Finding the shortest path in a n-dimensional grid I have an $n$-dimensional grid space with two points on it defined by ordered pairs. I want to find the shortest path between the two points, but I can only increase one number in the ordered pair at a time. Is there an algorithm for this or at least one I can refer to?
It's easy: first get the 1st dimension right, then the 2nd dimension, then the 3rd dimension, etc.

For example, if you want to get from $(1,3,0)$ to $(3,4,1)$, you go via the following sequence of points: $(1,3,0), (2,3,0), (3,3,0), (3,4,0), (3,4,1)$.