Incremental median computation with max memory efficiency

Question

I have a process that generates values and that I observe. When the process terminates, I want to compute the median of those values.

If I had to compute the mean, I

Answer 1

You can

• Use statistics, if that's acceptable - for example, you could use sampling.
• Use knowledge about your number stream
  • using a counting sort like approach: k distinct values means storing O(k) memory)
  • or toss out known outliers and keep a (high,low) counter.
  • If you know you have no duplicates, you could use a bitmap... but that's just a smaller constant for O(n).