input: 
  class StringComparator:
      """A class that receives two strings and has methods for comparing them.
      The methods include checking if the strings are equal, different, or
      similar up to a provided threshold using edit distance.
      
      >>> comparator = StringComparator("hello", "hella")
      >>> comparator.is_equal()
      False
      >>> comparator.is_different()
      True
      >>> comparator.is_similar(0.2)
      False
      >>> comparator.is_similar(0.4)
      True
      """
  
      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
  
output:     def edit_distance(str1, str2):
          m, n = len(str1), len(str2)
          dp = [[0] * (n + 1) for _ in range(m + 1)]
          
          for i in range(m + 1):
              for j in range(n + 1):
                  if i == 0:
                      dp[i][j] = j
                  elif j == 0:
                      dp[i][j] = i
                  elif str1[i - 1] == str2[j - 1]:
                      dp[i][j] = dp[i - 1][j - 1]
                  else:
                      dp[i][j] = 1 + min(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1])
          
          return dp[m][n]