code: 
  '''simple docstring'''
  
  
  
  import numpy as np
  
  
  
  
  
  class 			A							:
  
  
  
  			def __init__(					self       ,     lowerCamelCase__=5       ,     lowerCamelCase__=5       )			->		Any:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									lowercase__							 =       depth
  									lowercase__							 =       0
  									lowercase__							 =       None
  									lowercase__							 =       None
  									lowercase__							 =       min_leaf_size
  									lowercase__							 =       None
  
  
  
  			def A__ (					self       ,     lowerCamelCase__       ,     lowerCamelCase__       )			->		Optional[int]:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									if labels.ndim != 1:
  															print("""Error: Input labels must be one dimensional"""       )
  
  									return np.mean((labels - prediction) ** 2       )
  
  
  
  			def A__ (					self       ,     lowerCamelCase__       ,     lowerCamelCase__       )			->		Optional[int]:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									if x.ndim != 1:
  															print("""Error: Input data set must be one dimensional"""       )
  															return
  									if len(lowerCamelCase__       ) != len(lowerCamelCase__       ):
  															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(lowerCamelCase__       ) < 2 * self.min_leaf_size:
  															lowercase__							 =       np.mean(lowerCamelCase__       )
  															return
  
  									if self.depth == 1:
  															lowercase__							 =       np.mean(lowerCamelCase__       )
  															return
  
  									lowercase__							 =       0
  									lowercase__							 =       self.mean_squared_error(lowerCamelCase__       ,     np.mean(lowerCamelCase__       )       ) * 2
  									for i in range(len(lowerCamelCase__       )       ):
  															if len(x[:i]       ) < self.min_leaf_size:
  																					continue
  															elif len(x[i:]       ) < self.min_leaf_size:
  																					continue
  															else:
  																					lowercase__							 =       self.mean_squared_error(x[:i]       ,     np.mean(y[:i]       )       )
  																					lowercase__							 =       self.mean_squared_error(x[i:]       ,     np.mean(y[i:]       )       )
  																					lowercase__							 =       error_left + error_right
  																					if error < min_error:
  																											lowercase__							 =       i
  																											lowercase__							 =       error
  
  									if best_split != 0:
  															lowercase__							 =       x[:best_split]
  															lowercase__							 =       y[:best_split]
  															lowercase__							 =       x[best_split:]
  															lowercase__							 =       y[best_split:]
  
  															lowercase__							 =       x[best_split]
  															lowercase__							 =       DecisionTree(
  															    depth=self.depth - 1       ,     min_leaf_size=self.min_leaf_size       )
  															lowercase__							 =       DecisionTree(
  															    depth=self.depth - 1       ,     min_leaf_size=self.min_leaf_size       )
  															self.left.train(lowerCamelCase__       ,     lowerCamelCase__       )
  															self.right.train(lowerCamelCase__       ,     lowerCamelCase__       )
  									else:
  															lowercase__							 =       np.mean(lowerCamelCase__       )
  
  									return
  
  
  
  			def A__ (					self       ,     lowerCamelCase__       )			->		Optional[Any]:
  
  
  
  
  									'''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(lowerCamelCase__       )
  															else:
  																					return self.left.predict(lowerCamelCase__       )
  									else:
  															print("""Error: Decision tree not yet trained"""       )
  															return None
  
  
  
  
  
  class 			A							:
  
  
  
  			@staticmethod
  			def A__ (					lowerCamelCase__       ,     lowerCamelCase__       )			->		Tuple:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									lowercase__							 =       float(0       )
  									for label in labels:
  															squared_error_sum += (label - prediction) ** 2
  
  									return float(squared_error_sum / labels.size       )
  
  
  
  
  
  def  _A		(							):
  						lowercase__							 =       np.arange(-1.0		,		1.0		,		0.0_0_5	)
  						lowercase__							 =       np.sin(lowercase__	)
  
  						lowercase__							 =       DecisionTree(depth=10		,		min_leaf_size=10	)
  						tree.train(lowercase__		,		lowercase__	)
  
  						lowercase__							 =       (np.random.rand(10	) * 2) - 1
  						lowercase__							 =       np.array([tree.predict(lowercase__	) for x in test_cases]	)
  						lowercase__							 =       np.mean((predictions - test_cases) ** 2	)
  
  						print("""Test values: """ + str(lowercase__	)	)
  						print("""Predictions: """ + str(lowercase__	)	)
  						print("""Average error: """ + str(lowercase__	)	)
  
  
  if __name__ == "__main__":
  				main()
  				import doctest
  
  				doctest.testmod(name="mean_squarred_error", verbose=True)
style_context: 
  '''simple docstring'''
  
  
  
  def  _A		(							lowercase__	):
  
  						# validate:
  						if not isinstance(lowercase__		,		lowercase__	) or not all(
  						    isinstance(lowercase__		,		lowercase__	) and item >= 0 for item in citations	):
  												raise ValueError("""The citations should be a list of non negative integers."""	)
  
  						citations.sort()
  						lowercase__							 =       len(lowercase__	)
  
  						for i in range(lowercase__	):
  												if citations[len_citations - 1 - i] <= i:
  																		return i
  
  						return len_citations
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  
  
  
  
  
  