





"""simple docstring"""



from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass
@dataclass
class 					__magic_name__		:
       __A			:      int
       __A			:      TreeNode | None        =   None
       __A			:      TreeNode | None        =   None







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






def       lowerCamelCase					(a_						:TreeNode | None)     ->							int:

       if root is None:
              return 0

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

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

       def count_coins(a_						:TreeNode | None) -> 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_						:TreeNode | None) -> CoinsDistribResult:

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

              lowercase		:List[Any]       							=				get_distrib(node.left)
              lowercase		:List[str]       							=				get_distrib(node.right)

              lowercase		:str       							=				1 - left_distrib_excess
              lowercase		:List[str]       							=				1 - right_distrib_excess

              lowercase		:Any       							=				(
                  left_distrib_moves
                  + right_distrib_moves
                  + abs(a_)
                  + abs(a_)
              )
              lowercase		:Tuple       							=				node.data - coins_to_left - coins_to_right

              return CoinsDistribResult(a_				,				a_)

       return get_distrib(a_)[0]


if __name__ == "__main__":
 import doctest

 doctest.testmod()





"""simple docstring"""



from __future__ import annotations

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






def       lowerCamelCase					()     ->							tuple[list[int], int]:
       lowercase		:Any       							=				[randint(-1000				,				1000) for i in range(10)]
       lowercase		:Any       							=				randint(-5000				,				5000)
       return (arr, r)


UpperCAmelCase      		=			make_dataset()






def       lowerCamelCase					(a_						:list[int]				,				a_						:int)     ->							tuple[int, ...]:
       for triplet in permutations(a_				,				3):
              if sum(a_) == target:
                     return tuple(sorted(a_))
       return (0, 0, 0)






def       lowerCamelCase					(a_						:list[int]				,				a_						:int)     ->							tuple[int, int, int]:
       arr.sort()
       lowercase		:Union[str, Any]       							=				len(a_)
       for i in range(n - 1):
              lowercase							,  lowercase		:Union[str, Any]       							=				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       lowerCamelCase					()     ->							tuple[float, float]:
       lowercase		:int       							=				'''
from __main__ import dataset, triplet_sum1, triplet_sum2
'''
       lowercase		:Optional[Any]       							=				'''
triplet_sum1(*dataset)
'''
       lowercase		:Union[str, Any]       							=				'''
triplet_sum2(*dataset)
'''
       lowercase		:Dict       							=				repeat(setup=a_				,				stmt=a_				,				repeat=5				,				number=1_0000)
       lowercase		:Optional[int]       							=				repeat(setup=a_				,				stmt=a_				,				repeat=5				,				number=1_0000)
       return (min(a_), min(a_))


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

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

