No of comparisons to find 2nd smallest number?

I happen to remember this one from my algorithms class. Take your list of 32 numbers and try to find the smallest number. Compare the first and second numbers, the third and fourth, etc. until you reduce the list by half and repeat. It will take 31 comparisons to find the smallest number as each comparison eliminates one possibility.

Once this has been complete, make a list of the numbers the smallest number has been compared to. There should be 5. It will take 4 comparisons to find the smallest of these 5 numbers, for a total of 35 comparisons.

35 comparisons are optimal. Pair off the numbers and test them against each other. Take the winners, the winners' winners, and so forth to find the maximal element; this takes 31 comparisons in all. Now the maximal element was compared against five other elements, and the second-largest element is precisely the largest of these five. You can find it in four comparisons, for a total of 35 comparisons.