采用递归与栈结合的方式实现迷宫分析与走迷宫（python3)

一、场景

1. General presentation

2.Examples

The file named maze_1.txt has the following contents.

二、题目分析

题目首先给了我们一个迷宫，要我门做两件事：

第一件事：分析迷宫

第二件事：在分析的基础上画迷宫

对于迷宫的分析：

所谓的迷宫只给了我们一些数字，数字的范围是0-3。

0：代表当前这个点与右边和下面都不相连；

1：代表这个点和和右面的点相连；

2：代表这个点和和下面的点相连；

3：代表这个点和下面与右面的点相连。

通过一个二维数组，可以将迷宫的墙确定下来。

在上图中，蓝色的线就是迷宫的墙，所给文件的第一个数字是1，所以在迷宫中，第一行的第一个点和第一行的第二个点相连。

第一件事：分析迷宫：分析六个数据

1.分析迷宫有多少个门，也可以说是迷宫有多少个入口。

2.分析迷宫有多少个墙体集合.

3.分析迷宫有多少不可达区域,也可以说有多少个死角块,也就是某一块是死的,从外面进不来.

4.分析迷宫中有多少个可达区域.

5.分析迷宫中有多少个红叉X

6.分析迷宫有多少条路径即图中黄色路线有多少条

第二件事:画图

1.画蓝线

2.画绿点

3.画红叉

4.画黄线

题目输入与输出要求

输入:

迷宫由数字的文件组成的.

输出:

1.六项分析结果

2.一个latex文件

迷宫的建立来自文件maze_1.txt:

    1  0  2  2  1  2  3  0     3  2  2  1  2  0  2  2     3  0  1  1  3  1  0  0     2  0  3  0  0  1  2  0     3  2  2  0  1  2  3  2     1  0  0  1  1  0  0  0

以上文件规定了墙体的连线.

