code: def idf(posting, document_count):
      
      documents_with_term = 0
      for field_name in posting:
          if field_name == "_index":
              continue
          documents_with_term += len(posting[field_name].keys())
  
      x = (document_count - documents_with_term + 0.5) / (documents_with_term + 0.5)
      return math.log(1 + abs(x))
docs: A function to calculate the inverse document frequency for a posting.
      This is shared between the builder and the index.