Is it possible to calculate median of a list of numbers better than O(n log n)?

Question

I know that it is possible to calculate the mean of a list of numbers in O(n). But what about the median? Is there any better algorithm than sort (O(n log n)) and lookup middl

Answer 1

If the numbers are discrete (e.g. integers) and there is a manageable number of distinct values, you can use a "bucket sort" which is O(N), then iterate over the buckets to figure out which bucket holds the median. The complete calculation is O(N) in time and O(B) in space.