

"""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
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 		A    (       snake_case__      ):




			'''simple docstring'''


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

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

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

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

						SCREAMING_SNAKE_CASE__									= 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.
			SCREAMING_SNAKE_CASE__									= [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"""




def 		A    (       snake_case__						,			snake_case__      ):




			'''simple docstring'''


			return a + b


if __name__ == "__main__":
						A_							:     List[str]     =	5
						A_							:     Optional[int]     =	6
						print(F'The sum of {a} + {b} is {add(a, b)}')


