'''simple docstring'''

from __future__ import annotations

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







  """simple docstring"""
  lowercase   :      int
  lowercase   :      TreeNode | None       =							None
  lowercase   :      TreeNode | None       =							None

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



def 							UpperCamelCase__			(			a__      ):


      '''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      )

            _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(a__      )
                + abs(a__      )
            )
            _lowerCAmelCase										=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 typing import Any
class   SCREAMING_SNAKE_CASE			:







		"""simple docstring"""






		def __init__(   self		,						__A				) ->     None:
								_lowerCAmelCase										=num_of_nodes
								_lowerCAmelCase										=[]
								_lowerCAmelCase										={}






		def 		UpperCamelCase__       (   self		,						__A		,						__A		,						__A				) ->     None:
								self.m_edges.append([u_node, v_node, weight]				)






		def 		UpperCamelCase__       (   self		,						__A				) ->     int:

								if self.m_component[u_node] == u_node:
														return u_node
								return self.find_component(self.m_component[u_node]				)






		def 		UpperCamelCase__       (   self		,						__A				) ->     None:

								if self.m_component[u_node] != u_node:
														for k in self.m_component:
																				_lowerCAmelCase										=self.find_component(__A				)






		def 		UpperCamelCase__       (   self		,						__A		,						__A		,						__A				) ->     None:

								if component_size[u_node] <= component_size[v_node]:
														_lowerCAmelCase										=v_node
														component_size[v_node] += component_size[u_node]
														self.set_component(__A				)

								elif component_size[u_node] >= component_size[v_node]:
														_lowerCAmelCase										=self.find_component(__A				)
														component_size[u_node] += component_size[v_node]
														self.set_component(__A				)






		def 		UpperCamelCase__       (   self				) ->     None:
								_lowerCAmelCase										=[]
								_lowerCAmelCase										=0

								_lowerCAmelCase										=[-1] * self.m_num_of_nodes

								# A list of components (initialized to all of the nodes)
								for node in range(self.m_num_of_nodes				):
														self.m_component.update({node: node}				)
														component_size.append(1				)

								_lowerCAmelCase										=self.m_num_of_nodes

								while num_of_components > 1:
														for edge in self.m_edges:
																				_lowerCAmelCase						,				_lowerCAmelCase						,				_lowerCAmelCase										=edge

																				_lowerCAmelCase										=self.m_component[u]
																				_lowerCAmelCase										=self.m_component[v]

																				if u_component != v_component:

																										for component in (u_component, v_component):
																																if (
																																    minimum_weight_edge[component] == -1
																																    or minimum_weight_edge[component][2] > w
																																):
																																						_lowerCAmelCase										=[u, v, w]

														for edge in minimum_weight_edge:
																				if isinstance(__A		,						__A				):
																										_lowerCAmelCase						,				_lowerCAmelCase						,				_lowerCAmelCase										=edge

																										_lowerCAmelCase										=self.m_component[u]
																										_lowerCAmelCase										=self.m_component[v]

																										if u_component != v_component:
																																mst_weight += w
																																self.union(__A		,						__A		,						__A				)
																																print(F'''Added edge [{u} - {v}]\nAdded weight: {w}\n'''				)
																																num_of_components -= 1

														_lowerCAmelCase										=[-1] * self.m_num_of_nodes
								print(F'''The total weight of the minimal spanning tree is: {mst_weight}'''				)



def 							UpperCamelCase__			(			):


						'''simple docstring'''








if __name__ == "__main__":
							import doctest

							doctest.testmod()





