Recycled Numbers

recycle.rb

# Google Code Jam: http://code.google.com/codejam/contest/1460488/dashboard#s=p2

def rotate(n, digits, size)
  magnitude = (10 ** (size-digits))
  first = n / magnitude
  last  = n % magnitude
  result = last * (10**digits) + first
end

def num_pairs(s, e)
  count = 0
  size = s.to_s.size
  rotations = size - 1
  (s..(e-1)).each do |i|
    n = m = i
    rotations.times do |r|
      m = rotate n, (r+1), size
      break if m == n
      count += 1 if n < m and m <= e
    end
  end
  count
end

# Run all test cases
if __FILE__ == $0
  while tests = gets
    tests = tests.to_i # <= 50

    tests.times do |i|
      num = gets # <= 2_000_000
      s, e = num.rstrip!.split ' '
      recycled_nums = num_pairs s.to_i, e.to_i
      print "Case ##{i+1}: #{recycled_nums}\n"
    end

    break

  end
end