三、编写代码

class MazeError(Exception):def __init__(self, value):self.value = valueclass Road:up = Truedown = Trueleft = Trueright = Trueis_border = Falsedef __init__(self, up, down, left, right):self.up = upself.down = downself.left = leftself.right = rightclass Maze:file_name = ""model = [1, 2, 3, 0, "0", "1", "2", "3"]result = [0, 0, 0, 0, 0, 0, 0]  # 记录结果maze = list()  # 最初的迷宫b_maze = list()  # 扩大的迷宫road = list()  # 路径b_road = list()  # 扩大的路径viewed = list()  # 记录路的访问对应第5项viewed6 = list()  # 记录唯一路径的访问对应第6项viewed4 = list()  # 记录路的连通访问对应第4项viewed3 = list()  # 记录封闭点site_view = list()  # 记录点的访问entry = list()  # 记录死角个数death = 0  # 记录封闭路的个数death_list = list()  # 记录封闭路的起点success_path_start = list()  # 记录能够走出去的路径的起始点temp = list()  # 临时存储一条走出去的路径包括的点path = list()  # 存储所有路径的经过的点walls = list()  # 画图的墙pillars = list()  # 画图的点inner_points = list()  # 画X的块entry_exit_paths = list()  # 画路径def __init__(self, file_name):#  读取file到数组maze里面,存储所有墙体信息self.file_name = file_namefile = open(file_name).readlines()for line in file:a = list()for i in line:if i in self.model:a.append(i)if len(a) > 0:self.maze.append(a)# print(self.maze)# 检测maze是否满足条件self.check()# 扩大边界,和初始化点的访问for line in self.maze:b = list()b.append("0")x_site_view = list()x_site_view.append(False)for i in line:b.append(i)x_site_view.append(False)b.append("0")x_site_view.append(False)self.b_maze.append(b)self.site_view.append(x_site_view)tmp = list()for i in range(len(self.maze[0])):tmp.append(False)self.site_view.insert(0, tmp)self.site_view.append(tmp)self.b_maze.insert(0, ["0"] * len(self.b_maze[0]))self.b_maze.append(["0"]*len(self.b_maze[0]))# 根据墙体信息，设置路径信息# 以每个点的左上角的点为基准，读取其余影响该方格的点for y in range(len(self.maze)-1):x_line = list()for x in range(len(self.maze[0])-1):up = Truedown = Trueleft = Trueright = Trueif self.maze[y][x] == '1':up = Falseelif self.maze[y][x] == '2':left = Falseelif self.maze[y][x] == '3':up = Falseleft = Falseif self.maze[y+1][x] == "1" or self.maze[y+1][x] == "3":down = Falseif self.maze[y][x+1] == "2" or self.maze[y][x+1] == "3":right = Falseroad = Road(up, down, left, right)x_line.append(road)self.road.append(x_line)# 扩大路径,并初始化路径的访问for y in self.road:x_line = list()road = Road(True, True, True, True)road.is_border = Truex_line.append(road)for x in y:x_line.append(x)x_line.append(road)self.b_road.append(x_line)temp = list()for _ in self.b_road[0]:road = Road(True, True, True, True)road.is_border = Truetemp.append(road)self.b_road.insert(0, temp)self.b_road.append(temp)# 画图初始化self.pillars.append("% Pillars\n")self.inner_points.append("% Inner points in accessible cul-de-sacs\n")self.entry_exit_paths.append("% Entry-exit paths without intersections\n")def check(self):length = len(self.maze[0])for i in self.maze:if len(i) != length:raise MazeError("Incorrect input.")for i in self.maze[len(self.maze)-1]:if i in ["2", "3"]:raise MazeError("Input does not represent a maze.")for i in range(len(self.maze)):if self.maze[i][len(self.maze[0])-1] in ["3", "1"]:raise MazeError("Input does not represent a maze.")def init_road_view(self):self.viewed = list()self.viewed6 = list()self.viewed4 = list()self.viewed3 = list()for y in self.b_road:x_viewed = list()x_viewed6 = list()x_viewed4 = list()x_viewed3 = list()for _ in y:x_viewed.append(False)x_viewed6.append(False)x_viewed4.append(False)x_viewed3.append(False)self.viewed.append(x_viewed)self.viewed6.append(x_viewed6)self.viewed4.append(x_viewed4)self.viewed3.append(x_viewed3)def analyse(self):self.init_road_view()self.analyse_gates()  # 1self.analyse_wall_sets()  # 2self.analyse_sets()  # 5self.analyse_path()  # 6self.analyse_accessible_areas()  # 4self.analyse_inner_points()  # 3self.print_result()# 分析第一项：分析迷宫有多少个门def analyse_gates(self):# 分四条边考虑count = 0for i in self.road[0]:if i.up is True:count += 1for i in self.road[len(self.road)-1]:if i.down is True:count += 1for j in range(len(self.road)):if self.road[j][0].left is True:count += 1if self.road[j][len(self.road[0])-1].right is True:count += 1self.result[1] = count# 分析第二项：# 深度优先遍历def analyse_wall_sets(self):count = 0for y in range(1, len(self.b_maze)-1):for x in range(1, len(self.b_maze[0])-1):if self.site_view[y][x] is False:if not self.is_inner(y, x):count += 1self.deep(y, x)self.result[2] = countdef deep(self, y, x):if self.site_view[y][x] is True:returnelse:self.site_view[y][x] = True# 检测上面的线if