






"""simple docstring"""


_UpperCamelCase				:    Any     =						{hex(i)[2:]: i for i in range(16)}  # Use [:2] to strip off the leading '0x'




def 			snake_case  (A_      :str      ):







  '''simple docstring'''

  a     :			str				=   hex_string.strip().lower()
  if not hex_string:
    raise ValueError('Empty string was passed to the function'      )
  a     :			int				=   hex_string[0] == '-'
  if is_negative:
    a     :			List[str]				=   hex_string[1:]
  if not all(char in hex_table for char in hex_string      ):
    raise ValueError('Non-hexadecimal value was passed to the function'      )
  a     :			Optional[int]				=   0
  for char in hex_string:
    a     :			Optional[int]				=   1_6 * decimal_number + hex_table[char]
  return -decimal_number if is_negative else decimal_number


if __name__ == "__main__":
   from doctest import testmod

   testmod()









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
__A				    =						{
    '''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        __a     (    lowerCAmelCase_   :					dict[str, list[str]]				)      -> set[tuple[str, str]]:






						'''simple docstring'''



						UpperCAmelCase_=   {node: {node} for node in graph}

						UpperCAmelCase_=   {node: graph[node][:] for node in graph}

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

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

												UpperCAmelCase_=   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(lowerCAmelCase_				)
																		if v in graph_copy[neighbor]:
																								graph_copy[neighbor].remove(lowerCAmelCase_				)

    # Find cutset.
						UpperCAmelCase_=   [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))




