roman-with-explanation.rb

class Integer                                                            # so that 3.to_roman() will return a result
  Roman = 'IVXLCDM'                                                      # cardinally ordered roman numerals
  def to_roman
    raise "Number too large" if self > 4999                              # string does not contain characters for > 4999
    n, nsize = self, Math.log10(self).to_i                               # n = this number, nsize = number of digits in this number
    nsize.downto(0).map do |pow|                                         # pow = each digit from the left (i.e. 4,3,2,1 for 1000) - 1 (zero is the first index)
      mid = pow << 1                                                     # mid = pow * 2 (so that for every multiple of 10, there are two roman characters)
      current = n / (10 ** pow)                                          # current = T where Txxx is the current number and pow is digits from right; i.e. 1234 and pow is 3 -> T == 1
      n = n % (10 ** pow)                                                # n = the leftovers; i.e. if 1234 and pow is 3, then n == 234
      mods = current % 5                                                 # mods = remainder of current divided by 5; therefore, offset from a pure single-character roman digit
      out = ''                                                           # create a new string for output
      out << Roman[mid] if mods == 4                                     # if mods is 4, we have a pre-pointer digit (i.e. IV, IX, XL, ...); add that here
      out << Roman[mid + (current == 9 ? 2 : 1)] if current > 3          # add the main roman numeral; i.e. if n == 55 and pow == 1 (dealing with the 50), mid == 2 (zero index), current == 5, Roman[mid+1] == 'L' 
      out << (Roman[mid] * mods) if mods < 4                             # numbers after main roman digit; if % 5 is less than 4 (i.e. does not have a prefix digit), add Roman[mid] digits for each remaining digit (i.e. 3 returns III here)
      out                                                                # function return value (string)
    end.join                                                             # concatenate strings
  end
end