
class      A__       :





							def __init__(			self  :       Tuple					,			_UpperCAmelCase  :       Any    )						->		int:



											"""simple docstring"""


											__lowercase								= val
											# Number of nodes in left subtree
											__lowercase								= 0
											__lowercase								= None
											__lowercase								= None
											__lowercase								= None





							def       a__			(			self  :       List[str]					,			_UpperCAmelCase  :       Tuple    )						->		Tuple:



											"""simple docstring"""


											assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

											if self.val < other.val:
															__lowercase								= self.right
															__lowercase								= None
															if self.right:
																			__lowercase								= other
															__lowercase								= other
															__lowercase								= self.left_tree_size * 2 + 1
															return self
											else:
															__lowercase								= other.right
															__lowercase								= None
															if other.right:
																			__lowercase								= self
															__lowercase								= self
															__lowercase								= other.left_tree_size * 2 + 1
															return other






class      A__       :





							def __init__(			self  :       Optional[Any]					,			_UpperCAmelCase  :       List[str]=None					,			_UpperCAmelCase  :       Optional[Any]=None					,			_UpperCAmelCase  :       Optional[Any]=0    )						->		str:



											"""simple docstring"""


											__lowercase								= heap_size
											__lowercase								= bottom_root
											__lowercase								= min_node





							def       a__			(			self  :       Optional[int]					,			_UpperCAmelCase  :       str    )						->		List[str]:



											"""simple docstring"""


											if other.size == 0:
															return None
											if self.size == 0:
															__lowercase								= other.size
															__lowercase								= other.bottom_root
															__lowercase								= other.min_node
															return None
											# Update size
											__lowercase								= self.size + other.size

											# Update min.node
											if self.min_node.val > other.min_node.val:
															__lowercase								= other.min_node
											# Merge

											# Order roots by left_subtree_size
											__lowercase								= []
											__lowercase		, __lowercase								= self.bottom_root, other.bottom_root
											while i or j:
															if i and ((not j) or i.left_tree_size < j.left_tree_size):
																			combined_roots_list.append((i, True)    )
																			__lowercase								= i.parent
															else:
																			combined_roots_list.append((j, False)    )
																			__lowercase								= j.parent
        # Insert links between them
											for i in range(len(_UpperCAmelCase    ) - 1    ):
															if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
																			__lowercase								= combined_roots_list[i + 1][0]
																			__lowercase								= combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
											__lowercase								= combined_roots_list[0][0]
											while i.parent:
															if (
															    (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
															) or (
															    i.left_tree_size == i.parent.left_tree_size
															    and i.left_tree_size != i.parent.parent.left_tree_size
															):
																			# Neighbouring Nodes
																			__lowercase								= i.left
																			__lowercase								= i.parent.parent

																			# Merging trees
																			__lowercase								= i.merge_trees(i.parent    )

																			# Updating links
																			__lowercase								= previous_node
																			__lowercase								= next_node
																			if previous_node:
																							__lowercase								= i
																			if next_node:
																							__lowercase								= i
															else:
																			__lowercase								= i.parent
        # Updating self.bottom_root
											while i.left:
															__lowercase								= i.left
											__lowercase								= i

											# Update other
											__lowercase								= self.size
											__lowercase								= self.bottom_root
											__lowercase								= self.min_node

											# Return the merged heap
											return self





							def       a__			(			self  :       Union[str, Any]					,			_UpperCAmelCase  :       List[Any]    )						->		Union[str, Any]:



											"""simple docstring"""


											if self.size == 0:
															__lowercase								= Node(_UpperCAmelCase    )
															__lowercase								= 1
															__lowercase								= self.bottom_root
											else:
															# Create new node
															__lowercase								= Node(_UpperCAmelCase    )

															# Update size
															self.size += 1

															# update min_node
															if val < self.min_node.val:
																			__lowercase								= new_node
															# Put new_node as a bottom_root in heap
															__lowercase								= new_node
															__lowercase								= self.bottom_root
															__lowercase								= new_node

															# Consecutively merge roots with same left_tree_size
															while (
															    self.bottom_root.parent
															    and self.bottom_root.left_tree_size
															    == self.bottom_root.parent.left_tree_size
															):
																			# Next node
																			__lowercase								= self.bottom_root.parent.parent

																			# Merge
																			__lowercase								= self.bottom_root.merge_trees(self.bottom_root.parent    )

																			# Update Links
																			__lowercase								= next_node
																			__lowercase								= None
																			if next_node:
																							__lowercase								= self.bottom_root





							def       a__			(			self  :       Optional[int]    )						->		Tuple:



											"""simple docstring"""


											return self.min_node.val





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



											"""simple docstring"""


											return self.size == 0





							def       a__			(			self  :       Optional[int]    )						->		Optional[Any]:



