






def 						_UpperCamelCase (     UpperCamelCase_							:       int		)	-> str:

						"""simple docstring"""



						lowerCAmelCase__         =    1
						lowerCAmelCase__         =    0
						lowerCAmelCase__         =    1
						lowerCAmelCase__         =    1
						lowerCAmelCase__         =    3
						lowerCAmelCase__         =    3
						lowerCAmelCase__         =    limit
						lowerCAmelCase__         =    0

						lowerCAmelCase__         =    ''
						while counter != decimal + 1:
												if 4 * q + r - t < n * t:
																		result += str(UpperCamelCase_		)
																		if counter == 0:
																								result += "."

																		if decimal == counter:
																								break

																		counter += 1
																		lowerCAmelCase__         =    10 * (r - n * t)
																		lowerCAmelCase__         =    ((10 * (3 * q + r)) // t) - 10 * n
																		q *= 10
																		lowerCAmelCase__         =    nr
												else:
																		lowerCAmelCase__         =    (2 * q + r) * l
																		lowerCAmelCase__         =    (q * (7 * k) + 2 + (r * l)) // (t * l)
																		q *= k
																		t *= l
																		l += 2
																		k += 1
																		lowerCAmelCase__         =    nn
																		lowerCAmelCase__         =    nr
						return result







def 						_UpperCamelCase (     )	-> None:

						"""simple docstring"""



						print(F"{calculate_pi(50		) = }"		)
						import doctest

						doctest.testmod()


if __name__ == "__main__":
					main()













import numpy as np


class      __SCREAMING_SNAKE_CASE       :






						def __init__(						self  ,    _UpperCamelCase=5  ,    _UpperCamelCase=5 ):






												"""simple docstring"""
												lowerCAmelCase__         =    depth
												lowerCAmelCase__         =    0
												lowerCAmelCase__         =    None
												lowerCAmelCase__         =    None
												lowerCAmelCase__         =    min_leaf_size
												lowerCAmelCase__         =    None






						def    UpperCamelCase__   (						self  ,    _UpperCamelCase  ,    _UpperCamelCase ):






												"""simple docstring"""
												if labels.ndim != 1:
																		print('Error: Input labels must be one dimensional' )

												return np.mean((labels - prediction) ** 2 )






						def    UpperCamelCase__   (						self  ,    _UpperCamelCase  ,    _UpperCamelCase ):






												"""simple docstring"""
												if x.ndim != 1:
																		print('Error: Input data set must be one dimensional' )
																		return
												if len(_UpperCamelCase ) != len(_UpperCamelCase ):
																		print('Error: X and y have different lengths' )
																		return
												if y.ndim != 1:
																		print('Error: Data set labels must be one dimensional' )
																		return

												if len(_UpperCamelCase ) < 2 * self.min_leaf_size:
																		lowerCAmelCase__         =    np.mean(_UpperCamelCase )
																		return

												if self.depth == 1:
																		lowerCAmelCase__         =    np.mean(_UpperCamelCase )
																		return

												lowerCAmelCase__         =    0
												lowerCAmelCase__         =    self.mean_squared_error(_UpperCamelCase  ,    np.mean(_UpperCamelCase ) ) * 2
												for i in range(len(_UpperCamelCase ) ):
																		if len(x[:i] ) < self.min_leaf_size:
																								continue
																		elif len(x[i:] ) < self.min_leaf_size:
																								continue
																		else:
																								lowerCAmelCase__         =    self.mean_squared_error(x[:i]  ,    np.mean(y[:i] ) )
																								lowerCAmelCase__         =    self.mean_squared_error(x[i:]  ,    np.mean(y[i:] ) )
																								lowerCAmelCase__         =    error_left + error_right
																								if error < min_error:
																														lowerCAmelCase__         =    i
																														lowerCAmelCase__         =    error

												if best_split != 0:
																		lowerCAmelCase__         =    x[:best_split]
																		lowerCAmelCase__         =    y[:best_split]
																		lowerCAmelCase__         =    x[best_split:]
																		lowerCAmelCase__         =    y[best_split:]

																		lowerCAmelCase__         =    x[best_split]
																		lowerCAmelCase__         =    DecisionTree(
																		    depth=self.depth - 1  ,    min_leaf_size=self.min_leaf_size )
																		lowerCAmelCase__         =    DecisionTree(
																		    depth=self.depth - 1  ,    min_leaf_size=self.min_leaf_size )
																		self.left.train(_UpperCamelCase  ,    _UpperCamelCase )
																		self.right.train(_UpperCamelCase  ,    _UpperCamelCase )
												else:
																		lowerCAmelCase__         =    np.mean(_UpperCamelCase )

												return







						def    UpperCamelCase__   (						self  ,    _UpperCamelCase ):






												"""simple docstring"""
												if self.prediction is not None:
																		return self.prediction
												elif self.left or self.right is not None:
																		if x >= self.decision_boundary:
																								return self.right.predict(_UpperCamelCase )
																		else:
																								return self.left.predict(_UpperCamelCase )
												else:
																		print('Error: Decision tree not yet trained' )
																		return None




class      __SCREAMING_SNAKE_CASE       :






						@staticmethod
						def    UpperCamelCase__   (						_UpperCamelCase  ,    _UpperCamelCase ):






												"""simple docstring"""
												lowerCAmelCase__         =    float(0 )
												for label in labels:
																		squared_error_sum += (label - prediction) ** 2

												return float(squared_error_sum / labels.size )







def 						_UpperCamelCase (     )	-> List[Any]:

						"""simple docstring"""



						lowerCAmelCase__         =    np.arange(-1.0     ,							1.0     ,							0.005		)
						lowerCAmelCase__         =    np.sin(UpperCamelCase_		)

						lowerCAmelCase__         =    DecisionTree(depth=10     ,							min_leaf_size=10		)
						tree.train(UpperCamelCase_     ,							UpperCamelCase_		)

						lowerCAmelCase__         =    (np.random.rand(10		) * 2) - 1
						lowerCAmelCase__         =    np.array([tree.predict(UpperCamelCase_		) for x in test_cases]		)
						lowerCAmelCase__         =    np.mean((predictions - test_cases) ** 2		)

						print('Test values: ' + str(UpperCamelCase_		)		)
						print('Predictions: ' + str(UpperCamelCase_		)		)
						print('Average error: ' + str(UpperCamelCase_		)		)


if __name__ == "__main__":
					main()
					import doctest

					doctest.testmod(name="""mean_squarred_error""", verbose=True)





