



import numpy as np

class 			__snake_case   :







							'''simple docstring'''






							def __init__(				self	,	a_=5	,	a_=5		):
											a__					   =		depth
											a__					   =		0
											a__					   =		None
											a__					   =		None
											a__					   =		min_leaf_size
											a__					   =		None


							def _a   (				self	,	a_	,	a_		):
											if labels.ndim != 1:
															print("""Error: Input labels must be one dimensional"""		)

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


							def _a   (				self	,	a_	,	a_		):
											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__					   =		np.mean(a_		)
															return

											if self.depth == 1:
															a__					   =		np.mean(a_		)
															return

											a__					   =		0
											a__					   =		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__					   =		self.mean_squared_error(x[:i]	,	np.mean(y[:i]		)		)
																			a__					   =		self.mean_squared_error(x[i:]	,	np.mean(y[i:]		)		)
																			a__					   =		error_left + error_right
																			if error < min_error:
																							a__					   =		i
																							a__					   =		error

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

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

											return







							def _a   (				self	,	a_		):
											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 			__snake_case   :







							'''simple docstring'''






							@staticmethod
							def _a   (				a_	,	a_		):
											a__					   =		float(0		)
											for label in labels:
															squared_error_sum += (label - prediction) ** 2

											return float(squared_error_sum / labels.size		)




def       A_   (						):

				"""simple docstring"""
				a__					   =		np.arange(-1.0			,		1.0			,		0.0_0_5		)
				a__					   =		np.sin(__a		)

				a__					   =		DecisionTree(depth=10			,		min_leaf_size=10		)
				tree.train(__a			,		__a		)

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

				print("""Test values: """ + str(__a		)		)
				print("""Predictions: """ + str(__a		)		)
				print("""Average error: """ + str(__a		)		)


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

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







from __future__ import annotations

from math import pi, pow



def     lowerCAmelCase		(		_lowerCAmelCase				: int | float						):




 """simple docstring"""







 if side_length < 0:
  raise ValueError("vol_cube() only accepts non-negative values"						)
 return pow(_lowerCAmelCase    ,				3						)



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or radius < 0:
  raise ValueError("vol_spherical_cap() only accepts non-negative values"						)
 # Volume is 1/3 pi * height squared * (3 * radius - height)
 return 1 / 3 * pi * pow(_lowerCAmelCase    ,				2						) * (3 * radius - height)



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if radius_a < 0 or radius_a < 0 or centers_distance < 0:
  raise ValueError("vol_spheres_intersect() only accepts non-negative values"						)
 if centers_distance == 0:
  return vol_sphere(min(_lowerCAmelCase    ,				_lowerCAmelCase						)						)

 UpperCAmelCase__							=    (
     (radius_a - radius_a + centers_distance)
     * (radius_a + radius_a - centers_distance)
     / (2 * centers_distance)
 )
 UpperCAmelCase__							=    (
     (radius_a - radius_a + centers_distance)
     * (radius_a + radius_a - centers_distance)
     / (2 * centers_distance)
 )

 return vol_spherical_cap(_lowerCAmelCase    ,				_lowerCAmelCase						) + vol_spherical_cap(_lowerCAmelCase    ,				_lowerCAmelCase						)



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
  raise ValueError(
      "vol_spheres_union() only accepts non-negative values, non-zero radius"						)

 if centers_distance == 0:
  return vol_sphere(max(_lowerCAmelCase    ,				_lowerCAmelCase						)						)

 return (
     vol_sphere(_lowerCAmelCase						)
     + vol_sphere(_lowerCAmelCase						)
     - vol_spheres_intersect(_lowerCAmelCase    ,				_lowerCAmelCase    ,				_lowerCAmelCase						)
 )



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if width < 0 or height < 0 or length < 0:
  raise ValueError("vol_cuboid() only accepts non-negative values"						)
 return float(width * height * length						)



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or area_of_base < 0:
  raise ValueError("vol_cone() only accepts non-negative values"						)
 return area_of_base * height / 3.0



