






import inspect
import warnings

import torch

from .state import AcceleratorState, GradientState
from .utils import DistributedType, honor_type, is_tpu_available


if is_tpu_available(check_device=False):
      import torch_xla.core.xla_model as xm





def 						A_					(						lowercase_	,  lowercase_			)				->Tuple:







 """simple docstring"""

 if isinstance(lowercase_	,  (list, tuple)			):
  return honor_type(lowercase_	,  (move_to_device(lowercase_	,  lowercase_			) for t in state)			)
 elif isinstance(lowercase_	,  lowercase_			):
  return type(lowercase_			)({k: move_to_device(lowercase_	,  lowercase_			) for k, v in state.items()}			)
 elif isinstance(lowercase_	,  torch.Tensor			):
  return state.to(lowercase_			)
 return state
class 	a_(		torch.optim.Optimizer	):



     """simple docstring"""



     def __init__(		self					:	Union[str, Any]  ,  lowerCAmelCase__					:	Any  ,  lowerCAmelCase__					:	str=True  ,  lowerCAmelCase__					:	Union[str, Any]=None)							->	Dict:

      """simple docstring"""
      SCREAMING_SNAKE_CASE				    =		optimizer
      SCREAMING_SNAKE_CASE				    =		scaler
      SCREAMING_SNAKE_CASE				    =		AcceleratorState()
      SCREAMING_SNAKE_CASE				    =		GradientState()
      SCREAMING_SNAKE_CASE				    =		device_placement
      SCREAMING_SNAKE_CASE				    =		False
      SCREAMING_SNAKE_CASE				    =		None

      # Handle device placement
      if device_placement:
       SCREAMING_SNAKE_CASE				    =		self.optimizer.state_dict()
       if self.accelerator_state.distributed_type == DistributedType.TPU:
        xm.send_cpu_data_to_device(lowerCAmelCase__  ,  self.accelerator_state.device)
       else:
        SCREAMING_SNAKE_CASE				    =		move_to_device(lowerCAmelCase__  ,  self.accelerator_state.device)
       self.optimizer.load_state_dict(lowerCAmelCase__)





     @property
     def     __UpperCamelCase						(		self					:	List[str])							->	List[Any]:

      """simple docstring"""
      return self.optimizer.state





     @state.setter
     def     __UpperCamelCase						(		self					:	Tuple  ,  lowerCAmelCase__					:	List[str])							->	Optional[int]:

      """simple docstring"""
      SCREAMING_SNAKE_CASE				    =		state





     @property
     def     __UpperCamelCase						(		self					:	Union[str, Any])							->	str:

      """simple docstring"""
      return self.optimizer.param_groups





     @param_groups.setter
     def     __UpperCamelCase						(		self					:	List[Any]  ,  lowerCAmelCase__					:	Optional[int])							->	Union[str, Any]:

      """simple docstring"""
      SCREAMING_SNAKE_CASE				    =		param_groups





     @property
     def     __UpperCamelCase						(		self					:	Tuple)							->	List[Any]:

      """simple docstring"""
      return self.optimizer.defaults





     @defaults.setter
     def     __UpperCamelCase						(		self					:	Tuple  ,  lowerCAmelCase__					:	int)							->	Dict:

      """simple docstring"""
      SCREAMING_SNAKE_CASE				    =		defaults





     def     __UpperCamelCase						(		self					:	Union[str, Any]  ,  lowerCAmelCase__					:	Optional[int])							->	Tuple:

      """simple docstring"""
      self.optimizer.add_param_group(lowerCAmelCase__)





     def     __UpperCamelCase						(		self					:	List[str]  ,  lowerCAmelCase__					:	str)							->	List[Any]:

      """simple docstring"""
      if self.accelerator_state.distributed_type == DistributedType.TPU and self.device_placement:
       xm.send_cpu_data_to_device(lowerCAmelCase__  ,  self.accelerator_state.device)
      self.optimizer.load_state_dict(lowerCAmelCase__)





     def     __UpperCamelCase						(		self					:	str)							->	Optional[Any]:

