算法之迷宮問題

題目：給一個二維列表，表示迷宮（0表示通道，1表示圍牆）。給出算法，求一條走出迷宮的路徑。

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]
 ]

解決思路：

• 在一個迷宮節點(x,y)上，可以進行四個方向的探查：maze[x-1][y], maze[x+1][y], maze[x][y-1], maze[x][y+1]
• 思路：從一個節點開始，任意找下一個能走的點，當找不到能走的點時，退回上一個點尋找是否有其他方向的點。
• 方法：創建一個空棧，首先將入口位置進棧。當棧不空時循環：獲取棧頂元素，尋找下一個可走的相鄰方塊，如果找不到可走的相鄰方塊，說明當前位置是死胡同，進行回溯（就是講當前位置出棧，看前面的點是否還有別的出路）

用棧實現：

 

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:   # 當棧不空循環
        cur_node = stack[-1]
        if cur_node == (x2,y2): #到達終點
            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:   #找到一個能走的方向
                stack.append(next_node)
                maze[next_node[0]][next_node[1]] = 2  # 2表示已經走過的點
                break
        else: #如果一個方向也找不到
            stack.pop()
    else:
        print("無路可走")
        return False

 

 

 

用隊列實現：

解決思路：

• 思路：從一個節點開始，尋找所有下面能繼續走的點。繼續尋找，直到找到出口。
• 方法：創建一個空隊列，將起點位置進隊。在隊列不為空時循環：出隊一次。如果當前位置為出口，則結束算法；否則找出當前方塊的4個相鄰方塊中可走的方塊，全部進隊。

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 = []    # 記錄出隊之后的節點
    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:  #到終點
            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 # 標記為已經走過
    else:
        print("無路可走")
        return False

solve_maze2(1,1,8,8)