


from __future__ import annotations

from typing import Any




class       lowercase_					:





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





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





				def 						__UpperCamelCase    (				self       ,  lowercase_)  -> int:

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





				def 						__UpperCamelCase    (				self       ,  lowercase_)  -> None:

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





				def 						__UpperCamelCase    (				self       ,  lowercase_       ,  lowercase_       ,  lowercase_)  -> None:

											if component_size[u_node] <= component_size[v_node]:
																		a__      =v_node
																		component_size[v_node] += component_size[u_node]
																		self.set_component(lowercase_)

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





				def 						__UpperCamelCase    (				self)  -> None:
											a__      =[]
											a__      =0

											a__      =[-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)

											a__      =self.m_num_of_nodes

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

																									a__      =self.m_component[u]
																									a__      =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
																																							):
																																														a__      =[u, v, w]

																		for edge in minimum_weight_edge:
																									if isinstance(lowercase_       ,  lowercase_):
																																a__    ,     a__    ,     a__      =edge

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

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

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







def   _lowercase(					):
							pass


if __name__ == "__main__":
	import doctest

	doctest.testmod()



def   __lowerCAmelCase    (				UpperCAmelCase__					:   int							)	->     int:

							if not isinstance(UpperCAmelCase__      ,					UpperCAmelCase__							):
														raise ValueError("""multiplicative_persistence() only accepts integral values"""							)
							if num < 0:
														raise ValueError("""multiplicative_persistence() does not accept negative values"""							)

							lowerCamelCase_					=       0
							lowerCamelCase_					=       str(UpperCAmelCase__							)

							while len(UpperCAmelCase__							) != 1:
														lowerCamelCase_					=       [int(UpperCAmelCase__							) for i in num_string]

														lowerCamelCase_					=       1
														for i in range(0      ,					len(UpperCAmelCase__							)							):
																					total *= numbers[i]

														lowerCamelCase_					=       str(UpperCAmelCase__							)

														steps += 1
							return steps



def   __lowerCAmelCase    (				UpperCAmelCase__					:   int							)	->     int:

							if not isinstance(UpperCAmelCase__      ,					UpperCAmelCase__							):
														raise ValueError("""additive_persistence() only accepts integral values"""							)
							if num < 0:
														raise ValueError("""additive_persistence() does not accept negative values"""							)

							lowerCamelCase_					=       0
							lowerCamelCase_					=       str(UpperCAmelCase__							)

							while len(UpperCAmelCase__							) != 1:
														lowerCamelCase_					=       [int(UpperCAmelCase__							) for i in num_string]

														lowerCamelCase_					=       0
														for i in range(0      ,					len(UpperCAmelCase__							)							):
																					total += numbers[i]

														lowerCamelCase_					=       str(UpperCAmelCase__							)

														steps += 1
							return steps


if __name__ == "__main__":
		import doctest

		doctest.testmod()





