






"""simple docstring"""

class 	__lowerCamelCase       :





		'''simple docstring'''






		def __init__(     self							:			Optional[Any]		,    a_							:			str=None			):
				lowerCAmelCase_     :							Optional[Any]             =    data
				lowerCAmelCase_     :							Optional[int]             =    None





		def __repr__(     self							:			Optional[Any]			):
				lowerCAmelCase_     :							str             =    ""
				lowerCAmelCase_     :							str             =    self
				while temp:
						string_rep += f'''<{temp.data}> ---> '''
						lowerCAmelCase_     :							Tuple             =    temp.next
				string_rep += "<END>"
				return string_rep







def 	__lowerCamelCase			(						__UpperCamelCase )		->					Optional[int]:

		"""simple docstring"""







		if not elements_list:
				raise Exception("The Elements List is empty" )

		# Set first element as Head
		lowerCAmelCase_     :							Any             =    Node(elements_list[0] )
		lowerCAmelCase_     :							List[str]             =    head
		# Loop through elements from position 1
		for data in elements_list[1:]:
				lowerCAmelCase_     :							Tuple             =    Node(__UpperCamelCase )
				lowerCAmelCase_     :							Any             =    current.next
		return head


lowercase__      =				[1, 3, 5, 32, 44, 12, 43]
print(F"""List: {list_data}""")
print("""Creating Linked List from List.""")
lowercase__      =				make_linked_list(list_data)
print("""Linked List:""")



print(linked_list)








"""simple docstring"""

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
lowercase__      =				{
    """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 	__lowerCamelCase			(						__UpperCamelCase )		->					set[tuple[str, str]]:

		"""simple docstring"""







		lowerCAmelCase_     :							Union[str, Any]             =    {node: {node} for node in graph}

		lowerCAmelCase_     :							List[str]             =    {node: graph[node][:] for node in graph}

		while len(__UpperCamelCase ) > 2:
				# Choose a random edge.
				lowerCAmelCase_     :							int             =    random.choice(list(graph_copy.keys() ) )
				lowerCAmelCase_     :							Any             =    random.choice(graph_copy[u] )

				# Contract edge (u, v) to new node uv
				lowerCAmelCase_     :							Union[str, Any]             =    u + v
				lowerCAmelCase_     :							List[Any]             =    list(set(graph_copy[u] + graph_copy[v] ) )
				uv_neighbors.remove(__UpperCamelCase )
				uv_neighbors.remove(__UpperCamelCase )
				lowerCAmelCase_     :							str             =    uv_neighbors
				for neighbor in uv_neighbors:
						graph_copy[neighbor].append(__UpperCamelCase )

				lowerCAmelCase_     :							Optional[int]             =    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(__UpperCamelCase )
						if v in graph_copy[neighbor]:
								graph_copy[neighbor].remove(__UpperCamelCase )

    # Find cutset.
		lowerCAmelCase_     :							Union[str, Any]             =    [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))
