




class  _lowerCamelCase						:

      """simple docstring"""

      def __init__(     self					: int ,       snake_case					: Any ,       snake_case					: Any ,       snake_case					: Optional[Any]				):
          __UpperCamelCase  		=						None
          __UpperCamelCase  		=						None
          __UpperCamelCase  		=						graph

          self._normalize_graph(snake_case ,       snake_case				)
          __UpperCamelCase  		=						len(snake_case				)
          __UpperCamelCase  		=						None







      def       snake_case	(     self					: str ,       snake_case					: Optional[int] ,       snake_case					: int				):
          if sources is int:
              __UpperCamelCase  		=						[sources]
          if sinks is int:
              __UpperCamelCase  		=						[sinks]

          if len(snake_case				) == 0 or len(snake_case				) == 0:
              return

          __UpperCamelCase  		=						sources[0]
          __UpperCamelCase  		=						sinks[0]

          # make fake vertex if there are more
          # than one source or sink
          if len(snake_case				) > 1 or len(snake_case				) > 1:
              __UpperCamelCase  		=						0
              for i in sources:
                  max_input_flow += sum(self.graph[i]				)

              __UpperCamelCase  		=						len(self.graph				) + 1
              for room in self.graph:
                  room.insert(0 ,       0				)
              self.graph.insert(0 ,       [0] * size				)
              for i in sources:
                  __UpperCamelCase  		=						max_input_flow
              __UpperCamelCase  		=						0

              __UpperCamelCase  		=						len(self.graph				) + 1
              for room in self.graph:
                  room.append(0				)
              self.graph.append([0] * size				)
              for i in sinks:
                  __UpperCamelCase  		=						max_input_flow
              __UpperCamelCase  		=						size - 1







      def       snake_case	(     self					: Dict				):
          if self.maximum_flow_algorithm is None:
              raise Exception('''You need to set maximum flow algorithm before.'''				)
          if self.source_index is None or self.sink_index is None:
              return 0

          self.maximum_flow_algorithm.execute()
          return self.maximum_flow_algorithm.getMaximumFlow()







      def       snake_case	(     self					: List[Any] ,       snake_case					: List[str]				):
          __UpperCamelCase  		=						algorithm(self				)







class  _lowerCamelCase						:

      """simple docstring"""

      def __init__(     self					: str ,       snake_case					: Any				):
          __UpperCamelCase  		=						flow_network
          __UpperCamelCase  		=						flow_network.verticesCount
          __UpperCamelCase  		=						flow_network.sourceIndex
          __UpperCamelCase  		=						flow_network.sinkIndex
          # it's just a reference, so you shouldn't change
          # it in your algorithms, use deep copy before doing that
          __UpperCamelCase  		=						flow_network.graph
          __UpperCamelCase  		=						False







      def       snake_case	(     self					: List[str]				):
          if not self.executed:
              self._algorithm()
              __UpperCamelCase  		=						True







      def       snake_case	(     self					: Optional[int]				):
          pass







class  _lowerCamelCase						(			_SCREAMING_SNAKE_CASE   ):

      """simple docstring"""

      def __init__(     self					: Tuple ,       snake_case					: Optional[int]				):
          super().__init__(snake_case				)
          # use this to save your result
          __UpperCamelCase  		=						-1







      def       snake_case	(     self					: Tuple				):
          if not self.executed:
              raise Exception('''You should execute algorithm before using its result!'''				)

          return self.maximum_flow







class  _lowerCamelCase						(			_SCREAMING_SNAKE_CASE   ):

      """simple docstring"""

      def __init__(     self					: Optional[int] ,       snake_case					: Tuple				):
          super().__init__(snake_case				)

          __UpperCamelCase  		=						[[0] * self.verticies_count for i in range(self.verticies_count				)]

          __UpperCamelCase  		=						[0] * self.verticies_count
          __UpperCamelCase  		=						[0] * self.verticies_count







      def       snake_case	(     self					: Union[str, Any]				):
          __UpperCamelCase  		=						self.verticies_count

          # push some substance to graph
          for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]				):
              self.preflow[self.source_index][nextvertex_index] += bandwidth
              self.preflow[nextvertex_index][self.source_index] -= bandwidth
              self.excesses[nextvertex_index] += bandwidth

          # Relabel-to-front selection rule
          __UpperCamelCase  		=						[
              i
              for i in range(self.verticies_count				)
              if i != self.source_index and i != self.sink_index
          ]

