


"""simple docstring"""







def 					lowercase      (    A_	)->				int:
  '''simple docstring'''







  a						:		List[str]											=      0
  a						:		Union[str, Any]											=      len(A_	)

  for i in range(n - 1	):
    for j in range(i + 1  ,       A_	):
      if arr[i] > arr[j]:
        num_inversions += 1

  return num_inversions


def 					lowercase      (    A_	)->				Union[str, Any]:
  '''simple docstring'''







  if len(A_	) <= 1:
    return arr, 0
  a						:		Any											=      len(A_	) // 2
  a						:		str											=      arr[0:mid]
  a						:		int											=      arr[mid:]

  a							,		a						:		Union[str, Any]											=      count_inversions_recursive(A_	)
  a							,		a						:		str											=      count_inversions_recursive(A_	)
  a							,		a						:		Optional[Any]											=      _count_cross_inversions(A_  ,       A_	)

  a						:		Dict											=      inversion_p + inversions_q + cross_inversions
  return c, num_inversions


def 					lowercase      (    A_  ,       A_	)->				Any:
  '''simple docstring'''







  a						:		Optional[int]											=      []
  a						:		Optional[int]											=      0
  while i < len(A_	) and j < len(A_	):
    if p[i] > q[j]:
      # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
      # These are all inversions. The claim emerges from the
      # property that P is sorted.
      num_inversion += len(A_	) - i
      r.append(q[j]	)
      j += 1
    else:
      r.append(p[i]	)
      i += 1

  if i < len(A_	):
    r.extend(p[i:]	)
  else:
    r.extend(q[j:]	)

  return r, num_inversion


def 					lowercase      (    )->				List[Any]:
  '''simple docstring'''







  a						:		List[Any]											=      [10, 2, 1, 5, 5, 2, 11]

  # this arr has 8 inversions:
  # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

  a						:		str											=      count_inversions_bf(A_	)
  a							,		a						:		Dict											=      count_inversions_recursive(A_	)

  assert num_inversions_bf == num_inversions_recursive == 8

  print("number of inversions = "  ,       A_	)

  # testing an array with zero inversion (a sorted arr_1)

  arr_a.sort()
  a						:		Union[str, Any]											=      count_inversions_bf(A_	)
  a							,		a						:		Optional[int]											=      count_inversions_recursive(A_	)

  assert num_inversions_bf == num_inversions_recursive == 0
  print("number of inversions = "  ,       A_	)

  # an empty list should also have zero inversions
  a						:		str											=      []
  a						:		Optional[Any]											=      count_inversions_bf(A_	)
  a							,		a						:		Optional[int]											=      count_inversions_recursive(A_	)

  assert num_inversions_bf == num_inversions_recursive == 0
  print("number of inversions = "  ,       A_	)


if __name__ == "__main__":
 main()










"""simple docstring"""







def 					lowercase      (    A_  ,       A_	)->				float:
  '''simple docstring'''







  def get_matched_characters(A_  ,       A_	) -> str:
    a						:		Optional[int]											=      []
    a						:		List[Any]											=      min(len(_stra	)  ,       len(_stra	)	) // 2
    for i, l in enumerate(_stra	):
      a						:		int											=      int(max(0  ,       i - limit	)	)
      a						:		Optional[int]											=      int(min(i + limit + 1  ,       len(_stra	)	)	)
      if l in _stra[left:right]:
        matched.append(A_	)
        a						:		int											=      F'''{_stra[0:_stra.index(A_	)]} {_stra[_stra.index(A_	) + 1:]}'''

    return "".join(A_	)

  # matching characters
  a						:		Tuple											=      get_matched_characters(A_  ,       A_	)
  a						:		str											=      get_matched_characters(A_  ,       A_	)
  a						:		List[str]											=      len(A_	)

  # transposition
  a						:		Union[str, Any]											=      (
      len([(ca, ca) for ca, ca in zip(A_  ,       A_	) if ca != ca]	) // 2
  )

  if not match_count:
    a						:		Tuple											=      0.0
  else:
    a						:		List[str]											=      (
        1
        / 3
        * (
            match_count / len(A_	)
            + match_count / len(A_	)
            + (match_count - transpositions) / match_count
        )
    )

  # common prefix up to 4 characters
  a						:		Union[str, Any]											=      0
  for ca, ca in zip(stra[:4]  ,       stra[:4]	):
    if ca == ca:
      prefix_len += 1
    else:
      break

  return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(jaro_winkler("""hello""", """world"""))