      """simple docstring"""
      return self.optimizer.state_dict()





     def     __UpperCamelCase						(		self					:	int  ,  lowerCAmelCase__					:	List[str]=None)							->	str:

      """simple docstring"""
      if self.gradient_state.sync_gradients:
       SCREAMING_SNAKE_CASE				    =		'set_to_none' in inspect.signature(self.optimizer.zero_grad).parameters
       if accept_arg:
        if set_to_none is None:
         SCREAMING_SNAKE_CASE				    =		False
        self.optimizer.zero_grad(set_to_none=lowerCAmelCase__)
       else:
        if set_to_none is not None:
         raise ValueError('`set_to_none` for Optimizer.zero_grad` is not supported by this optimizer.')
        self.optimizer.zero_grad()





     def     __UpperCamelCase						(		self					:	Any  ,  lowerCAmelCase__					:	str=None)							->	Any:

      """simple docstring"""
      if self.gradient_state.sync_gradients:
       if self.accelerator_state.distributed_type == DistributedType.TPU:
        SCREAMING_SNAKE_CASE				    =		{'closure': closure} if closure is not None else {}
        xm.optimizer_step(self.optimizer  ,  optimizer_args=lowerCAmelCase__)
       elif self.scaler is not None:
        SCREAMING_SNAKE_CASE				    =		False
        if self._last_scale is None:
         # `get_scale` is an async operation requiring full synchronization
         # on CPU and GPUs before finishing. As a result, we store away
         # the prior one to reduce the call overhead
         SCREAMING_SNAKE_CASE				    =		self.scaler.get_scale()
         SCREAMING_SNAKE_CASE				    =		True
        self.scaler.step(self.optimizer  ,  lowerCAmelCase__)
        self.scaler.update()
        SCREAMING_SNAKE_CASE				    =		self.scaler.get_scale()
        if not new_scale:
         # If we reduced the loss scale, it means the optimizer step was skipped because of gradient overflow.
         SCREAMING_SNAKE_CASE				    =		scale_after < self._last_scale
        SCREAMING_SNAKE_CASE				    =		scale_after

       else:
        self.optimizer.step(lowerCAmelCase__)





     def     __UpperCamelCase						(		self					:	Union[str, Any]  ,  lowerCAmelCase__					:	Optional[Any])							->	List[str]:

      """simple docstring"""
      for param_group in self.optimizer.param_groups:
       SCREAMING_SNAKE_CASE				    =		[parameters_map.get(lowerCAmelCase__  ,  lowerCAmelCase__) for p in param_group['params']]





     @property
     def     __UpperCamelCase						(		self					:	Optional[int])							->	Optional[int]:

      """simple docstring"""
      warnings.warn(
          'The `is_overflow` property is deprecated and will be removed in version 1.0 of Accelerate use '
          '`optimizer.step_was_skipped` instead.'  ,  lowerCAmelCase__  ,  )
      return self._is_overflow





     @property
     def     __UpperCamelCase						(		self					:	Optional[int])							->	str:

      """simple docstring"""
      return self._is_overflow





     def __getstate__(		self					:	List[Any])							->	Optional[Any]:

      """simple docstring"""
      return self.__dict__.copy()





     def __setstate__(		self					:	Optional[int]  ,  lowerCAmelCase__					:	Union[str, Any])							->	Union[str, Any]:

      """simple docstring"""
      self.__dict__.update(lowerCAmelCase__)











'''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
UpperCAmelCase       :		List[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     (				lowerCAmelCase_						):





      """simple docstring"""



      _snake_case		:						Dict         =  {node: {node} for node in graph}

      _snake_case		:						str         =  {node: graph[node][:] for node in graph}

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

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

            _snake_case		:						Tuple         =  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.
      _snake_case		:						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))


