
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								=					{
    '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_     (     _SCREAMING_SNAKE_CASE  )   ->      set[tuple[str, str]]:

							"""simple docstring"""






							_UpperCAmelCase  :			Optional[int]	       =		{node: {node} for node in graph}

							_UpperCAmelCase  :			Union[str, Any]	       =		{node: graph[node][:] for node in graph}

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

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

    # Find cutset.
							_UpperCAmelCase  :			str	       =		[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_     (     _SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )   ->      Dict:

							"""simple docstring"""






							if power < 0:
														return -1
							base %= mod
							_UpperCAmelCase  :			Optional[Any]	       =		1

							while power > 0:
														if power & 1:
																					_UpperCAmelCase  :			Optional[Any]	       =		(result * base) % mod
														_UpperCAmelCase  :			List[str]	       =		power >> 1
														_UpperCAmelCase  :			Optional[int]	       =		(base * base) % mod

							return result




def 		lowerCAmelCase_     (     )   ->      List[str]:

							"""simple docstring"""






							print(modular_exponential(3      ,	2_0_0      ,	1_3  )  )


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				main()




