


"""simple docstring"""







def    UpperCAmelCase__       (lowerCAmelCase_   ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				0
					__SCREAMING_SNAKE_CASE						   =				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    UpperCAmelCase__       (lowerCAmelCase_   ):




					'''simple docstring'''


					if len(lowerCAmelCase_   ) <= 1:
										return arr, 0
					__SCREAMING_SNAKE_CASE						   =				len(lowerCAmelCase_   ) // 2
					__SCREAMING_SNAKE_CASE						   =				arr[0:mid]
					__SCREAMING_SNAKE_CASE						   =				arr[mid:]

					__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				count_inversions_recursive(lowerCAmelCase_   )
					__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				count_inversions_recursive(lowerCAmelCase_   )
					__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				_count_cross_inversions(lowerCAmelCase_  ,						lowerCAmelCase_   )

					__SCREAMING_SNAKE_CASE						   =				inversion_p + inversions_q + cross_inversions
					return c, num_inversions




def    UpperCAmelCase__       (lowerCAmelCase_  ,						lowerCAmelCase_   ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				[]
					__SCREAMING_SNAKE_CASE						   =				__SCREAMING_SNAKE_CASE						   =				__SCREAMING_SNAKE_CASE						   =				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    UpperCAmelCase__       ():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				[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)

					__SCREAMING_SNAKE_CASE						   =				count_inversions_bf(lowerCAmelCase_   )
					__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				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()
					__SCREAMING_SNAKE_CASE						   =				count_inversions_bf(lowerCAmelCase_   )
					__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				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
					__SCREAMING_SNAKE_CASE						   =				[]
					__SCREAMING_SNAKE_CASE						   =				count_inversions_bf(lowerCAmelCase_   )
					__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				count_inversions_recursive(lowerCAmelCase_   )

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


if __name__ == "__main__":
		main()




"""simple docstring"""







import pytest

from datasets.utils.sharding import _distribute_shards, _number_of_shards_in_gen_kwargs, _split_gen_kwargs




@pytest.mark.parametrize(
    "kwargs, expected"  ,						[
        ({"num_shards": 0, "max_num_jobs": 1}, []),
        ({"num_shards": 10, "max_num_jobs": 1}, [range(10   )]),
        ({"num_shards": 10, "max_num_jobs": 10}, [range(lowerCAmelCase_  ,						i + 1   ) for i in range(10   )]),
        ({"num_shards": 1, "max_num_jobs": 10}, [range(1   )]),
        ({"num_shards": 10, "max_num_jobs": 3}, [range(0  ,						4   ), range(4  ,						7   ), range(7  ,						10   )]),
        ({"num_shards": 3, "max_num_jobs": 10}, [range(0  ,						1   ), range(1  ,						2   ), range(2  ,						3   )]),
    ]  ,						)
def    UpperCAmelCase__       (lowerCAmelCase_  ,						lowerCAmelCase_   ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				_distribute_shards(**lowerCAmelCase_   )
					assert out == expected




@pytest.mark.parametrize(
    "gen_kwargs, max_num_jobs, expected"  ,						[
        ({"foo": 0}, 10, [{"foo": 0}]),
        ({"shards": [0, 1, 2, 3]}, 1, [{"shards": [0, 1, 2, 3]}]),
        ({"shards": [0, 1, 2, 3]}, 4, [{"shards": [0]}, {"shards": [1]}, {"shards": [2]}, {"shards": [3]}]),
        ({"shards": [0, 1]}, 4, [{"shards": [0]}, {"shards": [1]}]),
        ({"shards": [0, 1, 2, 3]}, 2, [{"shards": [0, 1]}, {"shards": [2, 3]}]),
    ]  ,						)
def    UpperCAmelCase__       (lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_   ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				_split_gen_kwargs(lowerCAmelCase_  ,						lowerCAmelCase_   )
					assert out == expected




@pytest.mark.parametrize(
    "gen_kwargs, expected"  ,						[
        ({"foo": 0}, 1),
        ({"shards": [0]}, 1),
        ({"shards": [0, 1, 2, 3]}, 4),
        ({"shards": [0, 1, 2, 3], "foo": 0}, 4),
        ({"shards": [0, 1, 2, 3], "other": (0, 1)}, 4),
        ({"shards": [0, 1, 2, 3], "shards2": [0, 1]}, RuntimeError),
    ]  ,						)
def    UpperCAmelCase__       (lowerCAmelCase_  ,						lowerCAmelCase_   ):




					'''simple docstring'''


					if expected is RuntimeError:
										with pytest.raises(lowerCAmelCase_   ):
															_number_of_shards_in_gen_kwargs(lowerCAmelCase_   )
					else:
										__SCREAMING_SNAKE_CASE						   =				_number_of_shards_in_gen_kwargs(lowerCAmelCase_   )
										assert out == expected
