"""simple docstring"""



import numpy






class 				snake_case__     :


 def __init__(				self  ,						lowerCamelCase  ,						lowerCamelCase		):
        __a     				=  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.
        __a     				=  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.
        __a     				=  numpy.random.rand(
            4  ,						3		)

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

        # Real output values provided.
        __a     				=  output_array

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


 def 		a__ (				self		):
        __a     				=  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.
        __a     				=  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.
        __a     				=  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		):
        __a     				=  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		)  ,						)
        __a     				=  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		)  ,						)
        __a     				=  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  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase		):
        for iteration in range(1  ,						iterations + 1		):
               __a     				=  self.feedforward()
               self.back_propagation()
               if give_loss:
                      __a     				=  numpy.mean(numpy.square(output - self.feedforward()		)		)
                      print(F"Iteration {iteration} Loss: {loss}"		)






 def 		a__ (				self  ,						lowerCamelCase		):
        __a     				=  input_arr

        __a     				=  sigmoid(
            numpy.dot(self.array  ,						self.input_layer_and_first_hidden_layer_weights		)		)

        __a     				=  sigmoid(
            numpy.dot(
                self.layer_between_input_and_first_hidden_layer  ,						self.first_hidden_layer_and_second_hidden_layer_weights  ,						)		)

        __a     				=  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 					_lowerCamelCase(					a							):
       return 1 / (1 + numpy.exp(-value							))



def 					_lowerCamelCase(					a							):
       return (value) * (1 - (value))



def 					_lowerCamelCase(					):
       __a     				=  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.
       __a     				=  numpy.array(([0], [1], [1], [0], [1], [0], [0], [1]) ,  dtype=numpy.floataa							)

       # Calling neural network class.
       __a     				=  TwoHiddenLayerNeuralNetwork(
           input_array=a ,  output_array=a							)

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

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


if __name__ == "__main__":
   example()

"""simple docstring"""



def 					_lowerCamelCase(					a ,  a ,  a ,  a							):
       global f  # a global dp table for knapsack
       if f[i][j] < 0:
              if j < wt[i - 1]:
                     __a     				=  mf_knapsack(i - 1 ,  a ,  a ,  a							)
              else:
                     __a     				=  max(
                         mf_knapsack(i - 1 ,  a ,  a ,  a							) ,  mf_knapsack(i - 1 ,  a ,  a ,  j - wt[i - 1]							) + val[i - 1] ,  )
              __a     				=  val
       return f[i][j]



def 					_lowerCamelCase(					a ,  a ,  a ,  a							):
       __a     				=  [[0] * (w + 1) for _ in range(n + 1							)]

       for i in range(1 ,  n + 1							):
              for w_ in range(1 ,  w + 1							):
                     if wt[i - 1] <= w_:
                            __a     				=  max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]] ,  dp[i - 1][w_]							)
                     else:
                            __a     				=  dp[i - 1][w_]

       return dp[n][w_], dp



def 					_lowerCamelCase(					a ,  a ,  a							):
       if not (isinstance(a ,  (list, tuple)							) and isinstance(a ,  (list, tuple)							)):
              raise ValueError(
                  "Both the weights and values vectors must be either lists or tuples"							)

       __a     				=  len(a							)
       if num_items != len(a							):
              __a     				=  (
                  "The number of weights must be the same as the number of values.\n"
                  F"But got {num_items} weights and {len(a							)} values"
              )
              raise ValueError(a							)
       for i in range(a							):
              if not isinstance(wt[i] ,  a							):
                     __a     				=  (
                         "All weights must be integers but got weight of "
                         F"type {type(wt[i]							)} at index {i}"
                     )
                     raise TypeError(a							)

       __a				, __a     				=  knapsack(a ,  a ,  a ,  a							)
       __a     				=  set()
       _construct_solution(a ,  a ,  a ,  a ,  a							)

       return optimal_val, example_optional_set



def 					_lowerCamelCase(					a ,  a ,  a ,  a ,  a							):
       # for the current item i at a maximum weight j to be part of an optimal subset,
       # the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
       # where i - 1 means considering only the previous items at the given maximum weight
       if i > 0 and j > 0:
              if dp[i - 1][j] == dp[i][j]:
                     _construct_solution(a ,  a ,  i - 1 ,  a ,  a							)
              else:
                     optimal_set.add(a							)
                     _construct_solution(a ,  a ,  i - 1 ,  j - wt[i - 1] ,  a							)


if __name__ == "__main__":
   SCREAMING_SNAKE_CASE__:Tuple			=	[3, 2, 4, 4]
   SCREAMING_SNAKE_CASE__:List[str]			=	[4, 3, 2, 3]
   SCREAMING_SNAKE_CASE__:List[str]			=	4
   SCREAMING_SNAKE_CASE__:List[str]			=	6
   SCREAMING_SNAKE_CASE__:Optional[Any]			=	[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
   SCREAMING_SNAKE_CASE__	,      SCREAMING_SNAKE_CASE__:Optional[int]			=	knapsack(w, wt, val, n)
   print(optimal_solution)
   print(mf_knapsack(n, wt, val, w))  # switched the n and w

   # testing the dynamic programming problem with example
   # the optimal subset for the above example are items 3 and 4
   SCREAMING_SNAKE_CASE__	,      SCREAMING_SNAKE_CASE__:Optional[Any]			=	knapsack_with_example_solution(w, wt, val)
   assert optimal_solution == 8
   assert optimal_subset == {3, 4}
   print("""optimal_value = """, optimal_solution)
   print("""An optimal subset corresponding to the optimal value""", optimal_subset)
