The problem is called the Selection problem. It's been intensively studied and has a couple of very interesting algorithms that do the job. I'll be describing an algorithm called QuickSelect. The algorithm derives its name from QuickSort. You will probably recognise that most of the code directly borrows from QuickSort. The only difference being there is a single recursive call rather than 2 in QuickSort.

The naive solution is obvious, simply sort the array `O(nlogn)` and return the kth element. Infact, you can partially sort it and use the Selection sort to get the solution in `O(nk)`

An interesting side effect of finding the kth smallest element is you end up finding the k smallest elements. This also effectively gives you (n - k) largest elements in the array as well. These elements are not in any particular order though.

The version I'm using uses a random pivot selection, this part of the algorithm us…