code: from __future__ import annotations
  
  from abc import abstractmethod
  from collections.abc import Iterable
  from typing import Generic, