




"""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
_lowerCamelCase					:     Tuple				       =    {
    '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_ ( _UpperCAmelCase		):




	"""simple docstring"""






	A_					:			int						=						{node: {node} for node in graph}

	A_					:			Any						=						{node: graph[node][:] for node in graph}

	while len(_SCREAMING_SNAKE_CASE		) > 2:
		# Choose a random edge.
		A_					:			int						=						random.choice(list(graph_copy.keys()		)		)
		A_					:			Any						=						random.choice(graph_copy[u]		)

		# Contract edge (u, v) to new node uv
		A_					:			Any						=						u + v
		A_					:			List[str]						=						list(set(graph_copy[u] + graph_copy[v]		)		)
		uv_neighbors.remove(_SCREAMING_SNAKE_CASE		)
		uv_neighbors.remove(_SCREAMING_SNAKE_CASE		)
		A_					:			Tuple						=						uv_neighbors
		for neighbor in uv_neighbors:
			graph_copy[neighbor].append(_SCREAMING_SNAKE_CASE		)

		A_					:			str						=						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(_SCREAMING_SNAKE_CASE		)
			if v in graph_copy[neighbor]:
				graph_copy[neighbor].remove(_SCREAMING_SNAKE_CASE		)

    # Find cutset.
	A_					:			Union[str, Any]						=						[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 .chunk_utils import chunk_layer
from .data_transforms import make_atomaa_masks
from .feats import atomaa_to_atomaa, frames_and_literature_positions_to_atomaa_pos, torsion_angles_to_frames
from .loss import compute_predicted_aligned_error, compute_tm
from .protein import Protein as OFProtein
from .protein import to_pdb
from .rigid_utils import Rigid, Rotation
from .tensor_utils import dict_multimap, flatten_final_dims, permute_final_dims





