对Bellman-Ford算法使用带有numpy的矢量化

Question

我一直在尝试编写用于在图中寻找最短路径的Bellman Ford algoritm，虽然我已经有了一个有效的解决方案，但它运行得并不是很快，我相信如果我使用numpy而不是我目前的方法，它会更快。

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))  

输入文件如下所示的-> https://github.com/mneedham/algorithms2/blob/master/shortestpath/g_small.txt

除了大约一半的嵌套循环之外，它几乎是无趣的。我尝试使用numpy对其进行矢量化，但我不确定如何做，因为矩阵/2D数组在每次迭代时都会发生变化。

如果任何人有任何关于我需要做什么的想法，或者甚至是一些可以阅读的东西，那将是非常棒的。

==================

我写了一个更新的版本来考虑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)

================

和另一个新版本，这次使用了矢量化：

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])

Answer 1

在遵循了Jaime的建议后，我最终得到了以下矢量化代码：

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])