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

Since all the elements are distinct, there can be atmost 2 elements with the same difference from the mean. I think it is easier for me to have 2 arrays A[k] and B[k] the index representing the absolute value of the difference from the mean. Now the task is to just fill up the arrays and choose k elements by reading the first k non empty values of the arrays reading A[i] and B[i] before A[i+1] and B[i+1]. This can be done in O(n) time.