Dijkstra's algorithm in python

Question

I am trying to implement Dijkstra\'s algorithm in python using arrays. This is my implementation.

def extract(Q, w):
    m=0
    minimum=w[0]
    for i in range(l         


        

Answer 1

Set a breakpoint in extract. You will see that you delete entries from Q but never from w. Everything else is a dict, but Q/w are a paired array which you do not keep up to date. You have to keep those two in sync, or replace them with a dict. Special note: Eventually, after the algorithm is working, you may want to replace Q/w with a list of edges and re-code the "extract" function with a priority queue (heapq module).

Additionally, you will see that w always has weights of 0 for the source, and 'inf' for all other nodes. You completely skipped the critical step where you update the candidate distances.

So you are basically always taking the first path you encounter, rather than selecting the shortest path. You later compute the actual distance of that path, so the returned array of distances has actual values, but they were chosen arbitrarily, and you have no reason to expect them to be shortest.

After you (incorrectly) find the next node, you look at all of its edges. This should have been the critical step I mentioned above in the second paragraph, where you update the candidates for the next node. Instead you do something completely different: You appear to be looping through all the previous solutions (which are guaranteed correct and should be left alone, if you correctly implement dijkstra), and you look for a two-step solution from source->current->any. The correct intent for looking at those would have been to add the next candidate from previous paths to the next node, but because they never get added, you don't look at (previous shortest path) + (one step), you only look at literally two node solutions.

So basically, you are looping through all possible two-node paths from source in order to find the shortest paths. This is a complete error and has nothing to do with dijkstra. But it almost works on your tiny tiny graph where most of the correct shortest paths are two-step paths.

(ps: I agree with everyone about your variable names. You would have done much better if you use verbose names telling what those variables represent. I had to rename them before I got anywhere analyzing your code.)