Finding median of large set of numbers too big to fit into memory

Question

I was asked this question in an interview recently.

There are N numbers, too many to fit into memory. They are split across k database tables (unsorted), each of whi

Answer 1

There's a few potential solutions:

• External merge sort - O(n log n)
  You basically sort the numbers on the first pass, then find the median on the second.
• Order statistics distributed selection algorithm - O(n)
  Simplify the problem to the original problem of finding the kth number in an unsorted array.
• Counting sort histogram O(n)
  You have to assume some properties about the range of the numbers - can the range fit in the memory?
• If anything is known about the distribution of the numbers other algorithms can be produced.

For more details and implementation see:
http://www.fusu.us/2013/07/median-in-large-set-across-1000-servers.html