feat: add dijkstra with adjacency list and heap increasePriority

[caojoshua]

Add dijkstra shortest path algorithm for adjacency matrix.

We can get lower bounds on a graph with adjacency list representation using min/Fibonacci heap, but I think this solution is the lowest bound we can get for an adjacency matrix representation.

[appgurueu]

We can get lower bounds on a graph with adjacency list representation using min/Fibonacci heap, but I think this solution is the lowest bound we can get for an adjacency matrix representation.

Is there any reason not to convert the adjacency matrix representation into an adjacency list representation before executing Dijkstra?

[caojoshua]

Is there any reason not to convert the adjacency matrix representation into an adjacency list representation before executing Dijkstra?

If the algorithm itself is doing the conversion, it increases space complexity from O(V) -> O(V + E). Outside of complexity, one could also argue for the benefits for an adjacency matrix in general. For example, adjacency lists that use linked lists may use up more heap space and have worse data locality, especially for dense graphs.

I was not sure whether I should implement this with adjacency matrix or list, but the matrix implementation is easier. Going through existing thealgorithms implementations, I see a combination of both matrix and list implementations.

Maybe its reasonable to have two alternative implementations? I think its reasonable for educational purposes.

[caojoshua]

Now that I think about it, we could easily implement adjacency list with a 2-dimensional array. Each value is a 2-tuple with (destination_node_idx, weight).

[appgurueu]

Can you try to add a few (non-redundant) comments in the code?

[caojoshua]

I made changes for the small suggestions and pushed what I had. I tried an adjacency list implementation with this repo's MinHeap and found that its broken.

I have fixes in #135. I would like to get that merged first before this PR. I'll be sure to add comments as suggested as well.

[appgurueu]

otherwise lgtm

[caojoshua]

I think I messed up to git stuff. Sorry for force push.

I made changes for adjacency list, which now works since MinHeap was fixed. Added inline comments as suggested.

[caojoshua]

Sorry, i think I am using priority queue incorrectly here. Im pushing the node index, but it should be the distance to the node. Please hold off on review for now.

[appgurueu]

Indeed. If you override the comparison function of the priority queue to compare the distances of the nodes at the indices, you can keep working with indices. I believe this is a cleaner and more efficient solution than storing node - distance pairs.