
class 					lowerCamelCase		:





     def __init__(self				:   Tuple    ,   _A				:   int    ,   _A				:   Union[str, Any]    ,   _A				:   Optional[int]       )						->						Dict:
         snake_case								= None
         snake_case								= None
         snake_case								= graph

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





     def 		UpperCAmelCase(self				:   Any    ,   _A				:   List[str]    ,   _A				:   Union[str, Any]       )						->						str:
         if sources is int:
             snake_case								= [sources]
         if sinks is int:
             snake_case								= [sinks]

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

         snake_case								= sources[0]
         snake_case								= sinks[0]

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

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

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





     def 		UpperCAmelCase(self				:   Optional[int]       )						->						Tuple:
         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 		UpperCAmelCase(self				:   Dict    ,   _A				:   Optional[int]       )						->						Any:
         snake_case								= algorithm(self       )







class 					lowerCamelCase		:





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





     def 		UpperCAmelCase(self				:   List[Any]       )						->						Dict:
         if not self.executed:
             self._algorithm()
             snake_case								= True





     def 		UpperCAmelCase(self				:   List[Any]       )						->						int:
         pass







class 					lowerCamelCase		(  A__  ):





     def __init__(self				:   List[Any]    ,   _A				:   Tuple       )						->						Tuple:
         super().__init__(__snake_case       )
         # use this to save your result
         snake_case								= -1





     def 		UpperCAmelCase(self				:   Any       )						->						Optional[int]:
         if not self.executed:
             raise Exception("You should execute algorithm before using its result!"       )

         return self.maximum_flow







class 					lowerCamelCase		(  A__  ):





     def __init__(self				:   Tuple    ,   _A				:   Tuple       )						->						Tuple:
         super().__init__(__snake_case       )

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

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





     def 		UpperCAmelCase(self				:   int       )						->						Union[str, Any]:
         snake_case								= 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
         snake_case								= [
             i
             for i in range(self.verticies_count       )
             if i != self.source_index and i != self.sink_index
         ]

         # move through list
         snake_case								= 0
         while i < len(__snake_case       ):
             snake_case								= vertices_list[i]
             snake_case								= 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       )       )
                 snake_case								= 0
             else:
                 i += 1

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





     def 		UpperCAmelCase(self				:   List[Any]    ,   _A				:   Optional[Any]       )						->						str:
         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 		UpperCAmelCase(self				:   List[Any]    ,   _A				:   str    ,   _A				:   Optional[Any]       )						->						List[str]:
         snake_case								= 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 		UpperCAmelCase(self				:   Optional[Any]    ,   _A				:   Optional[int]       )						->						Tuple:
         snake_case								= 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):
                 snake_case								= self.heights[to_index]

         if min_height is not None:
             snake_case								= 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 ..utils import DummyObject, requires_backends







class 					lowerCamelCase		(  metaclass=A_  ):
     UpperCAmelCase__    :							Union[str, Any]									=		["onnx"]





     def __init__(self				:   Tuple    ,   *_A				:   Optional[int]    ,   **_A				:   Any       )						->						Dict:
         requires_backends(self    ,   ["onnx"]       )





     @classmethod
     def 		UpperCAmelCase(cls				:   int    ,   *_A				:   Dict    ,   **_A				:   List[Any]       )						->						Optional[Any]:
         requires_backends(cls    ,   ["onnx"]       )





     @classmethod
     def 		UpperCAmelCase(cls				:   Dict    ,   *_A				:   Tuple    ,   **_A				:   Optional[Any]       )						->						int:
         requires_backends(cls    ,   ["onnx"]       )

