Hi,

I have a programing problem of finding monotonic heuristics (in python).

I have this function which takes two points a and b in the n-dimensional space and returns the d-dimensional point r such that r_i = | a_i - b_i | for i = 1...d

def distance_in_each_coordinate(x, y):

res = [ abs(a-b) for (a,b) in zip(x, y) ]

return res

Then I have the following function, which receives coordinates of two grid points and return the estimated distance between them.

def grid_2D_heuristic(current, destination): # the grid is a classic 2D grid

dst_per_coor = distance_in_each_coordinate(current, destination)

return sum(dst_per_coor)

And similarly I would like to know how to calculate the distance in a 2D grid, where the edges correspond exactly to the movement of the rook on the chessboard where the movement distance is limited to 8 cells (for example, it contains {(0,0), (0,8)} and {(0,0), (-8,0)} but it does not include {(0,0), (9,0)})

def grid_rook_2D_heuristic(current, destination):

return 'WHAT DO I RETURN HERE?'

Could you please help me find the monotonic heuristic in a 2D grid with the rook movement?

Thank you! <3