




class       __lowerCAmelCase				:






       def __init__(      self:    List[Any]				,    _lowerCAmelCase:    Any				,    _lowerCAmelCase:    List[Any]				,    _lowerCAmelCase:    Dict ):
         lowercase			:List[Any]							=  None
         lowercase			:Any							=  None
         lowercase			:Tuple							=  graph

         self._normalize_graph(_lowerCAmelCase				,    _lowerCAmelCase )
         lowercase			:Union[str, Any]							=  len(_lowerCAmelCase )
         lowercase			:Tuple							=  None






       def     SCREAMING_SNAKE_CASE			(      self:    str				,    _lowerCAmelCase:    Dict				,    _lowerCAmelCase:    Tuple ):
         if sources is int:
           lowercase			:Tuple							=  [sources]
         if sinks is int:
           lowercase			:Dict							=  [sinks]

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

         lowercase			:int							=  sources[0]
         lowercase			:List[str]							=  sinks[0]

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

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

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






       def     SCREAMING_SNAKE_CASE			(      self:    Optional[Any] ):
         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     SCREAMING_SNAKE_CASE			(      self:    str				,    _lowerCAmelCase:    Union[str, Any] ):
         lowercase			:Optional[int]							=  algorithm(self )







class       __lowerCAmelCase				:






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






       def     SCREAMING_SNAKE_CASE			(      self:    Tuple ):
         if not self.executed:
           self._algorithm()
           lowercase			:str							=  True






       def     SCREAMING_SNAKE_CASE			(      self:    int ):
         pass







class       __lowerCAmelCase				(							lowerCAmelCase):






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






       def     SCREAMING_SNAKE_CASE			(      self:    List[Any] ):
         if not self.executed:
           raise Exception("You should execute algorithm before using its result!" )

         return self.maximum_flow







class       __lowerCAmelCase				(							lowerCAmelCase):






       def __init__(      self:    Tuple				,    _lowerCAmelCase:    str ):
         super().__init__(_lowerCAmelCase )

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

         lowercase			:int							=  [0] * self.verticies_count
         lowercase			:List[Any]							=  [0] * self.verticies_count






       def     SCREAMING_SNAKE_CASE			(      self:    Optional[Any] ):
         lowercase			:Dict							=  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
         lowercase			:int							=  [
             i
             for i in range(self.verticies_count )
             if i != self.source_index and i != self.sink_index
         ]

         # move through list
         lowercase			:Tuple							=  0
         while i < len(_lowerCAmelCase ):
           lowercase			:str							=  vertices_list[i]
           lowercase			: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 ) )
             lowercase			:str							=  0
           else:
             i += 1

         lowercase			:Optional[Any]							=  sum(self.preflow[self.source_index] )






       def     SCREAMING_SNAKE_CASE			(      self:    List[Any]				,    _lowerCAmelCase:    Dict ):
         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     SCREAMING_SNAKE_CASE			(      self:    str				,    _lowerCAmelCase:    Optional[int]				,    _lowerCAmelCase:    Optional[Any] ):
         lowercase			:List[Any]							=  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     SCREAMING_SNAKE_CASE			(      self:    Tuple				,    _lowerCAmelCase:    Optional[int] ):
         lowercase			:Optional[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):
             lowercase			:Tuple							=  self.heights[to_index]

         if min_height is not None:
           lowercase			:Tuple							=  min_height + 1


if __name__ == "__main__":
     _UpperCAmelCase		:  List[str]	=   [0]
     _UpperCAmelCase		:  Union[str, Any]	=   [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],
     # ]
     _UpperCAmelCase		:  Dict	=   [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

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

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









import numpy

# List of input, output pairs
_UpperCAmelCase		:  List[str]	=   (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
_UpperCAmelCase		:  Optional[Any]	=   (((515, 22, 13), 555), ((61, 35, 49), 150))
_UpperCAmelCase		:  Tuple	=   [2, 4, 1, 5]
_UpperCAmelCase		:  Union[str, Any]	=   len(train_data)
_UpperCAmelCase		:  Dict	=   0.0_0_9



def 					UpperCAmelCase__     (   lowerCamelCase,	lowerCamelCase="train"      ):
  return calculate_hypothesis_value(lowerCamelCase,	lowerCamelCase      ) - output(
      lowerCamelCase,	lowerCamelCase      )



def 					UpperCAmelCase__     (   lowerCamelCase      ):
  lowercase			:str							=  0
  for i in range(len(lowerCamelCase      ) - 1      ):
    hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
  hyp_val += parameter_vector[0]
  return hyp_val



def 					UpperCAmelCase__     (   lowerCamelCase,	lowerCamelCase      ):
  if data_set == "train":
    return train_data[example_no][1]
  elif data_set == "test":
    return test_data[example_no][1]
  return None



def 					UpperCAmelCase__     (   lowerCamelCase,	lowerCamelCase      ):
  if data_set == "train":
    return _hypothesis_value(train_data[example_no][0]      )
  elif data_set == "test":
    return _hypothesis_value(test_data[example_no][0]      )
  return None



def 					UpperCAmelCase__     (   lowerCamelCase,	lowerCamelCase=m      ):
  lowercase			:Union[str, Any]							=  0
  for i in range(lowerCamelCase      ):
    if index == -1:
      summation_value += _error(lowerCamelCase      )
    else:
      summation_value += _error(lowerCamelCase      ) * train_data[i][0][index]
  return summation_value



def 					UpperCAmelCase__     (   lowerCamelCase      ):
  lowercase			:int							=  summation_of_cost_derivative(lowerCamelCase,	lowerCamelCase      ) / m
  return cost_derivative_value



def 					UpperCAmelCase__     (   ):
  global parameter_vector
  # Tune these values to set a tolerance value for predicted output
  lowercase			:str							=  0.000_002
  lowercase			:Tuple							=  0
  lowercase			:Optional[int]							=  0
  while True:
    j += 1
    lowercase			:Union[str, Any]							=  [0, 0, 0, 0]
    for i in range(0,	len(lowerCamelCase      )      ):
      lowercase			:Dict							=  get_cost_derivative(i - 1      )
      lowercase			:Optional[Any]							=  (
          parameter_vector[i] - LEARNING_RATE * cost_derivative
      )
    if numpy.allclose(
        lowerCamelCase,	lowerCamelCase,	atol=lowerCamelCase,	rtol=lowerCamelCase,	):
      break
    lowercase			:Union[str, Any]							=  temp_parameter_vector
  print(("Number of iterations:", j)      )



def 					UpperCAmelCase__     (   ):
  for i in range(len(lowerCamelCase      )      ):
    print(("Actual output value:", output(lowerCamelCase,	"test"      ))      )
    print(("Hypothesis output:", calculate_hypothesis_value(lowerCamelCase,	"test"      ))      )


if __name__ == "__main__":
     run_gradient_descent()
     print("\nTesting gradient descent for a linear hypothesis function.\n")
     test_gradient_descent()



