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

You already know how to find the median in O(n)

if the order does not matter, selection of k smallest can be done in O(n) apply for k smallest to the rhs of the median and k largest to the lhs of the median

from wikipedia

 function findFirstK(list, left, right, k)
 if right > left
     select pivotIndex between left and right
     pivotNewIndex := partition(list, left, right, pivotIndex)
     if pivotNewIndex > k  // new condition
         findFirstK(list, left, pivotNewIndex-1, k)
     if pivotNewIndex < k
         findFirstK(list, pivotNewIndex+1, right, k)

don't forget the special case where k==n return the original list