levenshtein.rb

class String
  def self.levenshtein(a, b)
    case
      when a.empty?: b.length
      when b.empty?: a.length
      else [(a[0] == b[0] ? 0 : 1) + levenshtein(a[1..-1], b[1..-1]),
            1 + levenshtein(a[1..-1], b),
            1 + levenshtein(a, b[1..-1])].min
    end
  end
  
  def levenshtein(other)
    self.class.levenshtein(self, other)
  end
end

"Test".levenshtein("Test") # => 0
"Test".levenshtein("A Test") # => 2