实验任务一:astar求解八数码问题(astareighttest.py)

八数码问题是一种经典的搜索问题，目的是将一个3x3网格的数字方格从任意初始状态经过最少的移动步数变换成目标状态。该问题可以通过A*算法来求解。

astareighttest.py是一个实现八数码问题A*算法求解的Python脚本。该脚本包含以下几个关键步骤：

首先，根据初始状态和目标状态创建相应的8puzzle对象，并运用启发式函数h1和h2对搜索进行优化。其中，h1采用错误放置的方块数目作为估价函数，h2采用曼哈顿距离作为估价函数。

然后，通过A*算法进行搜索。首先将初始状态加入open集合中，然后进行循环，直到open集合为空或者找到目标状态为止。每次循环时，在open集合中选取f值最小的节点作为当前节点，然后将其所有邻居节点放入open集合中，并计算它们的f值和g值，最后将它们加入close集合中。如果遇到更优的路径，就更新节点的父节点和f值。

最后，返回路径并输出结果。如果找到了目标状态，则通过已找到的目标节点来回溯整个路径，最后输出路径长度和移动步骤。

总之，八数码问题的求解通过A*算法进行优化搜索，能够迅速找到最优解。该算法不仅广泛应用于八数码问题，也适用于其他搜索问题的求解。

相关问题

修改以下代码，使他避开障碍物：def Astar(Map): s = Point(Map.start, None, None) openlist = [s] closedlist = [] s.get_f(Map.goal) while openlist: n = openlist.pop(0) if n.position[0] == Map.goal[0] and n.position[1] == Map.goal[1]: return n else: closedlist.append(n) subp_list = Point.EXPAND(n, Map) for subp in subp_list: subp.get_f(Map.goal) for openp in openlist: if openp.position[0] == subp.position[0] and openp.position[1] == subp.position[1]: if subp.f < openp.f: openlist.remove(openp) openlist.append(subp) for closedp in closedlist: if closedp.position[0] == subp.position[0] and closedp.position[1] == subp.position[1]: if subp.f < closedp.f: closedlist.remove(closedp) openlist.append(subp) openlist.append(subp) openlist.sort(key= lambda x:x.f)

Sure, here's the modified code that avoids obstacles using A* algorithm:

def Astar(Map):
    s = Point(Map.start, None, None)
    openlist = [s]
    closedlist = []
    s.get_f(Map.goal)
    while openlist:
        n = openlist.pop(0)
        if n.position[0] == Map.goal[0] and n.position[1] == Map.goal[1]:
            return n
        else:
            closedlist.append(n)
            subp_list = Point.EXPAND(n, Map)
            for subp in subp_list:
                if Map.is_obstacle(subp.position[0], subp.position[1]):
                    continue
                subp.get_f(Map.goal)
                for openp in openlist:
                    if openp.position[0] == subp.position[0] and openp.position[1] == subp.position[1]:
                        if subp.f < openp.f:
                            openlist.remove(openp)
                            openlist.append(subp)
                            break
                else:
                    for closedp in closedlist:
                        if closedp.position[0] == subp.position[0] and closedp.position[1] == subp.position[1]:
                            if subp.f < closedp.f:
                                closedlist.remove(closedp)
                                openlist.append(subp)
                                break
                    else:
                        openlist.append(subp)
            openlist.sort(key=lambda x: x.f)

The modification is done by adding a check for obstacles in the sub-points list and skipping those points, as well as updating the open and closed lists based on the new condition.

用Python编写代码在此代码下利用Astar算法寻路，其中p为随机生成障碍物的概率：class randomMAP: def init(self, size, start, goal, p): self.size = size self.start = start self.goal = goal self.p = p def creatmap(self): self.map =np.zeros(self.size, dtype='int') for i in range(self.map.shape[0]): for j in range(self.map.shape[1]): if (i != self.start[0] or j != self.start[1]) and (i != self.goal[0] or j != self.goal[1]) and random.random() < self.p: self.map[i][j] = 5 map1 = randomMAP((20, 20), (0, 0), (19, 19), 0.3) map1.creatmap() print(map1.map) plt.matshow(map1.map) plt.show()

这段代码创建了一个随机地图，其中包含随机生成的障碍物。使用A*算法寻路需要先定义节点类，然后实现A*算法的具体逻辑。下面是一个简单的实现，可以根据自己的需求进行修改：

import numpy as np
import random
import heapq
import matplotlib.pyplot as plt

class Node:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self.g = 0
        self.h = 0
        self.f = 0
        self.parent = None

    def __lt__(self, other):
        return self.f < other.f

class AStar:
    def __init__(self, start, goal, map):
        self.start = start
        self.goal = goal
        self.map = map

    def heuristic(self, a, b):
        # 曼哈顿距离作为启发函数
        return abs(a.x - b.x) + abs(a.y - b.y)

    def get_neighbors(self, node):
        neighbors = []
        for i in range(-1, 2):
            for j in range(-1, 2):
                if i == 0 and j == 0:
                    continue
                x = node.x + i
                y = node.y + j
                if x < 0 or x >= self.map.shape[0] or y < 0 or y >= self.map.shape[1]:
                    continue
                if self.map[x][y] == 5:
                    continue
                neighbors.append(Node(x, y))
        return neighbors

    def search(self):
        open_list = []
        closed_list = []
        start_node = Node(self.start[0], self.start[1])
        goal_node = Node(self.goal[0], self.goal[1])
        heapq.heappush(open_list, start_node)

        while len(open_list) > 0:
            current_node = heapq.heappop(open_list)
            if current_node.x == goal_node.x and current_node.y == goal_node.y:
                path = []
                while current_node is not None:
                    path.append((current_node.x, current_node.y))
                    current_node = current_node.parent
                return path[::-1]
            closed_list.append(current_node)

            for neighbor in self.get_neighbors(current_node):
                if neighbor in closed_list:
                    continue
                neighbor.g = current_node.g + 1
                neighbor.h = self.heuristic(neighbor, goal_node)
                neighbor.f = neighbor.g + neighbor.h
                neighbor.parent = current_node

                if neighbor not in open_list:
                    heapq.heappush(open_list, neighbor)

        return None

class randomMAP:
    def __init__(self, size, start, goal, p):
        self.size = size
        self.start = start
        self.goal = goal
        self.p = p

    def creatmap(self):
        self.map = np.zeros(self.size, dtype='int')
        for i in range(self.map.shape[0]):
            for j in range(self.map.shape[1]):
                if (i != self.start[0] or j != self.start[1]) and (i != self.goal[0] or j != self.goal[1]) and random.random() < self.p:
                    self.map[i][j] = 5

map1 = randomMAP((20, 20), (0, 0), (19, 19), 0.3)
map1.creatmap()
print(map1.map)

astar = AStar(map1.start, map1.goal, map1.map)
path = astar.search()
if path is None:
    print("No path found")
else:
    print(path)

plt.matshow(map1.map)
if path is not None:
    path_x = [x for (x, y) in path]
    path_y = [y for (x, y) in path]
    plt.plot(path_y, path_x, 'r')
plt.show()

这个实现中，为了方便起见，启发函数使用的是曼哈顿距离。如果需要更高的精度，可以使用欧几里得距离或其他启发函数。