          # move through list
          __UpperCamelCase  		=						0
          while i < len(snake_case				):
              __UpperCamelCase  		=						vertices_list[i]
              __UpperCamelCase  		=						self.heights[vertex_index]
              self.process_vertex(snake_case				)
              if self.heights[vertex_index] > previous_height:
                  # if it was relabeled, swap elements
                  # and start from 0 index
                  vertices_list.insert(0 ,       vertices_list.pop(snake_case				)				)
                  __UpperCamelCase  		=						0
              else:
                  i += 1

          __UpperCamelCase  		=						sum(self.preflow[self.source_index]				)







      def       snake_case	(     self					: Union[str, Any] ,       snake_case					: Any				):
          while self.excesses[vertex_index] > 0:
              for neighbour_index in range(self.verticies_count				):
                  # if it's neighbour and current vertex is higher
                  if (
                      self.graph[vertex_index][neighbour_index]
                      - self.preflow[vertex_index][neighbour_index]
                      > 0
                      and self.heights[vertex_index] > self.heights[neighbour_index]
                  ):
                      self.push(snake_case ,       snake_case				)

              self.relabel(snake_case				)







      def       snake_case	(     self					: Union[str, Any] ,       snake_case					: List[str] ,       snake_case					: int				):
          __UpperCamelCase  		=						min(
              self.excesses[from_index] ,       self.graph[from_index][to_index] - self.preflow[from_index][to_index] ,       )
          self.preflow[from_index][to_index] += preflow_delta
          self.preflow[to_index][from_index] -= preflow_delta
          self.excesses[from_index] -= preflow_delta
          self.excesses[to_index] += preflow_delta







      def       snake_case	(     self					: Optional[Any] ,       snake_case					: Dict				):
          __UpperCamelCase  		=						None
          for to_index in range(self.verticies_count				):
              if (
                  self.graph[vertex_index][to_index]
                  - self.preflow[vertex_index][to_index]
                  > 0
              ) and (min_height is None or self.heights[to_index] < min_height):
                  __UpperCamelCase  		=						self.heights[to_index]

          if min_height is not None:
              __UpperCamelCase  		=						min_height + 1


if __name__ == "__main__":
 a_   		=     [0]
 a_   		=     [3]
 # graph = [
 #     [0, 0, 4, 6, 0, 0],
 #     [0, 0, 5, 2, 0, 0],
 #     [0, 0, 0, 0, 4, 4],
 #     [0, 0, 0, 0, 6, 6],
 #     [0, 0, 0, 0, 0, 0],
 #     [0, 0, 0, 0, 0, 0],
 # ]
 a_   		=     [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

 # prepare our network
 a_   		=     FlowNetwork(graph, entrances, exits)
 # set algorithm
 flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
 # and calculate
 a_   		=     flow_network.find_maximum_flow()

 print(f"""maximum flow is {maximum_flow}""")












from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


a_   		=     {
    "configuration_longformer": [
        "LONGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "LongformerConfig",
        "LongformerOnnxConfig",
    ],
    "tokenization_longformer": ["LongformerTokenizer"],
}

try:
 if not is_tokenizers_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 a_   		=     ["LongformerTokenizerFast"]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 a_   		=     [
     "LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
     "LongformerForMaskedLM",
     "LongformerForMultipleChoice",
     "LongformerForQuestionAnswering",
     "LongformerForSequenceClassification",
     "LongformerForTokenClassification",
     "LongformerModel",
     "LongformerPreTrainedModel",
     "LongformerSelfAttention",
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 a_   		=     [
     "TF_LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
     "TFLongformerForMaskedLM",
     "TFLongformerForMultipleChoice",
     "TFLongformerForQuestionAnswering",
     "TFLongformerForSequenceClassification",
     "TFLongformerForTokenClassification",
     "TFLongformerModel",
     "TFLongformerPreTrainedModel",
     "TFLongformerSelfAttention",
 ]


if TYPE_CHECKING:
 from .configuration_longformer import (
     LONGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
     LongformerConfig,
     LongformerOnnxConfig,
 )
 from .tokenization_longformer import LongformerTokenizer

 try:
  if not is_tokenizers_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_longformer_fast import LongformerTokenizerFast

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_longformer import (
      LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
      LongformerForMaskedLM,
      LongformerForMultipleChoice,
      LongformerForQuestionAnswering,
      LongformerForSequenceClassification,
      LongformerForTokenClassification,
      LongformerModel,
      LongformerPreTrainedModel,
      LongformerSelfAttention,
  )

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_longformer import (
      TF_LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
      TFLongformerForMaskedLM,
      TFLongformerForMultipleChoice,
      TFLongformerForQuestionAnswering,
      TFLongformerForSequenceClassification,
      TFLongformerForTokenClassification,
      TFLongformerModel,
      TFLongformerPreTrainedModel,
      TFLongformerSelfAttention,
  )

else:
 import sys

 a_   		=     _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)






