How to find all the paths from each router to the rest?

Question

map = {
    routers[0]: [routers[3], routers[4]],
    routers[1]: [routers[5], routers[6]],
    routers[2]: [routers[7], routers[8]],
    routers[3]: [routers[0], routers[4], routers[8]],
    routers[4]: [routers[0], routers[3], routers[5], routers[9]],
    routers[5]: [routers[1], routers[4], routers[6]],
    routers[6]: [routers[1], routers[5], routers[7], routers[9]],
    routers[7]: [routers[2], routers[6], routers[8]],
    routers[8]: [routers[2], routers[3], routers[7], routers[9]],
    routers[9]: [routers[4], routers[6], routers[8]]
}

The keys are the routers and their values are there neighbors.
For example, routers[0] is connected to both routers[3] and routers[4].

And I’m trying to create a table for each router like this:

routers[0] = {
    router[1]: router[x],
    router[2]: router[y],
    # and so on.
}

Where the keys are the destinations and the values are the next routers.
I did it, but it’s too messy. Is there a better way to do that?
Here is more info:

Asked By: Rozhyar Gaylan

||

Source

Answer 1

Not sure how you are making a dictionary where the keys are also dictionaries, but you can write a breadth-first-search function to find the shortest path and then just grab the first step at index 1.

routers = [f'router{i}' for i in range(10)]

router_map = {
    routers[0]: [routers[3], routers[4]],
    routers[1]: [routers[5], routers[6]],
    routers[2]: [routers[7], routers[8]],
    routers[3]: [routers[0], routers[4], routers[8]],
    routers[4]: [routers[0], routers[3], routers[5], routers[9]],
    routers[5]: [routers[1], routers[4], routers[6]],
    routers[6]: [routers[1], routers[5], routers[7], routers[9]],
    routers[7]: [routers[2], routers[6], routers[8]],
    routers[8]: [routers[2], routers[3], routers[7], routers[9]],
    routers[9]: [routers[4], routers[6], routers[8]]
}

def shortest_path(start, dest, router_map = router_map):
    visited = [start]
    
    paths = [[start]]

    while dest not in visited:
        paths = [path + [neighbor] 
                 for path in paths 
                 for neighbor in router_map[path[-1]]]

        visited = set([node for path in paths for node in path])



    return [path for path in paths if dest in path]

for i in range(1, 10):
    print(shortest_path(routers[0], routers[i]))

Answered By: Michael Cao

Answer 2

It seems you are looking for all_shortest_paths. You can use a library like networkx to do it for you.

Assuming your list of routers is definded like :

routers = list(range(len(map))

you could do:

import networkx as nx
G = nx.Graph()
for k, v in map.items():
    G.add_edges_from([(k, r) for r in v])
all_shortest_paths_dict = {
    k: {r: list(nx.all_shortest_paths(G, k, r)) for r in range(len(map)) if r != k}
    for k in map
}

print(all_shortest_paths_dict)

{0: {1: [[0, 4, 5, 1]],
  2: [[0, 3, 8, 2]],
  3: [[0, 3]],
  4: [[0, 4]],
  5: [[0, 4, 5]],
  6: [[0, 4, 5, 6], [0, 4, 9, 6]],
  7: [[0, 3, 8, 7]],
  8: [[0, 3, 8]],
  9: [[0, 4, 9]]},
 1: {0: [[1, 5, 4, 0]],
  2: [[1, 6, 7, 2]],
  3: [[1, 5, 4, 3]],
  4: [[1, 5, 4]],
  5: [[1, 5]],
  6: [[1, 6]],
  7: [[1, 6, 7]],
  8: [[1, 6, 7, 8], [1, 6, 9, 8]],
  9: [[1, 6, 9]]},
 ......

Answered By: SomeDude

How to find all the paths from each router to the rest?

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