input: class StringComparator:
      def __init__(self, string1: str, string2: str):
          """
          Initialize the StringComparator with two strings.
          """
          self.string1 = string1
          self.string2 = string2
  
      def is_equal(self) -> bool:
          """
          Check if the two strings are exactly equal.
          >>> StringComparator("hello", "hello").is_equal()
          True
          >>> StringComparator("hello", "world").is_equal()
          False
          """
          return self.string1 == self.string2
  
      def is_different(self) -> bool:
          """
          Check if the two strings are different.
          >>> StringComparator("hello", "hello").is_different()
          False
          >>> StringComparator("hello", "world").is_different()
          True
          """
          return self.string1 != self.string2
  
      def is_similar(self, threshold: float = 0.5) -> bool:
          """
          Check if the two strings are similar based on the provided threshold.
          Uses the edit distance (Levenshtein distance) to determine similarity.
          >>> StringComparator("hello", "hallo").is_similar(threshold=0.5)
          True
          >>> StringComparator("hello", "world").is_similar(threshold=0.5)
          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:
          """
          Calculate the edit distance (Levenshtein distance) between two strings.
          """
          if len(str1) < len(str2):
              return edit_distance(str2, str1)
  
          if len(str2) == 0:
              return len(str1)
  
          previous_row = range(len(str2) + 1)
          for i, c1 in enumerate(str1):
              current_row = [i + 1]
              for j, c2 in enumerate(str2):
                  insertions = previous_row[j + 1] + 1
                  deletions = current_row[j] + 1
                  substitutions = previous_row[j] + (c1 != c2)
                  current_row.append(min(insertions, deletions, substitutions))
              previous_row = current_row
  
          return previous_row[-1]