											"""simple docstring"""


											__lowercase								= self.min_node.val

											# Last element in heap corner case
											if self.size == 1:
															# Update size
															__lowercase								= 0

															# Update bottom root
															__lowercase								= None

															# Update min_node
															__lowercase								= None

															return min_value
											# No right subtree corner case
											# The structure of the tree implies that this should be the bottom root
											# and there is at least one other root
											if self.min_node.right is None:
															# Update size
															self.size -= 1

															# Update bottom root
															__lowercase								= self.bottom_root.parent
															__lowercase								= None

															# Update min_node
															__lowercase								= self.bottom_root
															__lowercase								= self.bottom_root.parent
															while i:
																			if i.val < self.min_node.val:
																							__lowercase								= i
																			__lowercase								= i.parent
															return min_value
											# General case
											# Find the BinomialHeap of the right subtree of min_node
											__lowercase								= self.min_node.right
											__lowercase								= None
											__lowercase								= bottom_of_new
											__lowercase								= 1

											# Size, min_node and bottom_root
											while bottom_of_new.left:
															__lowercase								= size_of_new * 2 + 1
															__lowercase								= bottom_of_new.left
															if bottom_of_new.val < min_of_new.val:
																			__lowercase								= bottom_of_new
        # Corner case of single root on top left path
											if (not self.min_node.left) and (not self.min_node.parent):
															__lowercase								= size_of_new
															__lowercase								= bottom_of_new
															__lowercase								= min_of_new
															# print("Single root, multiple nodes case")
															return min_value
											# Remaining cases
											# Construct heap of right subtree
											__lowercase								= BinomialHeap(
											    bottom_root=_UpperCAmelCase					,			min_node=_UpperCAmelCase					,			heap_size=_UpperCAmelCase    )

											# Update size
											__lowercase								= self.size - 1 - size_of_new

											# Neighbour nodes
											__lowercase								= self.min_node.left
											__lowercase								= self.min_node.parent

											# Initialize new bottom_root and min_node
											__lowercase								= previous_node or next_node
											__lowercase								= next_node

											# Update links of previous_node and search below for new min_node and
											# bottom_root
											if previous_node:
															__lowercase								= next_node

															# Update bottom_root and search for min_node below
															__lowercase								= previous_node
															__lowercase								= previous_node
															while self.bottom_root.left:
																			__lowercase								= self.bottom_root.left
																			if self.bottom_root.val < self.min_node.val:
																							__lowercase								= self.bottom_root
											if next_node:
															__lowercase								= previous_node

															# Search for new min_node above min_node
															__lowercase								= next_node
															while i:
																			if i.val < self.min_node.val:
																							__lowercase								= i
																			__lowercase								= i.parent
        # Merge heaps
											self.merge_heaps(_UpperCAmelCase    )

											return min_value





							def       a__			(			self  :       Optional[Any]    )						->		Tuple:



											"""simple docstring"""


											__lowercase								= self.bottom_root
											while top_root.parent:
															__lowercase								= top_root.parent
											# preorder
											__lowercase								= []
											self.__traversal(_UpperCAmelCase					,			_UpperCAmelCase    )
											return heap_pre_order





							def       a__			(			self  :       Tuple					,			_UpperCAmelCase  :       List[Any]					,			_UpperCAmelCase  :       Any					,			_UpperCAmelCase  :       Tuple=0    )						->		Any:



											"""simple docstring"""


											if curr_node:
															preorder.append((curr_node.val, level)    )
															self.__traversal(curr_node.left					,			_UpperCAmelCase					,			level + 1    )
															self.__traversal(curr_node.right					,			_UpperCAmelCase					,			level + 1    )
											else:
															preorder.append(('#', level)    )





							def __str__(			self  :       Optional[int]    )						->		Dict:



											"""simple docstring"""


											if self.is_empty():
															return ""
											__lowercase								= self.pre_order()

											return "\n".join(('-' * level + str(_UpperCAmelCase    )) for value, level in preorder_heap    )


# Unit Tests
if __name__ == "__main__":
							import doctest

							doctest.testmod()







