
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
lowercase__						: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 			UpperCamelCase       (				lowerCAmelCase__						):
					'''simple docstring'''
					lowercase		      =		{node: {node} for node in graph}

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

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

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

										lowercase		      =		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(lowerCAmelCase__						)
															if v in graph_copy[neighbor]:
																				graph_copy[neighbor].remove(lowerCAmelCase__						)

    # Find cutset.
					lowercase		      =		[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 torch

from accelerate import Accelerator, DistributedType







class 							lowercase						:




							def __enter__(							self):
												if self.enabled:
																	lowercase		      =		self.model.no_sync()
																	self.model_sync_obj.__enter__()

												return self




							def __exit__(							self  ,A__  ,A__  ,A__):
												if self.enabled:
																	# Average all models on exit
																	self._sync_and_avg_model_params()
																	self.model_sync_obj.__exit__(A__  ,A__  ,A__)




							def __init__(							self  ,A__  ,A__  ,A__  ,A__ = True):
												if accelerator.distributed_type not in [
												    DistributedType.NO,
												    DistributedType.MULTI_CPU,
												    DistributedType.MULTI_GPU,
												]:
																	raise NotImplementedError('''LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)''')
												lowercase		      =		enabled and accelerator.distributed_type != DistributedType.NO
												lowercase		      =		0
												if self.enabled:
																	lowercase		      =		accelerator
																	lowercase		      =		model
																	lowercase		      =		local_sgd_steps




							def 					A__ (							self):
												self.num_steps += 1
												if not self.enabled:
																	return

												if self.num_steps % self.local_sgd_steps == 0:
																	self._sync_and_avg_model_params()





							def 					A__ (							self):
												self.accelerator.wait_for_everyone()
												with self.accelerator.autocast():
																	for param in self.model.parameters():
																						lowercase		      =		self.accelerator.reduce(param.data  ,reduction='''mean''')




