以8数码问题实现A*算法的求解程序,要求设计两种不同的估价函数python生成代码

8数码问题也称为八皇后问题，是一个经典的回溯算法示例，用于在一个8x8的棋盘上放置八个皇后，使得任意两个皇后都不在同一行、同一列或同一对角线上。A*算法在此问题中可以用来寻找最短解决方案，结合合适的启发式估价函数。

以下是两种不同估价函数的Python代码实现，分别基于曼哈顿距离和欧几里得距离：

**曼哈顿距离估价函数：**

def manhattan_distance(position):
    distance = sum(abs(row - col) for row, col in enumerate(position))
    return distance

def a_star_search_manhattan(start, end, heuristic):
    open_list = [(start, 0)]
    closed_list = set()
    
    while open_list:
        current_state, cost_so_far = heappop(open_list)
        
        if current_state == end:
            path = reconstruct_path(closed_list, start, current_state)
            return path, cost_so_far
        
        closed_list.add(current_state)
        
        for neighbor, move_cost in generate_neighbors(current_state):
            new_cost = cost_so_far + move_cost + heuristic(neighbor)
            if neighbor not in closed_list or new_cost < graph[neighbor]:
                graph[neighbor] = new_cost
                heappush(open_list, (neighbor, new_cost))

# ...其他函数省略...

**欧几里得距离估价函数：**

def euclidean_distance(position):
    x_diff = abs(position[0] - position[1])
    y_diff = abs(position[2] - position[3])
    return x_diff + y_diff

def a_star_search_euclidean(start, end, heuristic):
    # ...同上，只需替换manhattan_distance为euclidean_distance即可...

# ...其他函数省略...

在这两个版本中，`generate_neighbors()`函数负责生成当前位置的所有合法邻居状态，`graph`是记录每个位置成本的数据结构。`reconstruct_path()`用于从结束节点逆向重建路径。