Select random element from a set, faster than linear time (Haskell)

Question

I\'d like to create this function, which selects a random element from a Set:

randElem :: (RandomGen g) => Set a -> g -> (a, g)

Si

Answer 1

If you had access to the internals of Data.Set, which is just a binary tree, you could recurse over the tree, at each node selecting one of the branches with probability according to their respective sizes. This is quite straight forward and gives you very good performance in terms of memory management and allocations, as you have no extra book-keeping to do. OTOH, you have to invoke the RNG O(log n) times.

A variant is using Jonas’ suggestion to first take the size and select the index of the random element based on that, and then use a (yet to be added elemAt) function to Data.Set.