


'''simple docstring'''



def       _UpperCamelCase (						UpperCamelCase__	, UpperCamelCase__   ):
   UpperCAmelCase__					:   Any       				=       0
   UpperCAmelCase__					:   Tuple       				=       len(_A   ) - 1

   while left <= right:
      # avoid divided by 0 during interpolation
      if sorted_collection[left] == sorted_collection[right]:
         if sorted_collection[left] == item:
            return left
         else:
            return None

      UpperCAmelCase__					:   Tuple       				=       left + ((item - sorted_collection[left]) * (right - left)) // (
          sorted_collection[right] - sorted_collection[left]
      )

      # out of range check
      if point < 0 or point >= len(_A   ):
         return None

      UpperCAmelCase__					:   List[str]       				=       sorted_collection[point]
      if current_item == item:
         return point
      else:
         if point < left:
            UpperCAmelCase__					:   Union[str, Any]       				=       left
            UpperCAmelCase__					:   Any       				=       point
         elif point > right:
            UpperCAmelCase__					:   Optional[Any]       				=       right
            UpperCAmelCase__					:   List[Any]       				=       point
         else:
            if item < current_item:
               UpperCAmelCase__					:   Any       				=       point - 1
            else:
               UpperCAmelCase__					:   Tuple       				=       point + 1
   return None







def       _UpperCamelCase (						UpperCamelCase__	, UpperCamelCase__	, UpperCamelCase__	, UpperCamelCase__   ):

   # avoid divided by 0 during interpolation
   if sorted_collection[left] == sorted_collection[right]:
      if sorted_collection[left] == item:
         return left
      else:
         return None

   UpperCAmelCase__					:   Tuple       				=       left + ((item - sorted_collection[left]) * (right - left)) // (
       sorted_collection[right] - sorted_collection[left]
   )

   # out of range check
   if point < 0 or point >= len(_A   ):
      return None

   if sorted_collection[point] == item:
      return point
   elif point < left:
      return interpolation_search_by_recursion(_A	, _A	, _A	, _A   )
   elif point > right:
      return interpolation_search_by_recursion(_A	, _A	, _A	, _A   )
   else:
      if sorted_collection[point] > item:
         return interpolation_search_by_recursion(
             _A	, _A	, _A	, point - 1   )
      else:
         return interpolation_search_by_recursion(
             _A	, _A	, point + 1	, _A   )







def       _UpperCamelCase (						UpperCamelCase__   ):
   if collection != sorted(_A   ):
      raise ValueError("""Collection must be ascending sorted"""   )
   return True


if __name__ == "__main__":
  import sys
  __A		=0
  if debug == 1:
    __A		=[10, 30, 40, 45, 50, 66, 77, 93]
    try:
      __assert_sorted(collection)
    except ValueError:
      sys.exit('Sequence must be ascending sorted to apply interpolation search')
    __A		=67

  __A		=interpolation_search(collection, target)
  if result is not None:
    print(f"""{target} found at positions: {result}""")
  else:
    print('Not found')



'''simple docstring'''



import numpy


class 						_snake_case   :




					def __init__( self							,							_lowerCamelCase							,							_lowerCamelCase):
								UpperCAmelCase__					:   Dict       				=       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.
								UpperCAmelCase__					:   Optional[Any]       				=       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.
								UpperCAmelCase__					:   Optional[int]       				=       numpy.random.rand(
								    4							,							3)

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

								# Real output values provided.
								UpperCAmelCase__					:   Tuple       				=       output_array

								# Predicted output values by the neural network.
								# Predicted_output array initially consists of zeroes.
								UpperCAmelCase__					:   Union[str, Any]       				=       numpy.zeros(output_array.shape)




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   List[str]       				=       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.
								UpperCAmelCase__					:   Any       				=       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.
								UpperCAmelCase__					:   Tuple       				=       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 			snake_case__  ( self):
								UpperCAmelCase__					:   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)							,							)
								UpperCAmelCase__					:   str       				=       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)							,							)
								UpperCAmelCase__					:   Any       				=       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 			snake_case__  ( self							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase):
								for iteration in range(1							,							iterations + 1):
											UpperCAmelCase__					:   Optional[Any]       				=       self.feedforward()
											self.back_propagation()
											if give_loss:
														UpperCAmelCase__					:   str       				=       numpy.mean(numpy.square(output - self.feedforward()))
														print(f'''Iteration {iteration} Loss: {loss}''')




					def 			snake_case__  ( self							,							_lowerCamelCase):
								UpperCAmelCase__					:   List[Any]       				=       input_arr

								UpperCAmelCase__					:   Tuple       				=       sigmoid(
								    numpy.dot(self.array							,							self.input_layer_and_first_hidden_layer_weights))

								UpperCAmelCase__					:   List[Any]       				=       sigmoid(
								    numpy.dot(
								        self.layer_between_input_and_first_hidden_layer							,							self.first_hidden_layer_and_second_hidden_layer_weights							,							))

								UpperCAmelCase__					:   Optional[Any]       				=       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 (						UpperCamelCase__   ):
			return 1 / (1 + numpy.exp(-value   ))







def       _UpperCamelCase (						UpperCamelCase__   ):
			return (value) * (1 - (value))







def       _UpperCamelCase (						):
			UpperCAmelCase__					:   Union[str, Any]       				=       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.
			UpperCAmelCase__					:   str       				=       numpy.array(([0], [1], [1], [0], [1], [0], [0], [1])	, dtype=numpy.floataa   )

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

			# Calling training function.
			# Set give_loss to True if you want to see loss in every iteration.
			neural_network.train(output=UpperCamelCase__	, iterations=1_0	, give_loss=UpperCamelCase__   )

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


if __name__ == "__main__":
		example()