How to find the best way to sort 8 elements and prove that there is no better way (no more efficient way)? [duplicate]

Answer 1

Mergesort/merge-insertion sort will require 16 comparisons for n=8, which is the minimum worst case number of comparisons.

http://oeis.org/A001768 (number of comparisons for mergesort)

http://oeis.org/A036604 (minimum number of comparisons in general)

see also Sorting an array with minimal number of comparisons

EDIT: without assuming "random numbers" are range restricted integers. If you can make assumptions about the range of values, then there are alternatives.

Answer 2

Radix sort requires no comparisons at all :)