




class 			__snake_case  :




					def __init__(       self   ,	__UpperCamelCase		)					->  None:



									'''simple docstring'''







									snake_case__ :     str 							=				data
									snake_case__ :     int 							=				42
									snake_case__ :     Tuple 							=				42




def 			UpperCamelCase__						(    A__   )       -> List[Any]:
				snake_case__ :     Union[str, Any] 							=				0
				snake_case__ :     Any 							=				x
def 			UpperCamelCase__						(    A__      ,			A__   )       -> Dict:
				snake_case__							,  snake_case__ :     Optional[Any] 							=				find_set(A_   ), find_set(A_   )
				if x == y:
								return

				elif x.rank > y.rank:
								snake_case__ :     Tuple 							=				x
				else:
								snake_case__ :     Dict 							=				y
								if x.rank == y.rank:
												y.rank += 1
def 			UpperCamelCase__						(    A__   )       -> Optional[int]:





				if x != x.parent:
								snake_case__ :     str 							=				find_set(x.parent   )
				return x.parent
def 			UpperCamelCase__						(    A__   )       -> List[str]:
				snake_case__ :     Optional[Any] 							=				({0, 1, 2}, {3, 4, 5})
				for s in sets:
								if node.data in s:
												return s
				snake_case__ :     Dict 							=				F"""{node.data} is not in {sets}"""
				raise ValueError(A_   )
def 			UpperCamelCase__						(    )       -> Dict:
				snake_case__ :     int 							=				[Node(A_   ) for i in range(6   )]
				for v in vertex:
								make_set(A_   )

				union_set(vertex[0]      ,			vertex[1]   )
				union_set(vertex[1]      ,			vertex[2]   )
				union_set(vertex[3]      ,			vertex[4]   )
				union_set(vertex[3]      ,			vertex[5]   )

				for nodea in vertex:
								for nodea in vertex:
												if find_python_set(A_   ).isdisjoint(find_python_set(A_   )   ):
																assert find_set(A_   ) != find_set(A_   )
												else:
																assert find_set(A_   ) == find_set(A_   )


if __name__ == "__main__":
				test_disjoint_set()



from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
lowerCAmelCase__					:       Dict		=       {
    '''1''': ['''2''', '''3''', '''4''', '''5'''],
    '''2''': ['''1''', '''3''', '''4''', '''5'''],
    '''3''': ['''1''', '''2''', '''4''', '''5''', '''10'''],
    '''4''': ['''1''', '''2''', '''3''', '''5''', '''6'''],
    '''5''': ['''1''', '''2''', '''3''', '''4''', '''7'''],
    '''6''': ['''7''', '''8''', '''9''', '''10''', '''4'''],
    '''7''': ['''6''', '''8''', '''9''', '''10''', '''5'''],
    '''8''': ['''6''', '''7''', '''9''', '''10'''],
    '''9''': ['''6''', '''7''', '''8''', '''10'''],
    '''10''': ['''6''', '''7''', '''8''', '''9''', '''3'''],
}
def 			UpperCamelCase__						(    A__   )       -> set[tuple[str, str]]:
				snake_case__ :     Tuple 							=				{node: {node} for node in graph}

				snake_case__ :     Tuple 							=				{node: graph[node][:] for node in graph}

				while len(A__   ) > 2:
								# Choose a random edge.
								snake_case__ :     Union[str, Any] 							=				random.choice(list(graph_copy.keys()   )   )
								snake_case__ :     Any 							=				random.choice(graph_copy[u]   )

								# Contract edge (u, v) to new node uv
								snake_case__ :     Tuple 							=				u + v
								snake_case__ :     Dict 							=				list(set(graph_copy[u] + graph_copy[v]   )   )
								uv_neighbors.remove(A__   )
								uv_neighbors.remove(A__   )
								snake_case__ :     Optional[Any] 							=				uv_neighbors
								for neighbor in uv_neighbors:
												graph_copy[neighbor].append(A__   )

								snake_case__ :     Tuple 							=				set(contracted_nodes[u].union(contracted_nodes[v]   )   )

								# Remove nodes u and v.
								del graph_copy[u]
								del graph_copy[v]
								for neighbor in uv_neighbors:
												if u in graph_copy[neighbor]:
																graph_copy[neighbor].remove(A__   )
												if v in graph_copy[neighbor]:
																graph_copy[neighbor].remove(A__   )

    # Find cutset.
				snake_case__ :     Tuple 							=				[contracted_nodes[node] for node in graph_copy]
				return {
				    (node, neighbor)
				    for node in groups[0]
				    for neighbor in graph[node]
				    if neighbor in groups[1]
				}


if __name__ == "__main__":
				print(partition_graph(TEST_GRAPH))


