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Dijkstra's algorithm in python: algorithms for beginners

Maria Boldyreva on July 10, 2018

Photo by Ishan @seefromthesky on Unsplash Dijkstra's algorithm can find for you the shortest path between two nodes on a graph. It's a must-know f...

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Natalia Alshevskaya • Jan 25 '20

This next could be written little bit shorter:

path, current_vertex = deque(), dest
while previous_vertices[current_vertex] is not None:
path.appendleft(current_vertex)
current_vertex = previous_vertices[current_vertex]
if path:
path.appendleft(current_vertex)

----->>>

path, current_vertex = deque(), dest
while current_vertex:
path.appendleft(current_vertex)
current_vertex = previous_vertices[current_vertex]

Phil Ashby • Jul 11 '18

Nicely done!

If you are only trying to get from A to B in a graph... then the A* algorithm usually performs slightly better: en.wikipedia.org/wiki/A*_search_al... That's what many SatNav packages use :)

Maria Boldyreva • Jul 11 '18

Yep! I will write about it soon. Thanks for reading :)

Aitor López • May 10 '19

Hello Maria,

First of all, thank you for taking the time to share your knowledge with all of us! I am sure that your code will be of much use to many people, me amongst them!

I actually have two questions.

First: do you know -or do you have heard of- how to change the weights of your graph after each movement?
In my case, I would like to impede my graph to move through certain edges setting them to 'Inf' in each iteration (later, I would remove these 'Inf' values and set them to other ones.

Second: Do you know how to include restrictions to Dijkstra, so that the path between certain vertices goes through a fixed number of edges?

Many thanks in advance, and best regards!

Aitor López • May 28 '19

Hello back,

I was finally able to find a solution to change the weights dynamically during the search process, however, I am still not sure about how to impose the condition of having a path of length >= N, being N the number of traversed edges. The only idea I have come up with would consist on turning to infinity the last edge towards my destination vertex if the overall distance lies below N. However, this would make this edge no longer available for use for the other paths that would arrive to destination vertex. Any ideas from your side folks? Many thanks in advance, and best regards!

nick9951 • Dec 17 '18

If we want to know the shortest path and total length at the same time
how to change the code?

Ruida Zeng • May 23 '19

Using Python object-oriented knowledge, I made the following modification to the dijkstra method:

return the distance between the nodes

    distance_between_nodes = 0
    for index in range(1, len(path)):
        for thing in self.edges:
            if thing.start == path[index - 1] and thing.end == path[index]:
                distance_between_nodes += thing.cost
    return distance_between_nodes       
    # return path

buecktobias • Dec 24 '18

I'd like to know that too.

neogeomat • May 14 '19

The algotithm says

6 Stop, if the destination node has been visited.

in the code

6. Stop, if the smallest distance

among the unvisited nodes is infinity.

if distances[current_vertex] == inf:
break

The code visits all nodes even after the destination has been visited.

Soumita Bose • Aug 14 '19

What changes should i do if i dont want to use the deque() data structure?
Also how to read the graph contents from a file with the below structure
a / b / 3
a / c / 5
...
Source node: a
Destination node: j

Ruida Zeng • May 23 '19 • Edited

Using Python object-oriented knowledge, I made the following modification to the dijkstra method to make it return the distance instead of the path as a deque object.

return the distance between the nodes
distance_between_nodes = 0
for index in range(1, len(path)):
for thing in self.edges:
if thing.start == path[index - 1] and thing.end == path[index]:
distance_between_nodes += thing.cost
return distance_between_nodes

# return path

Soumita Bose • Aug 14 '19

Mostafa Mohamed • Dec 13 '19 • Edited

This algorithm is working correctly only if the graph is directed,but if the graph is undireted it will not.

To make the algorithm work as directed graph you will have to edit neighbour function as

@property
def neighbours(self):
    neighbours = {vertex: set() for vertex in self.vertices}
    for edge in self.edges:
        neighbours[edge.start].add((edge.end, edge.cost))
        neighbours[edge.end].add((edge.start, edge.cost))
    return neighbours