A*算法解决8数码问题python实现

A*搜索算法是一种启发式搜索算法，用于寻找两点之间的最短路径，特别适用于图或网格环境中，如经典的八皇后问题。以下是使用Python实现A*算法解决八数码问题的一个简单版本：

import heapq

def heuristic(a, b):
    # 计算两个位置之间的曼哈顿距离
    return sum(abs(i - j) for i, j in zip(a, b))

def a_star(start, goal, graph):
    frontier = [(0, start)]  # 开放列表，初始状态优先级为0
    came_from = {}           # 记录每个节点的前驱
    cost_so_far = {start: 0}   # 路径成本从起点开始为0

    while frontier:
        current = heapq.heappop(frontier)[1]  # 取出优先级最低的状态

        if current == goal:
            break

        for neighbor, cost in graph[current].items():
            new_cost = cost_so_far[current] + cost  # 新的总代价
            if neighbor not in cost_so_far or new_cost < cost_so_far[neighbor]:
                cost_so_far[neighbor] = new_cost
                priority = new_cost + heuristic(neighbor, goal)
                heapq.heappush(frontier, (priority, neighbor))
                came_from[neighbor] = current  # 更新前驱节点

    path = [goal]
    while goal != start:
        goal = came_from[goal]
        path.append(goal)

    return path[::-1]  # 返回从起点到终点的路径

# 八数码问题的邻接矩阵或其他数据结构表示，这里假设已经定义好了
graph = {...}

start_state = [...]  # 初始化的棋盘状态
goal_state = [...]  # 目标状态

solution = a_star(start_state, goal_state, graph)
print("解决方案：", solution)