算法学习【第七篇】：算法之迷宫问题

目录

• 题目：给一个二维列表，表示迷宫（0表示通道，1表示围墙）。给出算法，求一条走出迷宫的路径

 

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题目：给一个二维列表，表示迷宫（0表示通道，1表示围墙）。给出算法，求一条走出迷宫的路径#

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maze = [     [1,1,1,1,1,1,1,1,1,1],     [1,0,0,1,0,0,0,1,0,1],     [1,0,0,1,0,0,0,1,0,1],     [1,0,0,0,0,1,1,0,0,1],     [1,0,1,1,1,0,0,0,0,1],     [1,0,0,0,1,0,0,0,0,1],     [1,0,1,0,0,0,1,0,0,1],     [1,0,1,1,1,0,1,1,0,1],     [1,1,0,0,0,0,0,0,0,1],     [1,1,1,1,1,1,1,1,1,1]  ]

解决思路：

• 在一个迷宫节点(x,y)上，可以进行四个方向的探查：maze[x-1][y], maze[x+1][y], maze[x][y-1], maze[x][y+1]
• 思路：从一个节点开始，任意找下一个能走的点，当找不到能走的点时，退回上一个点寻找是否有其他方向的点。
• 方法：创建一个空栈，首先将入口位置进栈。当栈不空时循环：获取栈顶元素，寻找下一个可走的相邻方块，如果找不到可走的相邻方块，说明当前位置是死胡同，进行回溯（就是讲当前位置出栈，看前面的点是否还有别的出路）

用栈实现#

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maze = [     [1,1,1,1,1,1,1,1,1,1],     [1,0,0,1,0,0,0,1,0,1],     [1,0,0,1,0,0,0,1,0,1],     [1,0,0,0,0,1,1,0,0,1],     [1,0,1,1,1,0,0,0,0,1],     [1,0,0,0,1,0,0,0,0,1],     [1,0,1,0,0,0,1,0,0,1],     [1,0,1,1,1,0,1,1,0,1],     [1,1,0,0,0,0,0,0,0,1],     [1,1,1,1,1,1,1,1,1,1] ]   dirs = [     lambda x,y:(x-1,y),  #上     lambda x,y:(x,y+1),  #右     lambda x,y:(x+1,y),  #下     lambda x,y:(x,y-1),  #左 ]   def solve_maze(x1, y1, x2, y2):     stack = []     stack.append((x1,y1))     maze[x1][y1] = 2     while len(stack) > 0:   # 当栈不空循环         cur_node = stack[-1]         if cur_node == (x2,y2): #到达终点             for p in stack:                 print(p)             return True         for dir in dirs:             next_node = dir(*cur_node)             if maze[next_node[0]][next_node[1]] == 0:   #找到一个能走的方向                 stack.append(next_node)                 maze[next_node[0]][next_node[1]] = 2  # 2表示已经走过的点                 break         else: #如果一个方向也找不到             stack.pop()     else:         print("无路可走")         return False

用队列实现#

解决思路：

• 思路：从一个节点开始，寻找所有下面能继续走的点。继续寻找，直到找到出口。
• 方法：创建一个空队列，将起点位置进队。在队列不为空时循环：出队一次。如果当前位置为出口，则结束算法；否则找出当前方块的4个相邻方块中可走的方块，全部进队。

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from collections import deque   maze = [     [1,1,1,1,1,1,1,1,1,1],     [1,0,0,1,0,0,0,1,0,1],     [1,0,0,1,0,0,0,1,0,1],     [1,0,0,0,0,1,1,0,0,1],     [1,0,1,1,1,0,0,0,0,1],     [1,0,0,0,1,0,0,0,0,1],     [1,0,1,0,0,0,1,0,0,1],     [1,0,1,1,1,0,1,1,0,1],     [1,1,0,0,0,0,0,0,0,1],     [1,1,1,1,1,1,1,1,1,1] ]   def solve_maze2(x1,y1,x2,y2):     queue = deque()     path = []    # 记录出队之后的节点     queue.append((x1,y1,-1))     maze[x1][y1] = 2     while len(queue) > 0:         cur_node = queue.popleft()         path.append(cur_node)         if cur_node[0] == x2 and cur_node[1] == y2:  #到终点             real_path = []             x,y,i = path[-1]             real_path.append((x,y))             while i >= 0:                 node = path[i]                 real_path.append(node[0:2])                 i = node[2]             real_path.reverse()             for p in real_path:                 print(p)             return True         for dir in dirs:             next_node = dir(cur_node[0], cur_node[1])             if maze[next_node[0]][next_node[1]] == 0:                 queue.append((next_node[0], next_node[1], len(path)-1))                 maze[next_node[0]][next_node[1]] = 2 # 标记为已经走过     else:         print("无路可走")         return False   solve_maze2(1,1,8,8)