






'''simple docstring'''


def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__       ,		SCREAMING_SNAKE_CASE__		):






 if not root or root not in binary_tree_mirror_dictionary:
  return
 __a    :	List[Any]									=						binary_tree_mirror_dictionary[root][:2]
 __a    :	Tuple									=						[right_child, left_child]
 binary_tree_mirror_dict(UpperCAmelCase_       ,		UpperCAmelCase_		)
 binary_tree_mirror_dict(UpperCAmelCase_       ,		UpperCAmelCase_		)






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__       ,		SCREAMING_SNAKE_CASE__ = 1		):






 if not binary_tree:
  raise ValueError('binary tree cannot be empty'		)
 if root not in binary_tree:
  __a    :	List[str]									=						f'''root {root} is not present in the binary_tree'''
  raise ValueError(UpperCAmelCase_		)
 __a    :	Dict									=						dict(UpperCAmelCase_		)
 binary_tree_mirror_dict(UpperCAmelCase_       ,		UpperCAmelCase_		)
 return binary_tree_mirror_dictionary


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












'''simple docstring'''


import math
from timeit import timeit






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__		):
 __a    :	Any									=						0
 __a    :	List[Any]									=						abs(SCREAMING_SNAKE_CASE__		)
 while True:
  __a    :	int									=						n // 10
  digits += 1
  if n == 0:
   break
 return digits






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__		):
 return 1 if n == 0 else math.floor(math.log(abs(SCREAMING_SNAKE_CASE__		)       ,		10		) + 1		)






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__		):
 return len(str(abs(SCREAMING_SNAKE_CASE__		)		)		)






def   lowerCAmelCase__			(					):
 from collections.abc import Callable

 def benchmark_a_function(SCREAMING_SNAKE_CASE__       ,		SCREAMING_SNAKE_CASE__		) -> None:
  __a    :	Tuple									=						f'''{func.__name__}({value})'''
  __a    :	List[Any]									=						timeit(f'''__main__.{call}'''       ,		setup='import __main__'		)
  print(f'''{call}: {func(SCREAMING_SNAKE_CASE__		)} -- {timing} seconds'''		)

 for value in (262144, 1125899906842624, 1267650600228229401496703205376):
  for func in (num_digits, num_digits_fast, num_digits_faster):
   benchmark_a_function(SCREAMING_SNAKE_CASE__       ,		SCREAMING_SNAKE_CASE__		)
  print()


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  benchmark()




