input: class StringComparator:
      def __init__(self, string1: str, string2: str):
          self.string1 = string1
          self.string2 = string2
  
      def is_equal(self) -> bool:
          return self.string1 == self.string2
  
      def is_different(self) -> bool:
          return self.string1 != self.string2
  
      def is_similar(self, threshold: float = 0.5) -> bool:
          distance = edit_distance(self.string1, self.string2)
          max_length = max(len(self.string1), len(self.string2))
  
          return distance / max_length < threshold
  
      """
      Calculate the edit distance between two strings and determine if they are similar 
      based on a provided threshold.
  
      >>> comparator = StringComparator('apple', 'aple')
      >>> comparator.is_equal()
      False
      >>> comparator.is_different()
      True
      >>> comparator.is_similar(threshold=0.3)
      False
      >>> comparator.is_similar(threshold=0.5)
      True
      """
output:     
  def edit_distance(s1: str, s2: str) -> int:
      if len(s1) < len(s2):
          return edit_distance(s2, s1)
  
      if len(s2) == 0:
          return len(s1)
  
      previous_row = range(len(s2) + 1)
      for i, c1 in enumerate(s1):
          current_row = [i + 1]
          for j, c2 in enumerate(s2):
              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]
  