


'''simple docstring'''






class   __snake_case			:







    """simple docstring"""



    def __init__(  self       :    str       ,		lowerCamelCase       :    Optional[int]       ,		lowerCamelCase       :    Optional[Any]       ,		lowerCamelCase       :    Any						)  ->    List[Any]:
      lowerCAmelCase_     : List[Any]     =  None
      lowerCAmelCase_     : Optional[int]     =  None
      lowerCAmelCase_     : List[Any]     =  graph

      self._normalize_graph(lowerCamelCase       ,		lowerCamelCase						)
      lowerCAmelCase_     : int     =  len(lowerCamelCase						)
      lowerCAmelCase_     : Any     =  None

    def __lowercase  (  self       :    List[str]       ,		lowerCamelCase       :    Dict       ,		lowerCamelCase       :    int						)  ->    Union[str, Any]:
      if sources is int:
        lowerCAmelCase_     : Optional[int]     =  [sources]
      if sinks is int:
        lowerCAmelCase_     : List[Any]     =  [sinks]

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

      lowerCAmelCase_     : Optional[int]     =  sources[0]
      lowerCAmelCase_     : int     =  sinks[0]

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

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

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

    def __lowercase  (  self       :    Union[str, Any]						)  ->    int:
      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 __lowercase  (  self       :    Any       ,		lowerCamelCase       :    List[str]						)  ->    Union[str, Any]:
      lowerCAmelCase_     : List[str]     =  algorithm(self						)







class   __snake_case			:







    """simple docstring"""



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

    def __lowercase  (  self       :    List[str]						)  ->    Optional[int]:
      if not self.executed:
        self._algorithm()
        lowerCAmelCase_     : Optional[Any]     =  True





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







class   __snake_case			(  _SCREAMING_SNAKE_CASE):







    """simple docstring"""



    def __init__(  self       :    Optional[int]       ,		lowerCamelCase       :    List[str]						)  ->    Tuple:
      super().__init__(lowerCamelCase						)
      # use this to save your result
      lowerCAmelCase_     : int     =  -1





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

      return self.maximum_flow







class   __snake_case			(  _SCREAMING_SNAKE_CASE):







    """simple docstring"""



    def __init__(  self       :    List[str]       ,		lowerCamelCase       :    Union[str, Any]						)  ->    Dict:
      super().__init__(lowerCamelCase						)

      lowerCAmelCase_     : Union[str, Any]     =  [[0] * self.verticies_count for i in range(self.verticies_count						)]

      lowerCAmelCase_     : Dict     =  [0] * self.verticies_count
      lowerCAmelCase_     : int     =  [0] * self.verticies_count

    def __lowercase  (  self       :    str						)  ->    str:
      lowerCAmelCase_     : Tuple     =  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
      lowerCAmelCase_     : Dict     =  [
          i
          for i in range(self.verticies_count						)
          if i != self.source_index and i != self.sink_index
      ]

      # move through list
      lowerCAmelCase_     : int     =  0
      while i < len(lowerCamelCase						):
        lowerCAmelCase_     : Dict     =  vertices_list[i]
        lowerCAmelCase_     : Union[str, Any]     =  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						)						)
          lowerCAmelCase_     : Dict     =  0
        else:
          i += 1

      lowerCAmelCase_     : List[Any]     =  sum(self.preflow[self.source_index]						)

    def __lowercase  (  self       :    Optional[Any]       ,		lowerCamelCase       :    int						)  ->    List[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(lowerCamelCase       ,		lowerCamelCase						)

        self.relabel(lowerCamelCase						)

    def __lowercase  (  self       :    str       ,		lowerCamelCase       :    str       ,		lowerCamelCase       :    Dict						)  ->    Optional[int]:
      lowerCAmelCase_     : Dict     =  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 __lowercase  (  self       :    Dict       ,		lowerCamelCase       :    List[Any]						)  ->    Any:
      lowerCAmelCase_     : List[str]     =  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):
          lowerCAmelCase_     : List[str]     =  self.heights[to_index]

      if min_height is not None:
        lowerCAmelCase_     : Optional[Any]     =  min_height + 1


if __name__ == "__main__":
  __A   :    Any											= [0]
  __A   :    int											= [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   :    List[str]											= [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

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

  print(F'''maximum flow is {maximum_flow}''')







'''simple docstring'''






def 							UpperCamelCase_     (       A__   :  list[list[int | float]]   ):
  '''simple docstring'''





  lowerCAmelCase_     : List[str]     =  len(A__   )
  lowerCAmelCase_     : Union[str, Any]     =  len(matrix[0]   )
  lowerCAmelCase_     : Optional[int]     =  min(A__				,       A__   )

  for row in range(A__   ):
    # Check if diagonal element is not zero
    if matrix[row][row] != 0:
      # Eliminate all the elements below the diagonal
      for col in range(row + 1				,       A__   ):
        lowerCAmelCase_     : int     =  matrix[col][row] / matrix[row][row]
        for i in range(A__				,       A__   ):
          matrix[col][i] -= multiplier * matrix[row][i]
    else:
      # Find a non-zero diagonal element to swap rows
      lowerCAmelCase_     : int     =  True
      for i in range(row + 1				,       A__   ):
        if matrix[i][row] != 0:
          lowerCAmelCase_,				lowerCAmelCase_     : List[Any]     =  matrix[i], matrix[row]
          lowerCAmelCase_     : Dict     =  False
          break
      if reduce:
        rank -= 1
        for i in range(A__   ):
          lowerCAmelCase_     : List[Any]     =  matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
      row -= 1

  return rank


if __name__ == "__main__":
  import doctest

  doctest.testmod()



