I am currently in the process of writing a program in VBA that will numerically "solve" a given n-body gravitational problem. I'm doing this pretty much just for fun and am by no means a programmer (had a 1 semester course in c++). The question I have is something that seems to keep coming into my mind as I write the code. When attempting to write an efficient program/code it seems as though you can optimize either for speed or memory. Is it a matter of deciding what is more important or trying to find the balance between the two? For example in the n-body problem I set up my code so that given "n" bodies, to find forces acting on all the bodies i calculate (n/2)(n-1) forces instead of the normal n^2 required amount. I am simply taking advantage of that fact that you can think of all the bodys as forming an nxn matrix. This matrix is symmetric since force (1,2) for bodies 1 and 2 is equal to (2,1) in magnitude and the diagonal is not valid (the forces (1,1)...). I figured that this would optimize memory, though I'm not sure about speed. My n-body code seem longer and more complicated (with many nested loops and if statments) than the more brute force method of simply having the computer just recalculate the other symmetric side of the nxn matrix. Obviously my method is still classified under the brute force method, though it cuts the number of calculated forces by 2. If you were to simulate a large number of bodies with the brute force method than it seems as though memory would be an issue, but speed as well. I mean I don't want to wait all day for the results from 1 simulation. Anyway if someone could shed alittle more light onto this that would be great.