
"""simple docstring"""
from __future__ import annotations

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



							'''simple docstring'''





							_snake_case			=						4_2
							_snake_case			=						None
							_snake_case			=						None
SCREAMING_SNAKE_CASE_ 			=     namedtuple('''CoinsDistribResult''', '''moves excess''')

def       lowercase			(_lowerCAmelCase		):

						if root is None:
												return 0

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

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

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

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

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

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

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

												__lowerCAmelCase					,			__lowerCAmelCase   					=   get_distrib(node.left		)
												__lowerCAmelCase					,			__lowerCAmelCase   					=   get_distrib(node.right		)

												__lowerCAmelCase   					=   1 - left_distrib_excess
												__lowerCAmelCase   					=   1 - right_distrib_excess

												__lowerCAmelCase   					=   (
												    left_distrib_moves
												    + right_distrib_moves
												    + abs(lowercase_		)
												    + abs(lowercase_		)
												)
												__lowerCAmelCase   					=   node.data - coins_to_left - coins_to_right

												return CoinsDistribResult(lowercase_      ,  lowercase_		)

						return get_distrib(lowercase_		)[0]


if __name__ == "__main__":
			import doctest

			doctest.testmod()






from __future__ import annotations







def SCREAMING_SNAKE_CASE				(       lowercase_ ,				lowercase_ ,				lowercase_						)   ->       tuple[float, list[float]]:



       """simple docstring"""

       A__       =    list(range(len(lowercase_						)						)						)
       A__       =    [v / w for v, w in zip(lowercase_ ,				lowercase_						)]
       index.sort(key=lambda lowercase_						: ratio[i] ,				reverse=lowercase_						)

       A__       =    0
       A__       =    [0] * len(lowercase_						)
       for i in index:
              if weight[i] <= capacity:
                     A__       =    1
                     max_value += value[i]
                     capacity -= weight[i]
              else:
                     A__       =    capacity / weight[i]
                     max_value += value[i] * capacity / weight[i]
                     break

       return max_value, fractions


if __name__ == "__main__":
  import doctest

  doctest.testmod()