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 							__SCREAMING_SNAKE_CASE       (		SCREAMING_SNAKE_CASE	:				int   ,							SCREAMING_SNAKE_CASE	:				int      )					->						Optional[Any]:
				if isinstance(SCREAMING_SNAKE_CASE   ,							(list, tuple)      ):
								return honor_type(SCREAMING_SNAKE_CASE   ,							(move_to_device(SCREAMING_SNAKE_CASE   ,							SCREAMING_SNAKE_CASE      ) for t in state)      )
				elif isinstance(SCREAMING_SNAKE_CASE   ,							SCREAMING_SNAKE_CASE      ):
								return type(SCREAMING_SNAKE_CASE      )({k: move_to_device(SCREAMING_SNAKE_CASE   ,							SCREAMING_SNAKE_CASE      ) for k, v in state.items()}      )
				elif isinstance(SCREAMING_SNAKE_CASE   ,							torch.Tensor      ):
								return state.to(SCREAMING_SNAKE_CASE      )
				return state
class      A__       (						torch.optim.Optimizer    ):





							def __init__(			self  :       Optional[Any]					,			_UpperCAmelCase  :       Optional[int]					,			_UpperCAmelCase  :       Optional[int]=True					,			_UpperCAmelCase  :       int=None    )						->		Optional[Any]:



											"""simple docstring"""


											__lowercase								= optimizer
											__lowercase								= scaler
											__lowercase								= AcceleratorState()
											__lowercase								= GradientState()
											__lowercase								= device_placement
											__lowercase								= False
											__lowercase								= None

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





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



											"""simple docstring"""


											return self.optimizer.state





							@state.setter
							def       a__			(			self  :       Union[str, Any]					,			_UpperCAmelCase  :       int    )						->		Optional[Any]:



											"""simple docstring"""


											__lowercase								= state





							@property
							def       a__			(			self  :       str    )						->		int:



											"""simple docstring"""


											return self.optimizer.param_groups





							@param_groups.setter
							def       a__			(			self  :       Tuple					,			_UpperCAmelCase  :       List[Any]    )						->		int:



											"""simple docstring"""


											__lowercase								= param_groups





							@property
							def       a__			(			self  :       List[Any]    )						->		Optional[Any]:



											"""simple docstring"""


											return self.optimizer.defaults





							@defaults.setter
							def       a__			(			self  :       List[str]					,			_UpperCAmelCase  :       int    )						->		Any:



											"""simple docstring"""


											__lowercase								= defaults





							def       a__			(			self  :       List[str]					,			_UpperCAmelCase  :       List[Any]    )						->		Any:



											"""simple docstring"""


											self.optimizer.add_param_group(_UpperCAmelCase    )





							def       a__			(			self  :       int					,			_UpperCAmelCase  :       Dict    )						->		Optional[int]:



											"""simple docstring"""


											if self.accelerator_state.distributed_type == DistributedType.TPU and self.device_placement:
															xm.send_cpu_data_to_device(_UpperCAmelCase					,			self.accelerator_state.device    )
											self.optimizer.load_state_dict(_UpperCAmelCase    )





							def       a__			(			self  :       str    )						->		Any:



											"""simple docstring"""


											return self.optimizer.state_dict()





							def       a__			(			self  :       Dict					,			_UpperCAmelCase  :       List[str]=None    )						->		Tuple:



											"""simple docstring"""


											if self.gradient_state.sync_gradients:
															__lowercase								= 'set_to_none' in inspect.signature(self.optimizer.zero_grad    ).parameters
															if accept_arg:
																			if set_to_none is None:
																							__lowercase								= False
																			self.optimizer.zero_grad(set_to_none=_UpperCAmelCase    )
															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       a__			(			self  :       List[str]					,			_UpperCAmelCase  :       Optional[Any]=None    )						->		int:



											"""simple docstring"""


											if self.gradient_state.sync_gradients:
															if self.accelerator_state.distributed_type == DistributedType.TPU:
																			__lowercase								= {'closure': closure} if closure is not None else {}
																			xm.optimizer_step(self.optimizer					,			optimizer_args=_UpperCAmelCase    )
															elif self.scaler is not None:
																			__lowercase								= 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
																							__lowercase								= self.scaler.get_scale()
																							__lowercase								= True
																			self.scaler.step(self.optimizer					,			_UpperCAmelCase    )
																			self.scaler.update()
																			__lowercase								= 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.
																							__lowercase								= scale_after < self._last_scale
																			__lowercase								= scale_after

															else:
																			self.optimizer.step(_UpperCAmelCase    )





							def       a__			(			self  :       Optional[int]					,			_UpperCAmelCase  :       int    )						->		Tuple:



											"""simple docstring"""


											for param_group in self.optimizer.param_groups:
															__lowercase								= [parameters_map.get(_UpperCAmelCase					,			_UpperCAmelCase    ) for p in param_group['params']]





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



											"""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.'					,			_UpperCAmelCase					,			)
											return self._is_overflow





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



											"""simple docstring"""


											return self._is_overflow





							def __getstate__(			self  :       Optional[int]    )						->		str:



											"""simple docstring"""


											return self.__dict__.copy()





							def __setstate__(			self  :       List[Any]					,			_UpperCAmelCase  :       Optional[int]    )						->		Any:



											"""simple docstring"""


											self.__dict__.update(_UpperCAmelCase    )





