I believe when you talk about "travelling distance" means "Dijkstra's algorithm"? If so, this will depend on application and how you apply an algorithm to it.

Hey thanks for the link. i read it and it says that for 4 movement, its recommended to use manhattan distance but i am not supposed to do the manhattan but instead use travelling distance. not sure what kind of formula i should use to calculate the algorithm 2 * (travelling distance)

On the page, it describe as weighing your terrain by multiplying with a constant greater than 1. The example that the author gave is to show that the grass square may cost 2 to move on. If you are doing the distance comparison in heuristic, you may need to consider this terrain weight as well. However, if the whole terrain is the same, you don't need to worry about the weighing.

In your test case, yes because of heuristic. However, there could be other cases that it is slower. You may try different cases like no obstacle at all, medium amount of obstacles, and plenty of obstacles. That way, you would see it clearer. :)

you have been contracted as a software develper to design a point of sales system, the system is to work in a way that ,if a customer purchase an item ...