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_:      Any        =			{
    '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			(  _A					):



							"""simple docstring"""


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

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

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

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

														_lowercase				=	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.
							_lowercase				=	[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))



def 					__lowerCAmelCase			(  _A					):



							"""simple docstring"""


							if len(_A					) <= 1:
														return data
							else:
														return [
														    *quick_sort([e for e in data[1:] if e <= data[0]]					),
														    data[0],
														    *quick_sort([e for e in data[1:] if e > data[0]]					),
														]


if __name__ == "__main__":
				import doctest

				doctest.testmod()


