


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  lowerCAmelCase__				(    a__:	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(a__ ) > 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(a__ )
														uv_neighbors.remove(a__ )
														_UpperCAmelCase					=    uv_neighbors
														for neighbor in uv_neighbors:
																					graph_copy[neighbor].append(a__ )

														_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(a__ )
																					if v in graph_copy[neighbor]:
																												graph_copy[neighbor].remove(a__ )

    # 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))




import warnings

from .generation import GenerationMixin

class 	__a   (       UpperCAmelCase    ):
		# warning at import time
		warnings.warn(
		    'Importing `GenerationMixin` from `src/transformers/generation_utils.py` is deprecated and will '
		    'be removed in Transformers v5. Import as `from transformers import GenerationMixin` instead.'					,   UpperCAmelCase					,   )
