input: Write a class to compare two strings and provide methods to check if they are equal, different, or similar within a given threshold based on the edit distance. If the edit distance divided by the maximum length of the two strings is less than the provided threshold, the strings are considered similar.
  
  class StringComparator:
      def __init__(self, string1, string2):
          self.string1 = string1
          self.string2 = string2
  
      def is_equal(self):
          return self.string1 == self.string2
  
      def is_different(self):
          return self.string1 != self.string2
  
      def is_similar(self, threshold=0.5):
          distance = edit_distance(self.string1, self.string2)
          max_length = max(len(self.string1), len(self.string2))
          return distance / max_length < threshold
  
  # Test Cases
  sc1 = StringComparator("hello", "hello")
  assert sc1.is_equal() == True
  
  sc2 = StringComparator("hello", "world")
  assert sc2.is_different() == True
  
  sc3 = StringComparator("hello", "hallo")
  assert sc3.is_similar(0.2) == True
  
  sc4 = StringComparator("kitten", "sitting")
  assert sc4.is_similar(0.2) == False
  
  sc5 = StringComparator("", "")
  assert sc5.is_equal() == True
output: 
  class StringComparator:
      def __init__(self, string1, string2):
          self.string1 = string1
          self.string2 = string2
  
      def is_equal(self):
          return self.string1 == self.string2
  
      def is_different(self):
          return self.string1 != self.string2
  
      def is_similar(self, threshold=0.5):
          def edit_distance(s1, s2):
              if len(s1) > len(s2):
                  s1, s2 = s2, s1
              distances = range(len(s1) + 1)
              for i2, c2 in enumerate(s2):
                  distances_ = [i2+1]
                  for i1, c1 in enumerate(s1):
                      if c1 == c2:
                          distances_.append(distances[i1])
                      else:
                          distances_.append(1 + min((distances[i1], distances[i1 + 1], distances_[-1])))
                  distances = distances_
              return distances[-1]
          
          distance = edit_distance(self.string1, self.string2)
          max_length = max(len(self.string1), len(self.string2))
          return distance / max_length < threshold
  