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or radius < 0:
  raise ValueError("vol_right_circ_cone() only accepts non-negative values"						)
 return pi * pow(_lowerCAmelCase    ,				2						) * height / 3.0



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or area_of_base < 0:
  raise ValueError("vol_prism() only accepts non-negative values"						)
 return float(area_of_base * height						)



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or area_of_base < 0:
  raise ValueError("vol_pyramid() only accepts non-negative values"						)
 return area_of_base * height / 3.0



def     lowerCAmelCase		(		_lowerCAmelCase				: float						):




 """simple docstring"""







 if radius < 0:
  raise ValueError("vol_sphere() only accepts non-negative values"						)
 # Volume is 4/3 * pi * radius cubed
 return 4 / 3 * pi * pow(_lowerCAmelCase    ,				3						)



def     lowerCAmelCase		(		_lowerCAmelCase				: float						):




 """simple docstring"""







 if radius < 0:
  raise ValueError("vol_hemisphere() only accepts non-negative values"						)
 # Volume is radius cubed * pi * 2/3
 return pow(_lowerCAmelCase    ,				3						) * pi * 2 / 3



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or radius < 0:
  raise ValueError("vol_circular_cylinder() only accepts non-negative values"						)
 # Volume is radius squared * height * pi
 return pow(_lowerCAmelCase    ,				2						) * height * pi



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if inner_radius < 0 or outer_radius < 0 or height < 0:
  raise ValueError(
      "vol_hollow_circular_cylinder() only accepts non-negative values"						)
 if outer_radius <= inner_radius:
  raise ValueError("outer_radius must be greater than inner_radius"						)
 return pi * (pow(_lowerCAmelCase    ,				2						) - pow(_lowerCAmelCase    ,				2						)) * height



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if radius_a < 0 or radius_a < 0 or height < 0:
  raise ValueError("vol_conical_frustum() only accepts non-negative values"						)
 return (
     1
     / 3
     * pi
     * height
     * (pow(_lowerCAmelCase    ,				2						) + pow(_lowerCAmelCase    ,				2						) + radius_a * radius_a)
 )



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if torus_radius < 0 or tube_radius < 0:
  raise ValueError("vol_torus() only accepts non-negative values"						)
 return 2 * pow(_lowerCAmelCase    ,				2						) * torus_radius * pow(_lowerCAmelCase    ,				2						)



def     lowerCAmelCase		(		):




 """simple docstring"""







 print("Volumes:"						)
 print(F'''Cube: {vol_cube(2						) = }'''						)  # = 8
 print(F'''Cuboid: {vol_cuboid(2    ,				2    ,				2						) = }'''						)  # = 8
 print(F'''Cone: {vol_cone(2    ,				2						) = }'''						)  # ~= 1.33
 print(F'''Right Circular Cone: {vol_right_circ_cone(2    ,				2						) = }'''						)  # ~= 8.38
 print(F'''Prism: {vol_prism(2    ,				2						) = }'''						)  # = 4
 print(F'''Pyramid: {vol_pyramid(2    ,				2						) = }'''						)  # ~= 1.33
 print(F'''Sphere: {vol_sphere(2						) = }'''						)  # ~= 33.5
 print(F'''Hemisphere: {vol_hemisphere(2						) = }'''						)  # ~= 16.75
 print(F'''Circular Cylinder: {vol_circular_cylinder(2    ,				2						) = }'''						)  # ~= 25.1
 print(F'''Torus: {vol_torus(2    ,				2						) = }'''						)  # ~= 157.9
 print(F'''Conical Frustum: {vol_conical_frustum(2    ,				2    ,				4						) = }'''						)  # ~= 58.6
 print(F'''Spherical cap: {vol_spherical_cap(1    ,				2						) = }'''						)  # ~= 5.24
 print(F'''Spheres intersetion: {vol_spheres_intersect(2    ,				2    ,				1						) = }'''						)  # ~= 21.21
 print(F'''Spheres union: {vol_spheres_union(2    ,				2    ,				1						) = }'''						)  # ~= 45.81
 print(
     F'''Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1    ,				2    ,				3						) = }'''						)  # ~= 28.3


if __name__ == "__main__":
  main()





