




'''simple docstring'''







def        lowerCamelCase__				(      __lowercase				):
     snake_case			:      int        =			0
     snake_case			:      Optional[Any]        =			len(lowerCamelCase_				)

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

     return num_inversions



def        lowerCamelCase__				(      __lowercase				):


     if len(lowerCamelCase_				) <= 1:
          return arr, 0
     snake_case			:      str        =			len(lowerCamelCase_				) // 2
     snake_case			:      Optional[Any]        =			arr[0:mid]
     snake_case			:      Any        =			arr[mid:]

     snake_case			:      Optional[int]        =			count_inversions_recursive(lowerCamelCase_				)
     snake_case			:      Dict        =			count_inversions_recursive(lowerCamelCase_				)
     snake_case			:      Optional[Any]        =			_count_cross_inversions(lowerCamelCase_     ,   lowerCamelCase_				)

     snake_case			:      Optional[int]        =			inversion_p + inversions_q + cross_inversions
     return c, num_inversions



def        lowerCamelCase__				(      __lowercase     ,   __lowercase				):
     snake_case			:      Dict        =			[]
     snake_case			:      List[str]        =			0
     while i < len(lowerCamelCase_				) and j < len(lowerCamelCase_				):
          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(lowerCamelCase_				) - i
               r.append(q[j]				)
               j += 1
          else:
               r.append(p[i]				)
               i += 1

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

     return r, num_inversion



def        lowerCamelCase__				(      ):
     snake_case			:      str        =			[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)

     snake_case			:      List[Any]        =			count_inversions_bf(lowerCamelCase_				)
     snake_case			:      Optional[Any]        =			count_inversions_recursive(lowerCamelCase_				)

     assert num_inversions_bf == num_inversions_recursive == 8

     print("""number of inversions = """     ,   lowerCamelCase_				)

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

     arr_a.sort()
     snake_case			:      Any        =			count_inversions_bf(lowerCamelCase_				)
     snake_case			:      Tuple        =			count_inversions_recursive(lowerCamelCase_				)

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

     # an empty list should also have zero inversions
     snake_case			:      Dict        =			[]
     snake_case			:      Any        =			count_inversions_bf(lowerCamelCase_				)
     snake_case			:      Optional[int]        =			count_inversions_recursive(lowerCamelCase_				)

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


if __name__ == "__main__":
      main()





'''simple docstring'''

import os


# All paths are set with the intent you should run this script from the root of the repo with the command
# python utils/check_doctest_list.py
snake_case									=    """."""


if __name__ == "__main__":
     snake_case									=    os.path.join(REPO_PATH, """utils/documentation_tests.txt""")
     snake_case									=    []
     snake_case									=    []
     with open(doctest_file_path) as fp:
          for line in fp:
               snake_case									=    line.strip()
               snake_case									=    os.path.join(REPO_PATH, line)
               if not (os.path.isfile(path) or os.path.isdir(path)):
                    non_existent_paths.append(line)
               all_paths.append(path)
     if len(non_existent_paths) > 0:
          snake_case									=    """\n""".join(non_existent_paths)
          raise ValueError(f'`utils/documentation_tests.txt` contains non-existent paths:\n{non_existent_paths}')
     if all_paths != sorted(all_paths):
          raise ValueError("""Files in `utils/documentation_tests.txt` are not in alphabetical order.""")





