input: 
  class StringComparator:
      def __init__(self, string1: str, string2: str):
          self.string1 = string1
          self.string2 = string2
  
      def is_equal(self) -> bool:
          """
          >>> comparator = StringComparator("apple", "apple")
          >>> comparator.is_equal()
          True
          >>> comparator = StringComparator("apple", "banana")
          >>> comparator.is_equal()
          False
          """
          return self.string1 == self.string2
  
      def is_different(self) -> bool:
          """
          >>> comparator = StringComparator("apple", "apple")
          >>> comparator.is_different()
          False
          >>> comparator = StringComparator("apple", "banana")
          >>> comparator.is_different()
          True
          """
          return self.string1 != self.string2
  
      def is_similar(self, threshold: float = 0.5) -> bool:
          """
          >>> comparator = StringComparator("apple", "aple")
          >>> comparator.is_similar()
          True
          >>> comparator = StringComparator("apple", "banana")
          >>> comparator.is_similar()
          False
          """
          distance = edit_distance(self.string1, self.string2)
          max_length = max(len(self.string1), len(self.string2))
          return distance / max_length < threshold
  
output:     def edit_distance(str1: str, str2: str) -> int:
          if len(str1) == 0:
              return len(str2)
          if len(str2) == 0:
              return len(str1)
          if str1[0] == str2[0]:
              return edit_distance(str1[1:], str2[1:])
          return 1 + min(edit_distance(str1[1:], str2), edit_distance(str1, str2[1:]), edit_distance(str1[1:], str2[1:]))