# Find both the largest and second largest elements from a set

Consider finding both the largest and second largest elements from a set of $n$ elements by means of comparisons.

Prove that $n+\lceil \log n \rceil -2$ comparisons are necessary and sufficient.

Could you give me some hints how I could do that ??

If you run an elimination tournament among the elements, you can find the largest in $n-1$ comparisons. The second largest could be any one of the elements that lost to he final winner. How many is that?