What is the fastest way to sort 1 million integers when integers are from the range [1,100]?

Question

Notes: I\'ve thought about Radix sort, bucket sort, counting sort.

Is there anyway to achieve big O(n)?

Answer 1

For anyone interested, I quickly threw together this piece of Ruby, before reading the answers:

module Enumerable
  def counting_sort(k)
    reduce(Array.new(k+1, 0)) {|counting, n| counting.tap { counting[n] += 1 }}.
    map.with_index {|count, n| [n] * count }.flatten
  end
end

ary = Array.new(1_000_000){ rand(100) + 1 }
ary.counting_sort(100) # I'll spare you the output :-)

I didn't even know it had a name. It should convey the idea even to someone who has never seen Ruby before. (The only thing you need to know is that the K combinator is spelled tap in Ruby.)

And it really is pretty darn fast, although unfortunately I have not been able to beat the builtin hand-optimized O(n log n) sort, which is written in C in MRI and YARV and Java in JRuby.