gistfile1.rb

# 0 < A < B を仮定

lower_num, lower_den = 0, 1
upper_num, upper_den = 1, 0
loop do
  m_num = lower_num + upper_num
  m_den = lower_den + upper_den
  case
  when m_num < A * m_den then lower_num, lower_den = m_num, m_den
  when B * m_den < m_num then upper_num, upper_den = m_num, m_den
  else p [:found, Rational(m_num, m_den)]
  end
end