我一直在尝试编写 Bellman Ford 算法以在图中找到最短路径,虽然我有一个可行的解决方案,但它运行得不是很快,我相信如果我可以更快使用 numpy 而不是我目前的方法。
这是我使用 for 循环的解决方案:
import os
file = open(os.path.dirname(os.path.realpath(__file__)) + "/g_small.txt")
vertices, edges = map(lambda x: int(x), file.readline().replace("\n", "").split(" "))
adjacency_list = [[] for k in xrange(vertices)]
for line in file.readlines():
tail, head, weight = line.split(" ")
adjacency_list[int(head)-1].append({"from" : int(tail), "weight" : int(weight)})
n = vertices
shortest_paths = []
s=2
cache = [[0 for k in xrange(vertices)] for j in xrange(vertices)]
cache[0][s] = 0
for v in range(0, vertices):
if v != s:
cache[0][v] = float("inf")
# this can be done with numpy I think?
for i in range(1, vertices):
for v in range(0, vertices):
adjacent_nodes = adjacency_list[v]
least_adjacent_cost = float("inf")
for node in adjacent_nodes:
adjacent_cost = cache[i-1][node["from"]-1] + node["weight"]
if adjacent_cost < least_adjacent_cost:
least_adjacent_cost = adjacent_cost
cache[i][v] = min(cache[i-1][v], least_adjacent_cost)
shortest_paths.append([s, cache[vertices-1]])
for path in shortest_paths:
print(str(path[1]))
shortest_path = min(reduce(lambda x, y: x + y, map(lambda x: x[1], shortest_paths)))
print("Shortest Path: " + str(shortest_path))
输入文件如下所示 -> https://github.com/mneedham/algorithms2/blob/master/shortestpath/g_small.txt
除了大约一半的嵌套循环之外,这几乎是无趣的。我尝试使用 numpy 对其进行矢量化,但考虑到矩阵/二维数组在每次迭代中都会发生变化,我不太确定该怎么做。
如果有人对我需要做的事情或什至要阅读的内容有任何想法,那将在我的道路上对我有所帮助,那就太棒了。
===================
我写了一个更新版本来考虑 Jaime 的评论:
s=0
def initialise_cache(vertices, s):
cache = [0 for k in xrange(vertices)]
cache[s] = 0
for v in range(0, vertices):
if v != s:
cache[v] = float("inf")
return cache
cache = initialise_cache(vertices, s)
for i in range(1, vertices):
previous_cache = deepcopy(cache)
cache = initialise_cache(vertices, s)
for v in range(0, vertices):
adjacent_nodes = adjacency_list[v]
least_adjacent_cost = float("inf")
for node in adjacent_nodes:
adjacent_cost = previous_cache[node["from"]-1] + node["weight"]
if adjacent_cost < least_adjacent_cost:
least_adjacent_cost = adjacent_cost
cache[v] = min(previous_cache[v], least_adjacent_cost)
=================
这次使用矢量化的另一个新版本:
def initialise_cache(vertices, s):
cache = empty(vertices)
cache[:] = float("inf")
cache[s] = 0
return cache
adjacency_matrix = zeros((vertices, vertices))
adjacency_matrix[:] = float("inf")
for line in file.readlines():
tail, head, weight = line.split(" ")
adjacency_matrix[int(head)-1][int(tail)-1] = int(weight)
n = vertices
shortest_paths = []
s=2
cache = initialise_cache(vertices, s)
for i in range(1, vertices):
previous_cache = cache
combined = (previous_cache.T + adjacency_matrix).min(axis=1)
cache = minimum(previous_cache, combined)
shortest_paths.append([s, cache])