def 					UpperCamelCase_						( snake_case_	:	dict						,		snake_case_	:	int				) ->					Dict:






 '''simple docstring'''

 if not root or root not in binary_tree_mirror_dictionary:
  return
 __lowerCAmelCase							,	__lowerCAmelCase    							=						binary_tree_mirror_dictionary[root][:2]
 __lowerCAmelCase    							=						[right_child, left_child]
 binary_tree_mirror_dict(snake_case_						,		snake_case_				)
 binary_tree_mirror_dict(snake_case_						,		snake_case_				)







def 					UpperCamelCase_						( snake_case_	:	dict						,		snake_case_	:	int = 1				) ->					dict:






 '''simple docstring'''

 if not binary_tree:
  raise ValueError("""binary tree cannot be empty"""				)
 if root not in binary_tree:
  __lowerCAmelCase    							=						f"""root {root} is not present in the binary_tree"""
  raise ValueError(snake_case_				)
 __lowerCAmelCase    							=						dict(snake_case_				)
 binary_tree_mirror_dict(snake_case_						,		snake_case_				)
 return binary_tree_mirror_dictionary


if __name__ == "__main__":
 _A      :				int 				=    {1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
 print(f'Binary tree: {binary_tree}')
 _A      :				Any 				=    binary_tree_mirror(binary_tree, 5)
 print(f'Binary tree mirror: {binary_tree_mirror_dictionary}')







'''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)






