





def       UpperCAmelCase							(     _lowerCamelCase      :  int			,   _lowerCamelCase      :  list     ):





						'''simple docstring'''


						_enforce_args(_lowerCamelCase			,   _lowerCamelCase     )
						if n == 0:
												return 0
						SCREAMING_SNAKE_CASE__     :				Dict   =					float("-inf"     )
						for i in range(1			,   n + 1     ):
												SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					max(
												    _lowerCamelCase			,   prices[i - 1] + naive_cut_rod_recursive(n - i			,   _lowerCamelCase     )     )

						return max_revue







def       UpperCAmelCase							(     _lowerCamelCase      :  int			,   _lowerCamelCase      :  list     ):





						'''simple docstring'''


						_enforce_args(_lowerCamelCase			,   _lowerCamelCase     )
						SCREAMING_SNAKE_CASE__     :				Tuple   =					[float("-inf"     ) for _ in range(n + 1     )]
						return _top_down_cut_rod_recursive(_lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase     )







def       UpperCAmelCase							(     _lowerCamelCase      :  int			,   _lowerCamelCase      :  list			,   _lowerCamelCase      :  list     ):





						'''simple docstring'''


						if max_rev[n] >= 0:
												return max_rev[n]
						elif n == 0:
												return 0
						else:
												SCREAMING_SNAKE_CASE__     :				str   =					float("-inf"     )
												for i in range(1			,   n + 1     ):
																		SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					max(
																		    _lowerCamelCase			,   prices[i - 1] + _top_down_cut_rod_recursive(n - i			,   _lowerCamelCase			,   _lowerCamelCase     )			,   )

												SCREAMING_SNAKE_CASE__     :				Optional[int]   =					max_revenue

						return max_rev[n]







def       UpperCAmelCase							(     _lowerCamelCase      :  int			,   _lowerCamelCase      :  list     ):





						'''simple docstring'''


						_enforce_args(_lowerCamelCase			,   _lowerCamelCase     )

						# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
						# length 0.
						SCREAMING_SNAKE_CASE__     :				Any   =					[float("-inf"     ) for _ in range(n + 1     )]
						SCREAMING_SNAKE_CASE__     :				Optional[int]   =					0

						for i in range(1			,   n + 1     ):
												SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					max_rev[i]
												for j in range(1			,   i + 1     ):
																		SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					max(_lowerCamelCase			,   prices[j - 1] + max_rev[i - j]     )

												SCREAMING_SNAKE_CASE__     :				str   =					max_revenue_i

						return max_rev[n]







def       UpperCAmelCase							(     _lowerCamelCase      :  int			,   _lowerCamelCase      :  list     ):





						'''simple docstring'''


						if n < 0:
												SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					f"""n must be greater than or equal to 0. Got n = {n}"""
												raise ValueError(_lowerCamelCase     )

						if n > len(_lowerCamelCase     ):
												SCREAMING_SNAKE_CASE__     :				Any   =					(
												    "Each integral piece of rod must have a corresponding price. "
												    f"""Got n = {n} but length of prices = {len(_lowerCamelCase     )}"""
												)
												raise ValueError(_lowerCamelCase     )







def       UpperCAmelCase							(     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				List[str]   =					[6, 10, 12, 15, 20, 23]
						SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					len(_lowerCamelCase     )

						# the best revenue comes from cutting the rod into 6 pieces, each
						# of length 1 resulting in a revenue of 6 * 6 = 36.
						SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					36

						SCREAMING_SNAKE_CASE__     :				Tuple   =					top_down_cut_rod(_lowerCamelCase			,   _lowerCamelCase     )
						SCREAMING_SNAKE_CASE__     :				Dict   =					bottom_up_cut_rod(_lowerCamelCase			,   _lowerCamelCase     )
						SCREAMING_SNAKE_CASE__     :				Optional[int]   =					naive_cut_rod_recursive(_lowerCamelCase			,   _lowerCamelCase     )

						assert expected_max_revenue == max_rev_top_down
						assert max_rev_top_down == max_rev_bottom_up
						assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
				main()






import numpy



class    _a     :






							"""simple docstring"""

							def __init__(      self				:     Optional[int]							,	a				:     numpy.ndarray							,	a				:     numpy.ndarray    )	->None:
													SCREAMING_SNAKE_CASE__     :				Any   =					input_array

													# Random initial weights are assigned where first argument is the
													# number of nodes in previous layer and second argument is the
													# number of nodes in the next layer.

													# Random initial weights are assigned.
													# self.input_array.shape[1] is used to represent number of nodes in input layer.
													# First hidden layer consists of 4 nodes.
													SCREAMING_SNAKE_CASE__     :				int   =					numpy.random.rand(
													    self.input_array.shape[1]							,	4    )

													# Random initial values for the first hidden layer.
													# First hidden layer has 4 nodes.
													# Second hidden layer has 3 nodes.
													SCREAMING_SNAKE_CASE__     :				Dict   =					numpy.random.rand(
													    4							,	3    )

													# Random initial values for the second hidden layer.
													# Second hidden layer has 3 nodes.
													# Output layer has 1 node.
													SCREAMING_SNAKE_CASE__     :				List[Any]   =					numpy.random.rand(3							,	1    )

													# Real output values provided.
													SCREAMING_SNAKE_CASE__     :				str   =					output_array

													# Predicted output values by the neural network.
													# Predicted_output array initially consists of zeroes.
													SCREAMING_SNAKE_CASE__     :				Tuple   =					numpy.zeros(output_array.shape    )

							def      A_  (      self				:     Union[str, Any]    )	->numpy.ndarray:
													SCREAMING_SNAKE_CASE__     :				List[Any]   =					sigmoid(
													    numpy.dot(self.input_array							,	self.input_layer_and_first_hidden_layer_weights    )    )

