How to efficiently select a random element from a std::set

Question

How can I efficiently select a random element from a std::set?

A std::set::iterator is not a random access iterator. So I can't directly index a randomly chosen element like I could for a std::deque or std::vector

I could take the iterator returned from std::set::begin() and increment it a random number of times in the range [0,std::set::size()), but that seems to be doing a lot of unnecessary work. For an "index" close to the set's size, I would end up traversing the entire first half of the internal tree structure, even though it's already known the element won't be found there.

Is there a better approach?

In the name of efficiency, I am willing to define "random" as less random than whatever approach I might have used to choose a random index in a vector. Call it "reasonably random".

Edit...

Many insightful answers below.

The short version is that even though you can find a specific element in log(n) time, you can't find an arbitrary element in that time through the std::set interface.

Answer 1

Use boost::container::flat_set instead:

boost::container::flat_set<int> set;
// ...
auto it = set.begin() + rand() % set.size();

Insertions and deletions become O(N) though, I don't know if that's a problem. You still have O(log N) lookups, and the fact that the container is contiguous gives an overall improvement that often outweighs the loss of O(log N) insertions and deletions.