I’ve been tasked (coursework @ university) to implement a form of path-finding. Now, in-spec, I could just implement a brute force, since there’s a limit on the number of nodes to search (begin, two in the middle, end), but I want to re-use this code and came to implement Dijkstra’s algorithm.
I’ve seen the pseudo on Wikipedia and a friend wrote some for me as well, but it flat out doesn’t make sense. The algorithm seems pretty simple and it’s not a problem for me to understand it, but I just can’t for the life of me visualize the code that would realize such a thing.
Any suggestions/tips?
Edit for some confusions:
Yes, there is a target node and a source node.
I’m looking to implement Dijkstra’s in a general case, not the “only two intermediate stops” case, because I want to use the code again afterwards. Else, I’d just write a brute-force implementation.
The specific issue that I’m having a little trouble with is storing the sub-optimal half-formed paths, in case they may become optimal. When I’m visiting a given node, I just don’t see how I’m going to update all the connections that go through it.
More edit:
Going through a couple of the answers now and having a go.
REALLY EDIT:
I forgot to mention a serious complication, which is that any two vertices can have up to UINT_MAX different distances between them. Sorry. Infact, the fact that I forgot to deal with this is probably the cause of the damn problem in the first place, although the solution: pick the shortest is fortunately obvious to me. No wonder other people’s pseudo for a distance variable didn’t take into account my variable distance.
Here’s a high level breakdown of Dijkstra’s algorithm:
You stick all of the vertices in a priority queue where all of the vertices have a priority (distance) of infinity except for the source vertex, which has a distance of zero (the source vertex is zero units of distance away from itself, right?).
Pop the priority queue. The vertex removed is the vertex with the shortest distance from the source. Obviously the first vertex popped from the queue is the source. Well call that popped vertex v.
Look at each of the neighbors of v. All of them will have a distance greater than v‘s distance (otherwise we would have already popped them from the queue, right?). Let’s say v has a distance of 3, and v has 3 neighbors x (dist-from-source: 5), y (dist-from-source: 10) and z (dist-from-source: infinity).
Now we look at each neighbors distance from v. Let’s say they are: x – 3, y – 2, z – 4. This means that the path from the source to x that goes through v has a distance of |v| + 3 (3 + 3 = 6), y has a distance of 5 (3 + 2 = 5) and z has a distance of 7 (3 + 4 = 7).
The path to x through v is longer than the current shortest path to x so we ignore it. However the paths to y and z that go through v are shorter than the previous known shortest path so we update them.
You keep doing this until you have gone through all the vertices. At each point, when you pop the min from the priority queue you know you have found the shortest path to that vertex because any possible shorter path must pass through a vertex with a distance less than v‘s, which means we would have already popped that from the queue.