													# layer_between_first_hidden_layer_and_second_hidden_layer is the layer
													# connecting the first hidden set of nodes with the second hidden set of nodes.
													SCREAMING_SNAKE_CASE__     :				Optional[int]   =					sigmoid(
													    numpy.dot(
													        self.layer_between_input_and_first_hidden_layer							,	self.first_hidden_layer_and_second_hidden_layer_weights							,	)    )

													# layer_between_second_hidden_layer_and_output is the layer connecting
													# second hidden layer with the output node.
													SCREAMING_SNAKE_CASE__     :				int   =					sigmoid(
													    numpy.dot(
													        self.layer_between_first_hidden_layer_and_second_hidden_layer							,	self.second_hidden_layer_and_output_layer_weights							,	)    )

													return self.layer_between_second_hidden_layer_and_output

							def      A_  (      self				:     int    )	->None:
													SCREAMING_SNAKE_CASE__     :				Optional[int]   =					numpy.dot(
													    self.layer_between_first_hidden_layer_and_second_hidden_layer.T							,	2
													    * (self.output_array - self.predicted_output)
													    * sigmoid_derivative(self.predicted_output    )							,	)
													SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					numpy.dot(
													    self.layer_between_input_and_first_hidden_layer.T							,	numpy.dot(
													        2
													        * (self.output_array - self.predicted_output)
													        * sigmoid_derivative(self.predicted_output    )							,	self.second_hidden_layer_and_output_layer_weights.T							,	)
													    * sigmoid_derivative(
													        self.layer_between_first_hidden_layer_and_second_hidden_layer    )							,	)
													SCREAMING_SNAKE_CASE__     :				int   =					numpy.dot(
													    self.input_array.T							,	numpy.dot(
													        numpy.dot(
													            2
													            * (self.output_array - self.predicted_output)
													            * sigmoid_derivative(self.predicted_output    )							,	self.second_hidden_layer_and_output_layer_weights.T							,	)
													        * sigmoid_derivative(
													            self.layer_between_first_hidden_layer_and_second_hidden_layer    )							,	self.first_hidden_layer_and_second_hidden_layer_weights.T							,	)
													    * sigmoid_derivative(self.layer_between_input_and_first_hidden_layer    )							,	)

													self.input_layer_and_first_hidden_layer_weights += (
													    updated_input_layer_and_first_hidden_layer_weights
													)
													self.first_hidden_layer_and_second_hidden_layer_weights += (
													    updated_first_hidden_layer_and_second_hidden_layer_weights
													)
													self.second_hidden_layer_and_output_layer_weights += (
													    updated_second_hidden_layer_and_output_layer_weights
													)

							def      A_  (      self				:     int							,	a				:     numpy.ndarray							,	a				:     int							,	a				:     bool    )	->None:
													for iteration in range(1							,	iterations + 1    ):
																			SCREAMING_SNAKE_CASE__     :				Dict   =					self.feedforward()
																			self.back_propagation()
																			if give_loss:
																									SCREAMING_SNAKE_CASE__     :				int   =					numpy.mean(numpy.square(output - self.feedforward()    )    )
																									print(f"""Iteration {iteration} Loss: {loss}"""    )






							def      A_  (      self				:     Tuple							,	a				:     numpy.ndarray    )	->int:
													SCREAMING_SNAKE_CASE__     :				Optional[int]   =					input_arr

													SCREAMING_SNAKE_CASE__     :				Dict   =					sigmoid(
													    numpy.dot(self.array							,	self.input_layer_and_first_hidden_layer_weights    )    )

													SCREAMING_SNAKE_CASE__     :				Any   =					sigmoid(
													    numpy.dot(
													        self.layer_between_input_and_first_hidden_layer							,	self.first_hidden_layer_and_second_hidden_layer_weights							,	)    )

													SCREAMING_SNAKE_CASE__     :				Optional[int]   =					sigmoid(
													    numpy.dot(
													        self.layer_between_first_hidden_layer_and_second_hidden_layer							,	self.second_hidden_layer_and_output_layer_weights							,	)    )

													return int(self.layer_between_second_hidden_layer_and_output > 0.6    )







def       UpperCAmelCase							(     _lowerCamelCase      :  numpy.ndarray     ):





						'''simple docstring'''


						return 1 / (1 + numpy.exp(-value     ))







def       UpperCAmelCase							(     _lowerCamelCase      :  numpy.ndarray     ):





						'''simple docstring'''


						return (value) * (1 - (value))







def       UpperCAmelCase							(     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				str   =					numpy.array(
						    (
						        [0, 0, 0],
						        [0, 0, 1],
						        [0, 1, 0],
						        [0, 1, 1],
						        [1, 0, 0],
						        [1, 0, 1],
						        [1, 1, 0],
						        [1, 1, 1],
						    )			,   dtype=numpy.floataa			,   )

						# True output values for the given input values.
						SCREAMING_SNAKE_CASE__     :				Any   =					numpy.array(([0], [1], [1], [0], [1], [0], [0], [1])			,   dtype=numpy.floataa     )

						# Calling neural network class.
						SCREAMING_SNAKE_CASE__     :				List[Any]   =					TwoHiddenLayerNeuralNetwork(
						    input_array=_lowerCamelCase			,   output_array=_lowerCamelCase     )

						# Calling training function.
						# Set give_loss to True if you want to see loss in every iteration.
						neural_network.train(output=_lowerCamelCase			,   iterations=10			,   give_loss=_lowerCamelCase     )

						return neural_network.predict(numpy.array(([1, 1, 1])			,   dtype=numpy.floataa     )     )


if __name__ == "__main__":
				example()