


'''simple docstring'''
from __future__ import annotations

from itertools import permutations
from random import randint
from timeit import repeat


def      a (     )    ->      tuple[list[int], int]:



					'''simple docstring'''






					UpperCamelCase__  :int				   =					[randint(-1000					,   1000  ) for i in range(10  )]
					UpperCamelCase__  :Tuple				   =					randint(-5000					,   5000  )
					return (arr, r)


__snake_case				 =	make_dataset()


def      a (     __a					,   __a  )    ->      tuple[int, ...]:



					'''simple docstring'''






					for triplet in permutations(__a					,   3  ):
										if sum(__a  ) == target:
															return tuple(sorted(__a  )  )
					return (0, 0, 0)


def      a (     __a					,   __a  )    ->      tuple[int, int, int]:



					'''simple docstring'''






					arr.sort()
					UpperCamelCase__  :Optional[int]				   =					len(__a  )
					for i in range(n - 1  ):
										UpperCamelCase__   ,							UpperCamelCase__  :Tuple				   =					i + 1, n - 1
										while left < right:
															if arr[i] + arr[left] + arr[right] == target:
																				return (arr[i], arr[left], arr[right])
															elif arr[i] + arr[left] + arr[right] < target:
																				left += 1
															elif arr[i] + arr[left] + arr[right] > target:
																				right -= 1
					return (0, 0, 0)


def      a (     )    ->      tuple[float, float]:



					'''simple docstring'''






					UpperCamelCase__  :List[Any]				   =					'''
from __main__ import dataset, triplet_sum1, triplet_sum2
'''
					UpperCamelCase__  :List[Any]				   =					'''
triplet_sum1(*dataset)
'''
					UpperCamelCase__  :Dict				   =					'''
triplet_sum2(*dataset)
'''
					UpperCamelCase__  :List[str]				   =					repeat(setup=__a					,   stmt=__a					,   repeat=5					,   number=10000  )
					UpperCamelCase__  :str				   =					repeat(setup=__a					,   stmt=__a					,   repeat=5					,   number=10000  )
					return (min(__a  ), min(__a  ))


if __name__ == "__main__":
		from doctest import testmod

		testmod()
		__snake_case				 =	solution_times()
		print(F"""The time for naive implementation is {times[0]}.""")
		print(F"""The time for optimized implementation is {times[1]}.""")



'''simple docstring'''
from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass
@dataclass
class   lowercase      :

		"""simple docstring"""

		_a       					=							42
		_a       					=							None
		_a       					=							None



__snake_case				 =	namedtuple('''CoinsDistribResult''', '''moves excess''')


def      a (     __a  )    ->      int:



					'''simple docstring'''






					if root is None:
										return 0

					# Validation
					def count_nodes(__a  ) -> int:
										if node is None:
															return 0

										return count_nodes(node.left  ) + count_nodes(node.right  ) + 1

					def count_coins(__a  ) -> int:
										if node is None:
															return 0

										return count_coins(node.left  ) + count_coins(node.right  ) + node.data

					if count_nodes(__a  ) != count_coins(__a  ):
										raise ValueError('''The nodes number should be same as the number of coins'''  )

					# Main calculation
					def get_distrib(__a  ) -> CoinsDistribResult:

										if node is None:
															return CoinsDistribResult(0					,   1  )

										UpperCamelCase__   ,							UpperCamelCase__  :Optional[Any]				   =					get_distrib(node.left  )
										UpperCamelCase__   ,							UpperCamelCase__  :Union[str, Any]				   =					get_distrib(node.right  )

										UpperCamelCase__  :Tuple				   =					1 - left_distrib_excess
										UpperCamelCase__  :Optional[int]				   =					1 - right_distrib_excess

										UpperCamelCase__  :int				   =					(
										    left_distrib_moves
										    + right_distrib_moves
										    + abs(__a  )
										    + abs(__a  )
										)
										UpperCamelCase__  :Optional[Any]				   =					node.data - coins_to_left - coins_to_right

										return CoinsDistribResult(__a					,   __a  )

					return get_distrib(__a  )[0]


if __name__ == "__main__":
		import doctest

		doctest.testmod()