You have a map of square tiles where you can move in any of the 8 directions. Given that you have function called cost(tile1, tile2)
which tells you the cost of moving from one adjacent tile to another, how do you find a heuristic function h(y, goal) that is both admissible and consistent? Can a method for finding the heuristic be generalized given this setting, or would it be vary differently depending on the cost
function?
Amit's tutorial is one of the best I've seen on A* (Amit's page). You should find some very useful hint about heuristics on this page .
Here is the quote about your problem :
On a square grid that allows 8 directions of movement, use Diagonal distance (L∞).