from __future__ import annotations

from math import pi, pow







def 					UpperCamelCase_						( snake_case_	:	int | float				) ->					List[str]:






 '''simple docstring'''

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







def 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float				) ->					Any:






 '''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(snake_case_						,		2				) * (3 * radius - height)







def 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float						,		snake_case_	:	float				) ->					Optional[Any]:






 '''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(snake_case_						,		snake_case_				)				)

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

 return vol_spherical_cap(snake_case_						,		snake_case_				) + vol_spherical_cap(snake_case_						,		snake_case_				)







def 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float						,		snake_case_	:	float				) ->					Union[str, Any]:






 '''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(snake_case_						,		snake_case_				)				)

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







def 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float						,		snake_case_	:	float				) ->					Optional[Any]:






 '''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 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float				) ->					Union[str, Any]:






 '''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 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float				) ->					List[str]:






 '''simple docstring'''

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







def 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float				) ->					Optional[int]:






 '''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 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float				) ->					Any:






 '''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 					UpperCamelCase_						( snake_case_	:	float				) ->					Optional[Any]:






 '''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(snake_case_						,		3				)







def 					UpperCamelCase_						( snake_case_	:	float				) ->					str:






 '''simple docstring'''

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







def 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float				) ->					List[Any]:






 '''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(snake_case_						,		2				) * height * pi







def 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float						,		snake_case_	:	float				) ->					str:






 '''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(snake_case_						,		2				) - pow(snake_case_						,		2				)) * height







def 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float						,		snake_case_	:	float				) ->					int:






 '''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(snake_case_						,		2				) + pow(snake_case_						,		2				) + radius_a * radius_a)
 )







def 					UpperCamelCase_						( snake_case_	:	float						,		snake_case_	:	float				) ->					Optional[Any]:






 '''simple docstring'''

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







def 					UpperCamelCase_						( ) ->					Optional[Any]:






 '''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()







'''simple docstring'''

import functools
from math import sqrt
from time import time







def 					UpperCamelCase_						( snake_case_	:	Dict						,		*snake_case_	:	Union[str, Any]						,		**snake_case_	:	List[str]				) ->					List[str]:






 '''simple docstring'''

 __lowerCAmelCase    							=						time()
 __lowerCAmelCase    							=						func(*snake_case_						,		**snake_case_				)
 __lowerCAmelCase    							=						time()
 if int(end - start				) > 0:
  print(f"""{func.__name__} runtime: {(end - start):0.4f} s"""				)
 else:
  print(f"""{func.__name__} runtime: {(end - start) * 10_00:0.4f} ms"""				)
 return output







def 					UpperCamelCase_						( snake_case_	:	int				) ->					list[int]:






 '''simple docstring'''

 if n < 0:
  raise Exception("""n is negative"""				)
 if n == 0:
  return [0]
 __lowerCAmelCase    							=						[0, 1]
 for _ in range(n - 1				):
  fib.append(fib[-1] + fib[-2]				)
 return fib







def 					UpperCamelCase_						( snake_case_	:	int				) ->					list[int]:






 '''simple docstring'''

 def fib_recursive_term(snake_case_	:	int				) -> int:
  if i < 0:
   raise Exception("""n is negative"""				)
  if i < 2:
   return i
  return fib_recursive_term(i - 1				) + fib_recursive_term(i - 2				)

 if n < 0:
  raise Exception("""n is negative"""				)
 return [fib_recursive_term(snake_case_				) for i in range(n + 1				)]







def 					UpperCamelCase_						( snake_case_	:	int				) ->					list[int]:






 '''simple docstring'''

 @functools.cache
 def fib_recursive_term(snake_case_	:	int				) -> int:
  if i < 0:
   raise Exception("""n is negative"""				)
  if i < 2:
   return i
  return fib_recursive_term(i - 1				) + fib_recursive_term(i - 2				)

 if n < 0:
  raise Exception("""n is negative"""				)
 return [fib_recursive_term(snake_case_				) for i in range(n + 1				)]







def 					UpperCamelCase_						( snake_case_	:	int				) ->					list[int]:






 '''simple docstring'''

 if n < 0:
  raise Exception("""n is negative"""				)
 # Cache must be outside recursuive function
 # other it will reset every time it calls itself.
 __lowerCAmelCase    							=						{0: 0, 1: 1, 2: 1}  # Prefilled cache

 def rec_fn_memoized(snake_case_	:	int				) -> int:
  if num in cache:
   return cache[num]

  __lowerCAmelCase    							=						rec_fn_memoized(num - 1				) + rec_fn_memoized(num - 2				)
  __lowerCAmelCase    							=						value
  return value

 return [rec_fn_memoized(snake_case_				) for i in range(n + 1				)]







def 					UpperCamelCase_						( snake_case_	:	int				) ->					list[int]:






 '''simple docstring'''

 if n < 0:
  raise Exception("""n is negative"""				)
 if n >= 14_75:
  raise Exception("""n is too large"""				)
 __lowerCAmelCase    							=						sqrt(5				)
 __lowerCAmelCase    							=						(1 + sqrt_a) / 2
 return [round(phi**i / sqrt_a				) for i in range(n + 1				)]


if __name__ == "__main__":
 _A      :				Optional[Any] 				=    30
 time_func(fib_iterative, num)
 time_func(fib_recursive, num)  # Around 3s runtime
 time_func(fib_recursive_cached, num)  # Around 0ms runtime
 time_func(fib_memoization, num)
 time_func(fib_binet, num)






