Let's say we have a binary min-heap of size $n$, and we want to get an array of the smallest $\log n$ values in the heap, sorted. What is the best complexity that we can get and how do we implement it?
The simplest solution would be using $\text{Get-Min, Delete-Min}$, $\log n$ times, and that would be of time complexity of $O(\log ^2 n)$.
I've been told that this problem can be solved in time complexity of $O(\log n \log \log n)$, but I couldn't figure out an algorithm that reaches that time complexity.