Given a max heap with extract-max operation.
The basic version takes $2 \log n$ steps. How can I make it in $\log n + \log\log n$ and how in $\log n + \log\log\log n $?
I thought of putting $-\infty$ on the heap root but not really sure what to do with it as it can go anywhere.
To be more precise, steps are considered only compares between array item values. I'm reading CLRS Chapter 6 (MAX-HEAPIFY and HEAP-EXTRACT-MAX).