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

Four Steps:

1. Use Median of medians to locate the median of the array - O(n)
2. Determine the absolute difference between the median and each element in the array and store them in a new array - O(n)
3. Use Quickselect or Introselect to pick k smallest elements out of the new array - O(k*n)
4. Retrieve the k nearest neighbors by indexing the original array - O(k)

When k is small enough, the overall time complexity becomes O(n).