You would be DEAD WRONG. Here N represents the number of elements in the list to be sorted. o(N) means order of N, o(N*log(N)) means order of N*log(N) etc.

In grad school, I learned that the sorting algorithm that uses the FEWEST comparisons was either Tony Hoare's Quicksort, or von Neumanns Mergesort. Each uses N*log(N) comparisons (steps) of pairs of list elements. This cannot be improved upon. That is a theorem.

HOWEVER, it is possible to sort a list WITHOUT DOING ANY COMPARISONS of list elements using a method called Radix Sort. This algorithm uses N steps. How can you sort a list without comparing any pairs elements? The answer is in the following three videos. It is called the Radix Sort. I suspect that similar calculations (such as Fourier Transform) can improve on many other computing methods.