



'''simple docstring'''
import numpy

# List of input, output pairs
snake_case_					:      List[Any]    			=    (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
snake_case_					:      Optional[int]    			=    (((515, 22, 13), 555), ((61, 35, 49), 150))
snake_case_					:      str    			=    [2, 4, 1, 5]
snake_case_					:      Union[str, Any]    			=    len(train_data)
snake_case_					:      List[Any]    			=    0.0_09






def A__       (	UpperCAmelCase_    ,    UpperCAmelCase_="train"				):
						return calculate_hypothesis_value(UpperCAmelCase_    ,    UpperCAmelCase_				) - output(
						    UpperCAmelCase_    ,    UpperCAmelCase_				)






def A__       (	UpperCAmelCase_				):
						_UpperCamelCase   :						Optional[Any]												=  0
						for i in range(len(UpperCAmelCase_				) - 1				):
												hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
						hyp_val += parameter_vector[0]
						return hyp_val






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






def A__       (	UpperCAmelCase_    ,    UpperCAmelCase_				):
						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 A__       (	UpperCAmelCase_    ,    UpperCAmelCase_=m				):
						_UpperCamelCase   :						str												=  0
						for i in range(UpperCAmelCase_				):
												if index == -1:
																		summation_value += _error(UpperCAmelCase_				)
												else:
																		summation_value += _error(UpperCAmelCase_				) * train_data[i][0][index]
						return summation_value






def A__       (	UpperCAmelCase_				):
						_UpperCamelCase   :						int												=  summation_of_cost_derivative(UpperCAmelCase_    ,    UpperCAmelCase_				) / m
						return cost_derivative_value






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






def A__       (	):
						for i in range(len(UpperCAmelCase_				)				):
												print(('Actual output value:', output(UpperCAmelCase_    ,    'test'				))				)
												print(('Hypothesis output:', calculate_hypothesis_value(UpperCAmelCase_    ,    'test'				))				)


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







'''simple docstring'''
from __future__ import annotations






def A__       (	UpperCAmelCase_    ,    UpperCAmelCase_				):
						_UpperCamelCase							,     _UpperCamelCase   :						Dict												=  position
						_UpperCamelCase   :						Any												=  [
						    (y + 1, x + 2),
						    (y - 1, x + 2),
						    (y + 1, x - 2),
						    (y - 1, x - 2),
						    (y + 2, x + 1),
						    (y + 2, x - 1),
						    (y - 2, x + 1),
						    (y - 2, x - 1),
						]
						_UpperCamelCase   :						Optional[Any]												=  []

						for position in positions:
												_UpperCamelCase							,     _UpperCamelCase   :						Any												=  position
												if 0 <= y_test < n and 0 <= x_test < n:
																		permissible_positions.append(UpperCAmelCase_				)

						return permissible_positions






def A__       (	UpperCAmelCase_				):
						return not any(elem == 0 for row in board for elem in row				)






def A__       (	UpperCAmelCase_    ,    UpperCAmelCase_    ,    UpperCAmelCase_				):

						if is_complete(UpperCAmelCase_				):
												return True

						for position in get_valid_pos(UpperCAmelCase_    ,    len(UpperCAmelCase_				)				):
												_UpperCamelCase							,     _UpperCamelCase   :						Any												=  position

												if board[y][x] == 0:
																		_UpperCamelCase   :						int												=  curr + 1
																		if open_knight_tour_helper(UpperCAmelCase_    ,    UpperCAmelCase_    ,    curr + 1				):
																								return True
																		_UpperCamelCase   :						Union[str, Any]												=  0

						return False






def A__       (	UpperCAmelCase_				):
						_UpperCamelCase   :						Dict												=  [[0 for i in range(UpperCAmelCase_				)] for j in range(UpperCAmelCase_				)]

						for i in range(UpperCAmelCase_				):
												for j in range(UpperCAmelCase_				):
																		_UpperCamelCase   :						Tuple												=  1
																		if open_knight_tour_helper(UpperCAmelCase_    ,    (i, j)    ,    1				):
																								return board
																		_UpperCamelCase   :						Union[str, Any]												=  0

						_UpperCamelCase   :						int												=  f'Open Kight Tour cannot be performed on a board of size {n}'
						raise ValueError(UpperCAmelCase_				)


if __name__ == "__main__":
					import doctest

					doctest.testmod()


