我正在尝试为带球的迷宫获得最短路径：球一直滚动直到撞到墙壁。我使用 Dijkstra 算法将 heapq 用于优先队列。但是，我得到了一条非最佳路径。
这是我的示例输入代码：
maze = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0],
[0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0],
[0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1],
[1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1],
[1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0],
[0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
start = (0, 0)
end = (22, 22)
def shortestDistance(maze: List[List[int]], start: List[int], destination: List[int]):
start, destination = tuple(start), tuple(destination)
row, col = len(maze), len(maze[0])
moves = [(-1, 0), (0, 1), (0, -1), (1, 0)]
dstr = ['u', 'r', 'l', 'd']
class Point:
def __init__(self, distance, coordinates, directions):
self.distance = distance
self.coordinates = coordinates
self.directions = directions
def __eq__(self, p):
if self.distance == p.distance:
return self.__lt__(self, p)
return self.distance - p.distance
def __lt__(self, p):
return len(self.directions) - len(p.directions)
heap = [(Point(0, start, ""))]
visited = set()
while heap:
point = heapq.heappop(heap)
dist = point.distance
node = point.coordinates
directions = point.directions
if node in visited: continue
if node == destination:
return directions
visited.add(node)
for idx, move in enumerate(moves):
dx, dy = move
newX = node[0]
newY = node[1]
distance = dist
newDirections = directions
while 0 <= newX + dx < row and 0 <= newY + dy < col and maze[newX + dx][newY + dy] == 0:
newX += dx
newY += dy
distance += 1
if (newX, newY) == destination:
break
if (newX, newY) not in visited:
heapq.heappush(heap, Point(distance, (newX, newY), newDirections + dstr[idx]))
return "Impossible"
path = shortestDistance(maze, start, end)
print(path)
这个想法是比较距离，如果相等，选择方向变化较少的路径。
我目前正在获取 rdrludlrdrudludldldr（即右下右左...）作为输出，但在索引 2 处找到的序列“rl”没有意义：“Right”应该后面不能跟“左”，也不应该跟“上”跟“下”，反之亦然。这样的顺序显然不是最佳的，因为可以省略这两个移动中的第一个，以使球在同一位置并移动更短的距离。
这个迷宫的预期输出是drururdrdrurdrd。
为什么我没有得到最短路径？
答案 0 :(得分：2)
问题在于 __lt__ 函数没有做它应该做的事情。
它应该返回一个布尔值，当 self 被认为小于 p 时为真。当您当前返回一个整数结果时，该结果通常是非零的，您会遇到这样的情况：一对 (p, q) 点将 p < q 和 q < p 都为真...这会导致不稳定的行为。
以下是您如何定义它：
def __lt__(self, p):
return ((self.distance, len(self.directions), self.directions) <
< (p.distance, len(p.directions), p.directions))
通过此更改返回的路径是
rdrdldldrdr
您可以使用命名元组，而不是创建类 Point，这使一切变得更容易（更快）。您只需要更改“属性”的顺序，以便这些点以所需的方式进行比较，即 directions 应该在 coordinates 之前，方向字符串的长度应该有自己的属性：
from collections import namedtuple
# change order of properties so comparison works as intended
Point = namedtuple("Point", "distance, length, directions, coordinates")
然后在调用 Point 的地方进行适当的更改：
heap = [Point(0, 0, "", start)]
# ...
heapq.heappush(heap, Point(distance, len(newDirections) + 1, newDirections + dstr[idx], (newX, newY)))