How to find k nearest neighbors to the median of n distinct numbers in O(n) time?

Question

I can use the median of medians selection algorithm to find the median in O(n). Also, I know that after the algorithm is done, all the elements to the left of the median are les

Answer 1

First select the median in O(n) time, using a standard algorithm of that complexity. Then run through the list again, selecting the elements that are nearest to the median (by storing the best known candidates and comparing new values against these candidates, just like one would search for a maximum element).

In each step of this additional run through the list O(k) steps are needed, and since k is constant this is O(1). So the total for time needed for the additional run is O(n), as is the total runtime of the full algorithm.