A*算法解决8数码问题Python代码

以下是一个基于A*算法的解决8数码问题的Python代码示例：

from queue import PriorityQueue

# 定义8数码问题的初始状态和目标状态
initial_state = [[2, 8, 3], [1, 6, 4], [7, 0, 5]]
goal_state = [[1, 2, 3], [8, 0, 4], [7, 6, 5]]

# 定义一个字典来记录每个数字所在的位置
positions = {}
for i in range(3):
    for j in range(3):
        positions[goal_state[i][j]] = (i, j)

# 定义一个函数来计算当前状态和目标状态之间的曼哈顿距离
def manhattan_distance(state):
    distance = 0
    for i in range(3):
        for j in range(3):
            if state[i][j] != 0:
                goal_position = positions[state[i][j]]
                distance += abs(i - goal_position[0]) + abs(j - goal_position[1])
    return distance

# 定义一个函数来检查当前状态是否为目标状态
def is_goal(state):
    return state == goal_state

# 定义一个函数来生成当前状态的所有合法子状态
def generate_states(state):
    states = []
    zero_position = None
    for i in range(3):
        for j in range(3):
            if state[i][j] == 0:
                zero_position = (i, j)
                break
    if zero_position[0] > 0:
        new_state = [row[:] for row in state]
        new_state[zero_position[0]][zero_position[1]] = new_state[zero_position[0]-1][zero_position[1]]
        new_state[zero_position[0]-1][zero_position[1]] = 0
        states.append(new_state)
    if zero_position[0] < 2:
        new_state = [row[:] for row in state]
        new_state[zero_position[0]][zero_position[1]] = new_state[zero_position[0]+1][zero_position[1]]
        new_state[zero_position[0]+1][zero_position[1]] = 0
        states.append(new_state)
    if zero_position[1] > 0:
        new_state = [row[:] for row in state]
        new_state[zero_position[0]][zero_position[1]] = new_state[zero_position[0]][zero_position[1]-1]
        new_state[zero_position[0]][zero_position[1]-1] = 0
        states.append(new_state)
    if zero_position[1] < 2:
        new_state = [row[:] for row in state]
        new_state[zero_position[0]][zero_position[1]] = new_state[zero_position[0]][zero_position[1]+1]
        new_state[zero_position[0]][zero_position[1]+1] = 0
        states.append(new_state)
    return states

# 定义一个类来表示每个搜索节点
class Node:
    def __init__(self, state, parent=None):
        self.state = state
        self.parent = parent
        self.g = 0 if parent is None else parent.g + 1
        self.h = manhattan_distance(state)
        self.f = self.g + self.h
    
    # 定义节点之间的比较方式，用于优先队列的排序
    def __lt__(self, other):
        return self.f < other.f

# 定义一个函数来解决8数码问题
def solve():
    # 初始化起始节点和优先队列
    start_node = Node(initial_state)
    frontier = PriorityQueue()
    frontier.put(start_node)
    explored = set()
    
    while not frontier.empty():
        # 取出队列中的第一个节点
        current_node = frontier.get()
        
        # 检查当前节点是否为目标状态
        if is_goal(current_node.state):
            path = []
            while current_node is not None:
                path.append(current_node.state)
                current_node = current_node.parent
            return path[::-1]
        
        # 将当前节点加入已探索集合
        explored.add(tuple(map(tuple, current_node.state)))
        
        # 生成当前节点的所有子节点
        for state in generate_states(current_node.state):
            # 检查子节点是否已经被探索过
            if tuple(map(tuple, state)) not in explored:
                # 将子节点加入优先队列
                frontier.put(Node(state, current_node))
    
    return None

# 解决8数码问题并输出解路径
path = solve()
for state in path:
    print(state)

该代码实现了A*算法来搜索8数码问题的解，并输出了解路径。在代码中，我们首先定义了8数码问题的初始状态和目标状态，然后定义了一个字典来记录每个数字所在的位置，以便计算曼哈顿距离。接着定义了几个函数来计算曼哈顿距离、检查当前状态是否为目标状态、生成当前状态的所有合法子状态等。最后，我们定义了一个Node类来表示每个搜索节点，并使用优先队列来实现A*算法的搜索过程。