code: 
  
  
  
  
  
  
  """simple docstring"""
  
  import math
  
  import torch
  from torch import nn
  from torch.nn import init
  
  from .binarizer import MagnitudeBinarizer, ThresholdBinarizer, TopKBinarizer
  
  
  class 	__lowerCamelCase       (				nn.Linear    ):
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  		def __init__(     self							:			Any		,    a_							:			int		,    a_							:			int		,    a_							:			bool = True		,    a_							:			str = "constant"		,    a_							:			float = 0.0		,    a_							:			str = "topK"		,    ):
  				super(a_		,    self			).__init__(in_features=a_		,    out_features=a_		,    bias=a_			)
  				assert pruning_method in ["topK", "threshold", "sigmoied_threshold", "magnitude", "l0"]
  				lowerCAmelCase_     :							Union[str, Any]             =    pruning_method
  
  				if self.pruning_method in ["topK", "threshold", "sigmoied_threshold", "l0"]:
  						lowerCAmelCase_     :							List[str]             =    mask_scale
  						lowerCAmelCase_     :							Optional[Any]             =    mask_init
  						lowerCAmelCase_     :							str             =    nn.Parameter(torch.empty(self.weight.size()			)			)
  						self.init_mask()
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Union[str, Any]			):
  				if self.mask_init == "constant":
  						init.constant_(self.mask_scores		,    val=self.mask_scale			)
  				elif self.mask_init == "uniform":
  						init.uniform_(self.mask_scores		,    a=-self.mask_scale		,    b=self.mask_scale			)
  				elif self.mask_init == "kaiming":
  						init.kaiming_uniform_(self.mask_scores		,    a=math.sqrt(5			)			)
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Union[str, Any]		,    a_							:			torch.tensor		,    a_							:			float			):
  				# Get the mask
  				if self.pruning_method == "topK":
  						lowerCAmelCase_     :							Optional[Any]             =    TopKBinarizer.apply(self.mask_scores		,    a_			)
  				elif self.pruning_method in ["threshold", "sigmoied_threshold"]:
  						lowerCAmelCase_     :							Dict             =    "sigmoied" in self.pruning_method
  						lowerCAmelCase_     :							int             =    ThresholdBinarizer.apply(self.mask_scores		,    a_		,    a_			)
  				elif self.pruning_method == "magnitude":
  						lowerCAmelCase_     :							Tuple             =    MagnitudeBinarizer.apply(self.weight		,    a_			)
  				elif self.pruning_method == "l0":
  						lowerCAmelCase_       ,			lowerCAmelCase_       ,			lowerCAmelCase_     :							List[Any]             =    -0.1, 1.1, 2 / 3
  						if self.training:
  								lowerCAmelCase_     :							int             =    torch.zeros_like(self.mask_scores			).uniform_().clamp(0.0001		,    0.9999			)
  								lowerCAmelCase_     :							Dict             =    torch.sigmoid((u.log() - (1 - u).log() + self.mask_scores) / b			)
  						else:
  								lowerCAmelCase_     :							Dict             =    torch.sigmoid(self.mask_scores			)
  						lowerCAmelCase_     :							Optional[Any]             =    s * (r - l) + l
  						lowerCAmelCase_     :							str             =    s_bar.clamp(min=0.0		,    max=1.0			)
  				# Mask weights with computed mask
  				lowerCAmelCase_     :							List[str]             =    mask * self.weight
  				# Compute output (linear layer) with masked weights
  				return nn.functional.linear(a_		,    a_		,    self.bias			)
  
style_context: 
  
  
  
  
  
  
  """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
  lowercase__      =				{
      """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			(						__UpperCamelCase )		->					set[tuple[str, str]]:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		lowerCAmelCase_     :							Union[str, Any]             =    {node: {node} for node in graph}
  
  		lowerCAmelCase_     :							List[str]             =    {node: graph[node][:] for node in graph}
  
  		while len(__UpperCamelCase ) > 2:
  				# Choose a random edge.
  				lowerCAmelCase_     :							int             =    random.choice(list(graph_copy.keys() ) )
  				lowerCAmelCase_     :							Any             =    random.choice(graph_copy[u] )
  
  				# Contract edge (u, v) to new node uv
  				lowerCAmelCase_     :							Union[str, Any]             =    u + v
  				lowerCAmelCase_     :							List[Any]             =    list(set(graph_copy[u] + graph_copy[v] ) )
  				uv_neighbors.remove(__UpperCamelCase )
  				uv_neighbors.remove(__UpperCamelCase )
  				lowerCAmelCase_     :							str             =    uv_neighbors
  				for neighbor in uv_neighbors:
  						graph_copy[neighbor].append(__UpperCamelCase )
  
  				lowerCAmelCase_     :							Optional[int]             =    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(__UpperCamelCase )
  						if v in graph_copy[neighbor]:
  								graph_copy[neighbor].remove(__UpperCamelCase )
  
      # Find cutset.
  		lowerCAmelCase_     :							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))
  