_state)))
        if zero_index % 3 != 0:
            new_state = self.state[:]
            new_state[zero_index], new_state[zero_index - 1] = new_state[zero_index - 1], new_state[zero_index]
            successors.append(EightPuzzleState(new_state, parent=self, action='left', depth=self.depth + 1, heuristic=self.get_heuristic(new_state)))
        if zero_index % 3 != 2:
            new_state = self.state[:]
            new_state[zero_index], new_state[zero_index + 1] = new_state[zero_index + 1], new_state[zero_index]
            successors.append(EightPuzzleState(new_state, parent=self, action='right', depth=self.depth + 1, heuristic=self.get_heuristic(new_state)))
        if zero_index < 6:
            new_state = self.state[:]
            new_state[zero_index], new_state[zero_index + 3] = new_state[zero_index + 3], new_state[zero_index]
            successors.append(EightPuzzleState(new_state, parent=self, action='down', depth=self.depth + 1, heuristic=self.get_heuristic(new_state)))
        return successors

    # 获取当前状态的启发值
    def get_heuristic(self, state):
        heuristic = 0
        for i in range(9):
            if state[i] == 0:
                continue
            goal_row = state[i] // 3
            goal_col = state[i] % 3
            curr_row = i // 3
            curr_col = i % 3
            heuristic += abs(goal_row - curr_row) + abs(goal_col - curr_col)
        return heuristic

    # 判断当前状态是否为目标状态
    def is_goal(self):
        return self.state == [0, 1, 2, 3, 4, 5, 6, 7, 8]

# 定义A*算法函数
def astar(start_state):
    frontier = []
    heapq.heappush(frontier, start_state)
    explored = set()
    while frontier:
        state = heapq.heappop(frontier)
        if state.is_goal():
            return state
        explored.add(state)
        for successor in state.get_successors():
            if successor not in explored:
                heapq.heappush(frontier, successor)
    return None

# 测试代码
start_state = EightPuzzleState([1, 2, 0, 3, 4, 5, 6, 7, 8])
goal_state = EightPuzzleState([0, 1, 2, 3, 4, 5, 6, 7, 8])
result = astar(start_state)
if result:
    path = []
    while result.parent:
        path.append(result.action)
        result = result.parent
    path.reverse()
    print(path)
else:
    print('No solution found')

在上面的代码中，我们首先定义了一个`EightPuzzleState`类，用于表示八数码问题的状态。该类包含以下几个属性：

- `state`：当前状态的数字序列；
- `parent`：当前状态的父状态；
- `action`：从父状态到当前状态的动作；
- `depth`：当前状态的深度；
- `heuristic`：当前状态的启发值。

该类还包含以下几个方法：

- `__lt__`：重载小于号，用于定义状态的优先级；
- `__eq__`：重载等于号，用于判断状态是否相等；
- `__hash__`：重载哈希函数，用于将状态存储到集合中；
- `__repr__`：重载字符串函数，用于打印状态的数字序列；
- `get_successors`：获取当前状态的子状态；
- `get_heuristic`：获取当前状态的启发值；
- `is_goal`：判断当前状态是否为目标状态。

接着，我们定义了一个`astar`函数，用于实现A*算法。该函数使用优先队列来存储候选状态，并使用集合来存储已经扩展过的状态。在每一次迭代中，我们从优先队列中弹出优先级最高的状态，并将其加入到已扩展状态集合中。然后，我们遍历当前状态的所有子状态，并将未扩展过的子状态加入到优先队列中。如果当前状态为目标状态，则返回该状态；否则，继续迭代直到优先队列为空。

最后，我们使用上述代码解决了一个八数码问题，并输出了从初始状态到目标状态的路径。