






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
__UpperCAmelCase										=		{
    '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   lowercase__   (  __snake_case					:							dict[str, list[str]]						):


					'''simple docstring'''


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

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

					while len(__snake_case						) > 2:
										# Choose a random edge.
										UpperCAmelCase_					:   Any   =		random.choice(list(graph_copy.keys()						)						)
										UpperCAmelCase_					:   Union[str, Any]   =		random.choice(graph_copy[u]						)

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

										UpperCAmelCase_					:   List[Any]   =		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(__snake_case						)
															if v in graph_copy[neighbor]:
																				graph_copy[neighbor].remove(__snake_case						)

    # Find cutset.
					UpperCAmelCase_					:   Tuple   =		[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))














from typing import TYPE_CHECKING

from ...utils import _LazyModule


__UpperCAmelCase										=		{'tokenization_phobert': ['PhobertTokenizer']}


if TYPE_CHECKING:
		from .tokenization_phobert import PhobertTokenizer

else:
		import sys

		__UpperCAmelCase										=		_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)






