python——迷宫问题总结

关于迷宫问题，常见会问能不能到达某点，以及打印到达的最短路径。可以用回溯法+递归来解决

代码一：dfs + 回溯

• 将矩阵外围以及路障统一设置为-1

• 设置current_step和next_step两个值。如果面临的点大于next_step，或者从未走过，就可以对它递归

• 存储矩阵：直接在原迷宫上修改，每个点标记的是从起点过来经过的步数，遇到0或者是比当前大至少2的，就考察

# -*- coding:utf-8 -*-
def init():
  global graph
  graph.append([-1,  -1, -1, -1, -1, -1,  -1])
  graph.append([-1,  0, 0, -1, 0, 0,  -1])
  graph.append([-1,  0, -1, 0, 0, 0,  -1])
  graph.append([-1,  0, -1, 0, -1, -1,  -1])
  graph.append([-1,  0, -1, 0, 0, 0,  -1])
  graph.append([-1,  0, 0, 0, -1, 0,  -1])
  graph.append([-1,  0, 0, 0, 0, 0,  -1])
  graph.append([-1,  -1, -1, -1, -1, -1,  -1])
#深度优先遍历
def deepFirstSearch( steps , x, y ):
  global graph
  current_step = steps + 1
  print(x, y, current_step )
  graph[x][y] = current_step
  next_step = current_step + 1
  '''
  遍历周围4个点:
    如果周围节点不是-1 说明 不是障碍 在此基础上：
        里面是0 说明没遍历过 我们把它修改成当前所在位置步数加1
        里面比当前的next_step大 说明不是最优方案 就修改它
        里面比当前next_step说明当前不是最优方案，不修改
  '''
  if not(x-1== 1 and y==1) and graph[x-1][y] != -1 and ( graph[x-1][y]>next_step or graph[x-1][y] ==0 ) : #上
    deepFirstSearch(current_step, x-1 , y )
  if not(x == 1 and y-1==1) and graph[x][y-1] != -1 and ( graph[x][y-1]>next_step or graph[x][y-1] ==0 ) : #左
    deepFirstSearch(current_step, x , y-1 )
  if not(x == 1 and y+1==1) and graph[x][y+1] != -1 and ( graph[x][y+1]>next_step or graph[x][y+1]==0 ) : #右
    deepFirstSearch(current_step, x , y+1 )
  if not(x+1== 1 and y==1) and graph[x+1][y] != -1 and ( graph[x+1][y]>next_step or graph[x+1][y]==0 ) : #下
    deepFirstSearch(current_step, x+1 , y )
if __name__ == "__main__":
  graph = []
  init()
  deepFirstSearch(-1,1,1)
  print(graph[1][5])

代码二：也是回溯

这里0是可走，1是路障，用while来做循环。如果某点的附近有判断可走的新点，就将新点append进stack，走过了标记为-1；如果四个方向都没有，就从旧点从stack中pop掉，标上-1，进行回溯。

存储矩阵：stack中存储的0是可走，1是路障，-1是走过的或者是死路

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],
    [1,1,0,0,0,0,0,1,0,1],
    [1,1,1,1,1,1,1,1,1,1]
]
dirs = [lambda x, y: (x + 1, y),
        lambda x, y: (x - 1, y),
        lambda x, y: (x, y - 1),
        lambda x, y: (x, y + 1)]
def mpath(x1, y1, x2, y2):
    stack = []
    stack.append((x1, y1))
    while len(stack) > 0:
        curNode = stack[-1]
        if curNode[0] == x2 and curNode[1] == y2:
            #到达终点
            for p in stack:
                print(p)
            return True
        for dir in dirs:
            nextNode = dir(curNode[0], curNode[1])
            if maze[nextNode[0]][nextNode[1]] == 0:
                #找到了下一个
                stack.append(nextNode)
                maze[nextNode[0]][nextNode[1]] = -1  # 标记为已经走过，防止死循环
                break
        else:#四个方向都没找到
            maze[curNode[0]][curNode[1]] = -1  # 死路一条,下次别走了
            stack.pop() #回溯
    print("没有路")
    return False

mpath(1,1,8,8)