self.b_maze[y-1][x] in ["2", "3"]:self.deep(y-1, x)# 检测左边的线if self.b_maze[y][x-1] in ["1", "3"]:self.deep(y, x-1)# 检测下面和右面的线if self.b_maze[y][x] == "1":self.deep(y, x+1)elif self.b_maze[y][x] == "2":self.deep(y+1, x)elif self.b_maze[y][x] == "3":self.deep(y+1, x)self.deep(y, x+1)else:returndef is_inner(self, i, j):if self.b_maze[i][j] == '0' and self.b_maze[i - 1][j] in ['0', '1'] and self.b_maze[i][j - 1] in ['0', '2']:return Trueelse:return False# 分析第三项：def analyse_inner_points(self):count = 0for i in self.death_list:self.go3(i[2], i[0], i[1])for line in self.viewed3:for i in line:if i is True:count += 1for y in range(1, len(self.b_maze)-1):for x in range(1, len(self.b_maze[0])-1):if not self.not_death_block(y, x):count += 1self.result[3] = count# 找到所有死角块def go3(self, direction, y, x):self.viewed3[y][x] = Truenext_y = ynext_x = xif direction == "up":next_y = y-1next_x = x# 走右面elif direction == "right":next_y = ynext_x = x + 1# 走下面elif direction == "down":next_y = y + 1next_x = x# 走左面elif direction == "left":next_y = ynext_x = x - 1# self.go(direction, y, x - 1)# direction 代表当前点的出口的方向up = Truedown = Trueleft = Trueright = Trueroad = self.b_road[next_y][next_x]if direction == "right" or road.left is False:left = Falseif direction == "left" or road.right is False:right = Falseif direction == "up" or road.down is False:down = Falseif direction == "down" or road.up is False:up = Falsenext_road = Road(up, down, left, right)next_direction = self.is_three_suround(next_road)if next_direction != "no":return self.go3(next_direction, next_y, next_x)elif next_road.up is False and next_road.down is False and next_road.left is False and next_road.right is False:self.viewed3[next_y][next_x] = Truereturn# 分析第四项：共有多少个连通块def analyse_accessible_areas(self):count = 0for y in range(1, len(self.b_road)-1):for x in range(1, len(self.b_road[0])-1):if self.viewed4[y][x] is False:if self.not_death_block(y, x):count += 1self.view(y, x)self.result[4] = count-self.deathdef not_death_block(self, y, x):# 不是四面的死角 返回True 是四面的死角返回Falsereturn self.b_road[y][x].up or self.b_road[y][x].down or self.b_road[y][x].left or self.b_road[y][x].rightdef view(self, y, x):if self.viewed4[y][x] is True:returnself.viewed4[y][x] = Trueif not self.not_death_block(y, x):returnelse:if self.b_road[y][x].is_border is True:returnelse:# 四条路的判定与遍历if self.b_road[y][x].up is True:self.view(y-1, x)if self.b_road[y][x].down is True:self.view(y+1, x)if self.b_road[y][x].left is True:self.view(y, x-1)if self.b_road[y][x].right is True:self.view(y, x+1)# 分析第五项：共有多少个死角# 思路：深度优先遍历def analyse_sets(self):for y in range(1, len(self.b_road)-1):for x in range(1, len(self.b_road[0])-1):if self.viewed[y][x] is True:continuedirection = self.is_three_suround(self.b_road[y][x])if direction != "no":b = self.go(direction, y, x)if b is False:self.death_list.append([y, x, direction])self.result[5] = len(self.entry)def go(self, direction, y, x):self.viewed[y][x] = Truenext_y = ynext_x = xif direction == "up":next_y = y-1next_x = x# 走右面elif direction == "right":next_y = ynext_x = x + 1# 走下面elif direction == "down":next_y = y + 1next_x = x# 走左面elif direction == "left":next_y = ynext_x = x - 1# self.go(direction, y, x - 1)if self.b_road[next_y][next_x].is_border is True:self.entry.append([-2, -2, "end"])return True# direction 代表当前点的出口的方向up = Truedown = Trueleft = Trueright = Trueroad = self.b_road[next_y][next_x]if direction == "right" or road.left is False:left = Falseif direction == "left" or road.right is False:right = Falseif direction == "up" or road.down is False:down = Falseif direction == "down" or road.up is False:up = Falsenext_road = Road(up, down, left, right)next_direction = self.is_three_suround(next_road)if next_direction != "no":return self.go(next_direction, next_y, next_x)elif self.is_two_surround(next_road):the_point = [next_y, next_x, direction]index = self.is_point_in_list(the_point)if index >= 0:# past_direction,direction是两个入口，转化成边之后即可与另一条边构成三环块，然后继续往下走past_direction = self.entry.pop(index)[2]the_direction = self.get_the_direction(past_direction, direction, next_y, next_x)# 找到出口，调用go方法if the_direction != "no":self.go(the_direction, next_y, next_x)# 该点入list，并记录该点的已知入口else:self.entry.append(the_point)return Trueelif next_road.up is False and next_road.down is False and next_road.left is False and next_road.right is