Fast algorithm implementation to sort very small list

Question

This is the problem I ran into long time ago. I thought I may ask your for your ideas. assume I have very small list of numbers (integers), 4 or 8 elements, that need to be

Answer 1

I see you already have a solution that uses 5 comparisons (assuming that s(i,j) compares the two numbers once, and either swaps them or not). If you stick to comparison-based sorting, then you can't do it with any fewer than 5 comparisons.

This can be proven because there are 4! = 24 possible ways to order 4 numbers. Each comparison can only cut the possibilities in half, so with 4 comparisons you could only distinguish between 2^4 = 16 possible orderings.