
"""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
__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     _lowerCamelCase(__UpperCamelCase       )				-> set[tuple[str, str]]:
	_lowerCAmelCase								={node: {node} for node in graph}

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

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

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

		_lowerCAmelCase								=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								=[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))





"""simple docstring"""


from .hash_table import HashTable







class 		lowerCamelCase__					(					__magic_name__				):





			'''simple docstring'''



			def __init__(							self     ,     *__UpperCAmelCase     ,     **__UpperCAmelCase  ) ->     List[str]:
				super().__init__(*__UpperCAmelCase     ,     **__UpperCAmelCase  )



			def 					_lowerCAmelCase		(							self     ,     __UpperCAmelCase     ,     __UpperCAmelCase=None  ) ->     Union[str, Any]:
				_lowerCAmelCase								=1
				_lowerCAmelCase								=self.hash_function(key + i * i  )

				while self.values[new_key] is not None and self.values[new_key] != key:
					i += 1
					_lowerCAmelCase								=(
					    self.hash_function(key + i * i  )
					    if not self.balanced_factor() >= self.lim_charge
					    else None
					)

					if new_key is None:
						break

				return new_key



