"""simple docstring"""






from __future__ import annotations

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




					"""simple docstring"""

					snake_case__				    = 42
					snake_case__				    = None
					snake_case__				    = None






lowerCAmelCase__  :  Union[str, Any]						     =	namedtuple('CoinsDistribResult', 'moves excess')



def   a_						(					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(lowerCamelCase       ) != count_coins(lowerCamelCase       ):
								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       )

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

								UpperCAmelCase__             =							1 - left_distrib_excess
								UpperCAmelCase__             =							1 - right_distrib_excess

								UpperCAmelCase__             =							(
								    left_distrib_moves
								    + right_distrib_moves
								    + abs(lowerCamelCase       )
								    + abs(lowerCamelCase       )
								)
								UpperCAmelCase__             =							node.data - coins_to_left - coins_to_right

								return CoinsDistribResult(lowerCamelCase					,			lowerCamelCase       )

				return get_distrib(lowerCamelCase       )[0]


if __name__ == "__main__":
						import doctest

						doctest.testmod()










'''simple docstring'''




import random






def        _lowerCAmelCase			(  __snake_case  : int ,							__snake_case  : float ,							__snake_case  : bool = False			)     ->     dict:
     __A						: dict      =       {i: [] for i in range(__snake_case			)}

     # if probability is greater or equal than 1, then generate a complete graph
     if probability >= 1:
          return complete_graph(__snake_case			)
     # if probability is lower or equal than 0, then return a graph without edges
     if probability <= 0:
          return graph

     # for each couple of nodes, add an edge from u to v
     # if the number randomly generated is greater than probability probability
     for i in range(__snake_case			):
          for j in range(i + 1 ,							__snake_case			):
               if random.random() < probability:
                    graph[i].append(__snake_case			)
                    if not directed:
                         # if the graph is undirected, add an edge in from j to i, either
                         graph[j].append(__snake_case			)
     return graph






def        _lowerCAmelCase			(  __snake_case  : int			)     ->     dict:
     return {
         i: [j for j in range(__snake_case			) if i != j] for i in range(__snake_case			)
     }


if __name__ == "__main__":
  import doctest

  doctest.testmod()