





class        _a    :

      """simple docstring"""


      def __init__(		self:			Union[str, Any]	,    __lowerCamelCase:			Optional[Any]	,    __lowerCamelCase:			int	,    __lowerCamelCase:			List[str]					):
          '''simple docstring'''


          UpperCamelCase__:	List[str]					=     None
          UpperCamelCase__:	Dict					=     None
          UpperCamelCase__:	Tuple					=     graph

          self._normalize_graph(__lowerCamelCase	,    __lowerCamelCase					)
          UpperCamelCase__:	Dict					=     len(__lowerCamelCase					)
          UpperCamelCase__:	Optional[Any]					=     None






      def 			UpperCAmelCase_       (		self:			Any	,    __lowerCamelCase:			str	,    __lowerCamelCase:			Optional[Any]					):
          '''simple docstring'''


          if sources is int:
              UpperCamelCase__:	List[str]					=     [sources]
          if sinks is int:
              UpperCamelCase__:	Any					=     [sinks]

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

          UpperCamelCase__:	Tuple					=     sources[0]
          UpperCamelCase__:	Optional[Any]					=     sinks[0]

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

              UpperCamelCase__:	Union[str, Any]					=     len(self.graph					) + 1
              for room in self.graph:
                  room.insert(0	,    0					)
              self.graph.insert(0	,    [0] * size					)
              for i in sources:
                  UpperCamelCase__:	Optional[int]					=     max_input_flow
              UpperCamelCase__:	List[str]					=     0

              UpperCamelCase__:	List[Any]					=     len(self.graph					) + 1
              for room in self.graph:
                  room.append(0					)
              self.graph.append([0] * size					)
              for i in sinks:
                  UpperCamelCase__:	Optional[Any]					=     max_input_flow
              UpperCamelCase__:	Tuple					=     size - 1






      def 			UpperCAmelCase_       (		self:			Union[str, Any]					):
          '''simple docstring'''


          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:			List[Any]	,    __lowerCamelCase:			List[Any]					):
          '''simple docstring'''


          UpperCamelCase__:	Optional[int]					=     algorithm(self					)




class        _a    :

      """simple docstring"""


      def __init__(		self:			Dict	,    __lowerCamelCase:			Any					):
          '''simple docstring'''


          UpperCamelCase__:	Tuple					=     flow_network
          UpperCamelCase__:	Optional[Any]					=     flow_network.verticesCount
          UpperCamelCase__:	Tuple					=     flow_network.sourceIndex
          UpperCamelCase__:	Union[str, Any]					=     flow_network.sinkIndex
          # it's just a reference, so you shouldn't change
          # it in your algorithms, use deep copy before doing that
          UpperCamelCase__:	Optional[Any]					=     flow_network.graph
          UpperCamelCase__:	Optional[Any]					=     False






      def 			UpperCAmelCase_       (		self:			str					):
          '''simple docstring'''


          if not self.executed:
              self._algorithm()
              UpperCamelCase__:	Optional[int]					=     True






      def 			UpperCAmelCase_       (		self:			Union[str, Any]					):
          '''simple docstring'''


          pass




class        _a    (    UpperCamelCase__):

      """simple docstring"""


      def __init__(		self:			Union[str, Any]	,    __lowerCamelCase:			str					):
          '''simple docstring'''


          super().__init__(__lowerCamelCase					)
          # use this to save your result
          UpperCamelCase__:	List[Any]					=     -1






      def 			UpperCAmelCase_       (		self:			Optional[Any]					):
          '''simple docstring'''


          if not self.executed:
              raise Exception("You should execute algorithm before using its result!"					)

          return self.maximum_flow




class        _a    (    UpperCamelCase__):

      """simple docstring"""


      def __init__(		self:			Tuple	,    __lowerCamelCase:			Union[str, Any]					):
          '''simple docstring'''


          super().__init__(__lowerCamelCase					)

          UpperCamelCase__:	Optional[Any]					=     [[0] * self.verticies_count for i in range(self.verticies_count					)]

          UpperCamelCase__:	Tuple					=     [0] * self.verticies_count
          UpperCamelCase__:	Dict					=     [0] * self.verticies_count






      def 			UpperCAmelCase_       (		self:			List[str]					):
          '''simple docstring'''


