I believe A* should always give the minimum path as long the heuristic is optimistic. It will become a greedy search if the heuristic is pessimistic. If the heuristic is "perfect" i.e heuristic(x to y) = min_cost(x to y) the the search will be optimal (i.e no nodes that do not belong with the path will be explored)

Yep after playing around with it for a bit it didn't give a minimum path. I believe something is wrong with the heuristic you are using.

Edit: You can prove A* will give a min path as long as: heuristic(x to y) <= min_cost(x to y). Problem seems to be here https://github.com/ssaric/algoviz/blob/master/src/util/GridN... I think it should be a matter of removing "times 100"

I believe the push and pull is between optimal path and time to find the path. The heuristic dictates whether the algorithm will lean towards Dijkstra or Greedy or somewhere in between.

I got my knowledge about heuristics from here:

http://theory.stanford.edu/~amitp/GameProgramming/Heuristics...

Whether a greedy heuristic is faster or not is dependent on the structure of the graph. For the example in the article about mountains and grassland, it makes sense that such a heuristic would speed up the search, since the algorithm can't get stuck in dead-ends.

But in a problem where the algorithm can get stuck in dead-ends, it's possible to construct examples where the greedy heuristic is (much) slower than plain Manhattan distance. Here's an example:

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Nice visualization!

I don’t think the algorithm is correct though. The heuristic seems to use Euclidean distance instead of “how the crow flies” and thus this implementation goes along the axis instead of directly towards the goal. This causes the algorithm to find the optimal route only occasionally and probably has little to no effect on average execution time.

I just realized my terminology was way wrong. Sorry.

You have Manhattan distance and you want Euclidean distance to make sure the path is always optimal. Execution speed should be the same or better in the average case with Euclidean distance.

One interesting heuristic is h(x) = 0, which is also [admissible](https://en.wikipedia.org/wiki/Admissible_heuristic) and transforms your A* into an uninformed heuristic as far as I remember.

In this case, wouldn't it be shorter to go down first, then to the right? What's happening here?

https://imgur.com/a/xfAtkML

A* is not guaranteed to find the optimal route - it depends on the heuristic and the environment.

Very cool. Definitely curious to see this part:

> I plan to add textual information on each step, to show how algorithm is "thinking"

I've set up the app in a way that I am sending "steps" from the worker. That way I can describe each step textually. I'll post updates here probably!