code: 
  
  
  '''simple docstring'''
  
  
  
  import numpy as np
  
  
  
  
  
  class 							__UpperCamelCase       :
  
  
  
  
  	def __init__(     self		,       __a=5		,       __a=5							):
  
  						'''simple docstring'''
  
  
  
  
  
  						__a    : Any      					=						depth
  						__a    : Union[str, Any]      					=						0
  						__a    : Union[str, Any]      					=						None
  						__a    : List[Any]      					=						None
  						__a    : Optional[int]      					=						min_leaf_size
  						__a    : Optional[Any]      					=						None
  
  
  
  
  	def    __UpperCAmelCase							(     self		,       __a		,       __a							):
  
  						'''simple docstring'''
  
  
  
  
  
  						if labels.ndim != 1:
  											print('Error: Input labels must be one dimensional'							)
  
  						return np.mean((labels - prediction) ** 2							)
  
  
  
  
  	def    __UpperCAmelCase							(     self		,       __a		,       __a							):
  
  						'''simple docstring'''
  
  
  
  
  
  						if x.ndim != 1:
  											print('Error: Input data set must be one dimensional'							)
  											return
  						if len(__a							) != len(__a							):
  											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(__a							) < 2 * self.min_leaf_size:
  											__a    : Any      					=						np.mean(__a							)
  											return
  
  						if self.depth == 1:
  											__a    : str      					=						np.mean(__a							)
  											return
  
  						__a    : List[Any]      					=						0
  						__a    : Optional[Any]      					=						self.mean_squared_error(__a		,       np.mean(__a							)							) * 2
  						for i in range(len(__a							)							):
  											if len(x[:i]							) < self.min_leaf_size:
  																continue
  											elif len(x[i:]							) < self.min_leaf_size:
  																continue
  											else:
  																__a    : List[str]      					=						self.mean_squared_error(x[:i]		,       np.mean(y[:i]							)							)
  																__a    : List[Any]      					=						self.mean_squared_error(x[i:]		,       np.mean(y[i:]							)							)
  																__a    : Any      					=						error_left + error_right
  																if error < min_error:
  																					__a    : List[Any]      					=						i
  																					__a    : Optional[int]      					=						error
  
  						if best_split != 0:
  											__a    : Dict      					=						x[:best_split]
  											__a    : str      					=						y[:best_split]
  											__a    : Any      					=						x[best_split:]
  											__a    : List[Any]      					=						y[best_split:]
  
  											__a    : str      					=						x[best_split]
  											__a    : Any      					=						DecisionTree(
  											    depth=self.depth - 1		,       min_leaf_size=self.min_leaf_size							)
  											__a    : List[Any]      					=						DecisionTree(
  											    depth=self.depth - 1		,       min_leaf_size=self.min_leaf_size							)
  											self.left.train(__a		,       __a							)
  											self.right.train(__a		,       __a							)
  						else:
  											__a    : Union[str, Any]      					=						np.mean(__a							)
  
  						return
  
  
  
  
  
  	def    __UpperCAmelCase							(     self		,       __a							):
  
  						'''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(__a							)
  											else:
  																return self.left.predict(__a							)
  						else:
  											print('Error: Decision tree not yet trained'							)
  											return None
  
  
  
  
  
  class 							__UpperCamelCase       :
  
  
  
  
  	@staticmethod
  	def    __UpperCAmelCase							(     __a		,       __a							):
  
  						'''simple docstring'''
  
  
  
  
  
  						__a    : Tuple      					=						float(0							)
  						for label in labels:
  											squared_error_sum += (label - prediction) ** 2
  
  						return float(squared_error_sum / labels.size							)
  
  
  
  
  
  
  def 						lowerCamelCase							():
  					__a    : List[Any]      					=						np.arange(-1.0		,   1.0		,   0.0_0_5     )
  					__a    : Dict      					=						np.sin(_SCREAMING_SNAKE_CASE     )
  
  					__a    : Union[str, Any]      					=						DecisionTree(depth=10		,   min_leaf_size=10     )
  					tree.train(_SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     )
  
  					__a    : Any      					=						(np.random.rand(10     ) * 2) - 1
  					__a    : Any      					=						np.array([tree.predict(_SCREAMING_SNAKE_CASE     ) for x in test_cases]     )
  					__a    : Union[str, Any]      					=						np.mean((predictions - test_cases) ** 2     )
  
  					print('Test values: ' + str(_SCREAMING_SNAKE_CASE     )     )
  					print('Predictions: ' + str(_SCREAMING_SNAKE_CASE     )     )
  					print('Average error: ' + str(_SCREAMING_SNAKE_CASE     )     )
  
  
  if __name__ == "__main__":
  		main()
  		import doctest
  
  		doctest.testmod(name='mean_squarred_error', verbose=True)
  
  
  
  
style_context: 
  
  
  '''simple docstring'''
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int = 30     ):
  					__a    : Dict      					=						exponent + 2
  					__a    : List[Any]      					=						(1 + 5**0.5) / 2
  					__a    : Any      					=						(phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5
  
  					return int(_SCREAMING_SNAKE_CASE     )
  
  
  if __name__ == "__main__":
  	print(f'''{solution() = }''')
  
  
  
  