MIDDLE = 5
REM_TO_REVERSE = 4
SYMBOLS = %w(I V X L C D M)

# @param {Integer} num
# @return {String}
def int_to_roman(num)
 num.to_s.reverse.chars.each_with_object(i: 0, result: '') do |val, memo|
  memo[:result] = num_to_roman(val.to_i, memo[:i] * 2) + memo[:result]
  memo[:i] += 1
 end[:result]
end

def num_to_roman(num, order = 0)
 return '' if num == 0
 int = num / MIDDLE
 rem = num % MIDDLE
 return SYMBOLS[order] + SYMBOLS[order+int+1] if rem == REM_TO_REVERSE
 return (int > 0 ? SYMBOLS[order+1] : '') + SYMBOLS[order] * rem
end