Question

Assuming I have a large set of Coordinates such us (3,4), (5,-6), etc., where x and y are integers; is it possible to order them using a BST?

How can I go about determining what should be on the left vs right node?

The reason why I’m looking at BST instead of simply using a list of coordinates is so that I can more efficiently (vs linear search) determine those coordinates that would be in the Moore neighborhood (Chebyshev distance 1) of another.

I’ve thought about alternating comparisons to x and y values; is that a good approach?

How else can I apply BST to this situation? Or is using BST untenable?

Answer 1

Despite the simplicity of the approach by aioobe to create a grid of cells (two dimensional array), it was a bit heavy handed/inefficient to store the state of all possible cells/coordinates especially when I may have cases where there is only have a handful of actual coordinates in a very large space (sparse array).

Ultimately I realised using a BST is feasible (there are other approaches) and this is what I did to find Moore Neighbours efficiently using a balanced BST:

1. Impose a ordinal relation on coordinates i.e. (x1,y1) > (x2,y2) => (x1 > x2) || (x1==x2 && y1 > y2)
2. Sort list of coordinates by that relationship (to generate a balanced tree)
3. Generate BST from sorted list recursively: insert median element as node, slice the list below and above the median and pass as parameter to recursive call for generating left and right sub-trees

Then to search for the Moore Neighbours of a coordinate, I can then just look up/search for the 8 possible neighbour coordinates in the tree (as aioobe suggests) in O(log n).