The Friday Fragment

It's Friday, and time again for the Friday Fragment: our weekly programming-related puzzle.

This Week's Fragment

Some future Friday Fragments will make use of web services. So we'll take it one step at a time, starting this week:

Code a simple REST web service that, when called via GET, will randomly answer rock, paper, or scissors.

Your result can be fancy (wrapped in XML or JSON syntax), or simple: just the word. To “play along”, provide either the URL or the code for the solution. You can post it as a comment or send it via email.

Last Week's Fragment - Solution

Last week's puzzle was to code a happy number finder. A happy number is a positive integer which you can replace by the sum of the squares of its digits and repeat the process until you get to 1. For example, 7 is a happy number because its series ends at 1: 72 = 49, 42 + 92 = 97, 92 + 72 = 130, 12 + 32 + 02 = 10, 12 + 02 = 1.

If you tried this, you know it's not only a study in happy numbers, but also happy cases. The basic solution is easy; I coded a quick inductive solution in Ruby as an extension to the Integer class:

  def is_happy
    return case
      when self == 1 then true
      when self < 1 then false
      else self.digits.inject(0) { | sum, ea | (ea * ea) + sum }.is_happy
    end
  end

That's nice and simple, and 0.is_happy, 1.is_happy, and 7.is_happy all work swimmingly. However, 2.is_happy loops forever until crashing with a stack overflow. The reason is that the sum of squares of digits calculations for unhappy numbers run in infinite cycles (perhaps that's why they're unhappy). We can prevent that with a cache of numbers we've seen before:

  @@cache = Hash.new
  def is_happy
    return @@cache[self] if @@cache.include?(self)
    @@cache[self] = false
    result = case
      when self == 1 then true
      when self < 1 then false
      else self.digits.inject(0) { | sum, ea | (ea * ea) + sum }.is_happy
    end
    @@cache[self] = result
    return result
  end

I posted the complete code as a comment to last week's puzzle.

No one sent a solution, so I'll keep the 2011 Corvette ZR1 prize to myself. But give this week's puzzle a try; fortune or fame (or at least happiness) may await you.