




'''simple docstring'''





def      UpperCamelCase_(	snake_case							:       Dict     ):

							'''simple docstring'''






							snake_case_						=      0
							snake_case_						=      len(snake_case     )

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

							return num_inversions


def      UpperCamelCase_(	snake_case							:       List[Any]     ):

							'''simple docstring'''






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

							snake_case_					,      snake_case_						=      count_inversions_recursive(snake_case     )
							snake_case_					,      snake_case_						=      count_inversions_recursive(snake_case     )
							snake_case_					,      snake_case_						=      _count_cross_inversions(snake_case							,				snake_case     )

							snake_case_						=      inversion_p + inversions_q + cross_inversions
							return c, num_inversions


def      UpperCamelCase_(	snake_case							:       Optional[Any]							,				snake_case							:       int     ):

							'''simple docstring'''






							snake_case_						=      []
							snake_case_						=      snake_case_						=      snake_case_						=      0
							while i < len(snake_case     ) and j < len(snake_case     ):
														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(snake_case     ) - i
																					r.append(q[j]     )
																					j += 1
														else:
																					r.append(p[i]     )
																					i += 1

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

							return r, num_inversion


def      UpperCamelCase_(	):

							'''simple docstring'''






							snake_case_						=      [1_0, 2, 1, 5, 5, 2, 1_1]

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

							snake_case_						=      count_inversions_bf(snake_case     )
							snake_case_					,      snake_case_						=      count_inversions_recursive(snake_case     )

							assert num_inversions_bf == num_inversions_recursive == 8

							print("number of inversions = "							,				snake_case     )

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

							arr_a.sort()
							snake_case_						=      count_inversions_bf(snake_case     )
							snake_case_					,      snake_case_						=      count_inversions_recursive(snake_case     )

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

							# an empty list should also have zero inversions
							snake_case_						=      []
							snake_case_						=      count_inversions_bf(snake_case     )
							snake_case_					,      snake_case_						=      count_inversions_recursive(snake_case     )

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


if __name__ == "__main__":
		main()








'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


lowerCamelCase							:   str  						=	{
    'configuration_rag': ['RagConfig'],
    'retrieval_rag': ['RagRetriever'],
    'tokenization_rag': ['RagTokenizer'],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCamelCase							:   Dict  						=	[
     'RagModel',
     'RagPreTrainedModel',
     'RagSequenceForGeneration',
     'RagTokenForGeneration',
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCamelCase							:   Optional[int]  						=	[
     'TFRagModel',
     'TFRagPreTrainedModel',
     'TFRagSequenceForGeneration',
     'TFRagTokenForGeneration',
 ]


if TYPE_CHECKING:
 from .configuration_rag import RagConfig
 from .retrieval_rag import RagRetriever
 from .tokenization_rag import RagTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_rag import RagModel, RagPreTrainedModel, RagSequenceForGeneration, RagTokenForGeneration

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_rag import (
      TFRagModel,
      TFRagPreTrainedModel,
      TFRagSequenceForGeneration,
      TFRagTokenForGeneration,
  )

else:
 import sys

 lowerCamelCase							:   Tuple  						=	_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