False:self.viewed[next_y][next_x] = Trueself.death += 1return Falseelse:self.entry.append([next_y, next_x, "end"])return Truedef is_three_suround(self, road):count = 0direction = "no"if road.up is False:count += 1else:direction = "up"if road.down is False:count += 1else:direction = "down"if road.left is False:count += 1else:direction = "left"if road.right is False:count += 1else:direction = "right"if count == 3:return directionelse:return "no"def is_two_surround(self,road):count = 0if road.up is False:count += 1if road.down is False:count += 1if road.left is False:count += 1if road.right is False:count += 1if count == 2:return Trueelse:return Falsedef is_point_in_list(self, point):b = -1for i in range(len(self.entry)):if self.entry[i][0] == point[0] and self.entry[i][1] == point[1] and self.entry[i][2] != "end":b = ibreakreturn bdef get_the_direction(self, past_direction, direction, next_y, next_x):# 寻找出口up = Truedown = Trueleft = Trueright = Trueif "up" in [past_direction, direction] or self.b_road[next_y][next_x].down is False:down = Falseif "down" in [past_direction, direction] or self.b_road[next_y][next_x].up is False:up = Falseif "right" in [past_direction, direction] or self.b_road[next_y][next_x].left is False:left = Falseif "left" in [past_direction, direction] or self.b_road[next_y][next_x].right is False:right = Falseroad = Road(up, down, left, right)return self.is_three_suround(road)# 分析第六项：共有多少个连通路径def analyse_path(self):# 分四面进入，上面的就从上面进入，下面的就从下面进入，左面从左面进入。count = 0for x1 in range(1, len(self.b_road[0])-1):if self.viewed6[1][x1] is False and self.b_road[1][x1].up is True:if self.cross("up", 1, x1) is True:self.success_path_start.append(["up", 1, x1])count += 1n = len(self.b_road)-2for xn in range(1, len(self.b_road[0])-1):if self.viewed6[n][xn] is False and self.b_road[n][xn].down is True:if self.cross("down", n, xn) is True:self.success_path_start.append(["down", n, xn])count += 1for y1 in range(1, len(self.b_road)-1):if self.viewed6[y1][1] is False and self.b_road[y1][1].left is True:if self.cross("left", y1, 1) is True:self.success_path_start.append(["left", y1, 1])count += 1n2 = len(self.b_road[0])-2for yn in range(1, len(self.b_road) - 1):if self.viewed6[yn][n2] is False and self.b_road[yn][n2].right is True:if self.cross("right", yn, n2) is True:self.success_path_start.append(["right", yn, n2])count += 1self.result[6] = countdef cross(self, direction, y, x):self.viewed6[y][x] = Trueup = Truedown = Trueleft = Trueright = Trueif direction == "left" or self.viewed[y][x-1] is True or self.b_road[y][x].left is False:left = Falseif direction == "right" or self.viewed[y][x+1] is True or self.b_road[y][x].right is False:right = Falseif direction == "down" or self.viewed[y+1][x] is True or self.b_road[y][x].down is False:down = Falseif direction == "up" or self.viewed[y-1][x] is True or self.b_road[y][x].up is False:up = Falseroad = Road(up, down, left, right)next_direction = self.is_three_suround(road)if next_direction != "no":n_direction = ""next_y = ynext_x = xif next_direction == "up":next_y = y - 1next_x = xn_direction = "down"# self.go(direction, y - 1, x)# 走右面elif next_direction == "right":next_y = ynext_x = x + 1n_direction = "left"# self.go(direction, y, x + 1)# 走下面elif next_direction == "down":next_y = y + 1next_x = xn_direction = "up"# self.go(direction, y + 1, x)# 走左面elif next_direction == "left":next_y = ynext_x = x - 1n_direction = "right"# self.go(direction, y, x - 1)if self.b_road[next_y][next_x].is_border is True:return Trueelse:return self.cross(n_direction, next_y, next_x)else:return Falsedef cross2(self, direction, y, x):self.temp.append([x-0.5, y-0.5])up = Truedown = Trueleft = Trueright = Trueif direction == "left" or self.viewed[y][x-1] is True or self.b_road[y][x].left is False:left = Falseif direction == "right" or self.viewed[y][x+1] is True or self.b_road[y][x].right is False:right = Falseif direction == "down" or self.viewed[y+1][x] is True or self.b_road[y][x].down is False:down = Falseif direction == "up" or self.viewed[y-1][x] is True or self.b_road[y][x].up is False:up = Falseroad = Road(up, down, left, right)next_direction = self.is_three_suround(road)if next_direction != "no":n_direction = ""next_y = ynext_x = xif next_direction == "up":next_y = y - 1next_x = xn_direction = "down"# 走右面elif next_direction == "right":next_y = ynext_x = x + 1n_direction = "left"# 走下面elif next_direction == "down":next_y = y + 1next_x = xn_direction = "up"# 走左面elif next_direction == "left":next_y = ynext_x = x - 1n_direction = "right"if self.b_road[next_y][next_x].is_border is True:self.temp.append([next_x-0.5, next_y-0.5])return Trueelse:self.cross2(n_direction, next_y, next_x)else:returndef go2(self, direction, y, x):self.viewed[y][x] = Falsenext_y = ynext_x = xif direction == "up":next_y = y-1next_x = x# self.go(direction, y - 1, x)# 走右面elif direction == "right":next_y = ynext_x = x + 1# self.go(direction, y, x + 1)# 走下面elif direction == "down":next_y = y + 1next_x = x# self.go(direction, y + 1, x)# 走左面elif direction == "left":next_y = ynext_x = x - 1# self.go(direction, y, x - 1)# direction 代表当前点的出口的方向up = Truedown = Trueleft = Trueright = Trueroad = self.b_road[next_y][next_x]if direction == "right" or road.left is False:left = Falseif direction == "left" or road.right is False:right = Falseif direction == "up" or road.down is False:down = Falseif direction == "down" or road.up is False:up = Falsenext_road = Road(up, down, left, right)next_direction = self.is_three_suround(next_road)if next_direction != "no":self.go(next_direction, next_y, next_x)elif next_road.up is False and next_road.down is False and next_road.left is False and next_road.right is False:self.viewed[next_y][next_x] = False# 输出结果def print_result(self):# print(self.result)out_result = list()for i in range(1, 7):if self.result[i] == 0:out_result.append(str('no'))elif self.result[i] == 1:out_result.append(str('a'))else:out_result.append(str(self.result[i]))# 输出print("The maze has "+out_result[0]+" gates. ")print("The maze has "+out_result[1]+" sets of walls that are all connected.")print("The maze has "+out_result[2]+" inaccessible inner point.")print("The maze has "+out_result[3]+" unique accessible area.")print("The maze has "+out_result[4]+" sets of accessible cul-de-sacs that are all connected.")print("The maze has "+out_result[5]+" unique entry-exit path with no intersection not to cul-de-sacs. ")# 展示def display(self):tex_file_name = self.file_name.split('.')[0] + ".tex"tex_file = open(tex_file_name, 'w')head =["\\documentclass[10pt]{article}\n","\\usepackage{tikz}\n","\\usetikzlibrary{shapes.misc}\n","\\usepackage[margin=0cm]{geometry}\n","\\pagestyle{empty}\n","\n","\\tikzstyle{every node}=[cross out, draw, red]\n","\n","\\begin{document}\n","\\vspace*{\\fill}\n","\\begin{center}\n","\\begin{tikzpicture}[x=0.5cm, y=-0.5cm, ultra thick, blue]\n","% Walls\n"]border = ["\\end{tikzpicture}\n","\\end{center}\n","\\vspace*{\\fill}\n","\n","\\end{document}\n"]# 开始画墙for y in range(len(self.maze)):for x in range(len(self.maze[0])):if self.maze[y][x] in ["1", "3"]:x1 = x+1y1 = ys = "    \\draw (" + str(x)+" ,"+str(y)+") -- ("+str(x1)+", "+str(y1)+");\n"self.walls.append(s)if self.maze[y][x] in ["2", "3"]:x1 = xy1 = y+1s = "    \\draw (" + str(x)+" ,"+str(y)+") -- ("+str(x1)+", "+str(y1)+");\n"self.walls.append(s)# 开始画点for i in range(1, len(self.b_maze) - 1):for j in range(1, len(self.b_maze[0]) - 1):if self.is_inner(i, j):s = "    \\fill[green] (" + str(j - 1) + "," + str(i - 1) + ") circle(0.2);\n"self.pillars.append(s)# 开始画pathfor i in self.success_path_start:self.temp = list()if i[0] == "up":self.temp.append([i[2]-0.5, -0.5])elif i[0] == "down":self.temp.append([i[2]-0.5, len(self.b_road) - 1.5])elif i[0] == "left":self.temp.append([-0.5, i[1]-0.5])elif i[0] == "right":self.temp.append([len(self.b_road[0]) - 1.5, i[1]-0.5])self.cross2(i[0], i[1], i[2])self.path.append(self.temp)for i in self.path:for j in range(len(i)-1):s = "    \draw[dashed, yellow] ("+str(i[j][0])+","+str(i[j][1])+") -- ("+str(i[j+1][0])+","+str(i[j+1][1])+");\n"self.entry_exit_paths.append(s)# 开始画 X ，# 1.计算出所有的死块，设置viewedfor i in self.death_list:self.go2(i[2], i[0], i[1])# 2.将所有visited中的点画上Xfor y in range(1, len(self.b_road)-1):for x in range(1, len(self.b_road[0])-1):if self.viewed[y][x] is True:y1 = str(y-0.5)x1 = str(x-0.5)s = "    \\node at ("+x1+","+y1+") {};\n"self.inner_points.append(s)tex_file.writelines(head)tex_file.writelines(self.walls)tex_file.writelines(self.pillars)tex_file.writelines(self.inner_points)tex_file.writelines(self.entry_exit_paths)tex_file.writelines(border)my_maze = Maze('maze_1.txt')
my_maze.analyse()
my_maze.display()