My first gut-level feel for "speed of algorithms" comes from my "how much
entropy did you undo with that calculation?". In this case, besides knowing
the minimum and maximum, you also knew (at one point, before you threw
it away) the second-smallest, third-smallest, on up to the second-largest.
It must have taken time to calculate those, so you've wasted time to calculate
things that don't affect the outcome.
Note that this is just for "back of the thumbnail" calculations. I've been wrong
using this method, but I'm not a theoretical mathematician... I'm a hacker. {grin}