Question

I am looking for an optimum way to create a table from n elements so that ideally there are no empty cells, but at the same time the proportion of the table dimensions columns / rows becomes as close to 1 as possible.

Of course if n is a square number it is easy since then

cols = rows = sqrt( n );

If n is a prime number it is also clear that there will be empty cells, so my current way to handle this is:

rows = floor( sqrt(n) );
cols = ceil( n / rows  );

For all other cases my plan is to get the prime factors of n and then search all possible permutations for those whose combination has proportions closest to 1.

So my question is: is there is a better way to do this? Or is there at least a way not having to test every possible combination of the prime factors?

Answer 1

Instead of doing a prime factorization of n, start from the square root and find the next larger (or smaller — makes no difference) factor. That pair of factors will the closest to the square root, and therefore the closest to a proportion of 1:1.