          UpperCamelCase__:	Union[str, Any]					=     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__:	Optional[int]					=     [
              i
              for i in range(self.verticies_count					)
              if i != self.source_index and i != self.sink_index
          ]

          # move through list
          UpperCamelCase__:	Tuple					=     0
          while i < len(__lowerCamelCase					):
              UpperCamelCase__:	int					=     vertices_list[i]
              UpperCamelCase__:	Tuple					=     self.heights[vertex_index]
              self.process_vertex(__lowerCamelCase					)
              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(__lowerCamelCase					)					)
                  UpperCamelCase__:	int					=     0
              else:
                  i += 1

          UpperCamelCase__:	List[str]					=     sum(self.preflow[self.source_index]					)






      def 			UpperCAmelCase_       (		self:			List[Any]	,    __lowerCamelCase:			Optional[int]					):
          '''simple docstring'''


          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(__lowerCamelCase	,    __lowerCamelCase					)

              self.relabel(__lowerCamelCase					)






      def 			UpperCAmelCase_       (		self:			Union[str, Any]	,    __lowerCamelCase:			str	,    __lowerCamelCase:			Optional[Any]					):
          '''simple docstring'''


          UpperCamelCase__:	Optional[int]					=     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:			Union[str, Any]	,    __lowerCamelCase:			Optional[Any]					):
          '''simple docstring'''


          UpperCamelCase__:	List[Any]					=     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__:	Any					=     self.heights[to_index]

          if min_height is not None:
              UpperCamelCase__:	List[Any]					=     min_height + 1


if __name__ == "__main__":
   A__:    Optional[Any]  	=	[0]
   A__:    List[str]  	=	[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__:    Dict  	=	[[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

   # prepare our network
   A__:    Union[str, Any]  	=	FlowNetwork(graph, entrances, exits)
   # set algorithm
   flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
   # and calculate
   A__:    Optional[int]  	=	flow_network.find_maximum_flow()

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








import unittest

from knapsack import knapsack as k




class        _a    (    unittest.TestCase):

      """simple docstring"""


      def 			UpperCAmelCase_       (		self:			Union[str, Any]					):
          '''simple docstring'''


          UpperCamelCase__:	Tuple					=     0
          UpperCamelCase__:	Optional[int]					=     [0]
          UpperCamelCase__:	Dict					=     [0]
          UpperCamelCase__:	str					=     len(__lowerCamelCase					)
          self.assertEqual(k.knapsack(__lowerCamelCase	,    __lowerCamelCase	,    __lowerCamelCase	,    __lowerCamelCase					)	,    0					)

          UpperCamelCase__:	Tuple					=     [60]
          UpperCamelCase__:	List[Any]					=     [10]
          UpperCamelCase__:	Any					=     len(__lowerCamelCase					)
          self.assertEqual(k.knapsack(__lowerCamelCase	,    __lowerCamelCase	,    __lowerCamelCase	,    __lowerCamelCase					)	,    0					)






      def 			UpperCAmelCase_       (		self:			Any					):
          '''simple docstring'''


          UpperCamelCase__:	List[str]					=     3
          UpperCamelCase__:	Any					=     [1, 2, 3]
          UpperCamelCase__:	Dict					=     [3, 2, 1]
          UpperCamelCase__:	List[str]					=     len(__lowerCamelCase					)
          self.assertEqual(k.knapsack(__lowerCamelCase	,    __lowerCamelCase	,    __lowerCamelCase	,    __lowerCamelCase					)	,    5					)






      def 			UpperCAmelCase_       (		self:			List[Any]					):
          '''simple docstring'''


          UpperCamelCase__:	List[str]					=     50
          UpperCamelCase__:	Optional[Any]					=     [60, 100, 120]
          UpperCamelCase__:	Optional[Any]					=     [10, 20, 30]
          UpperCamelCase__:	Any					=     len(__lowerCamelCase					)
          self.assertEqual(k.knapsack(__lowerCamelCase	,    __lowerCamelCase	,    __lowerCamelCase	,    __lowerCamelCase					)	,    220					)


if __name__ == "__main__":
   unittest.main()

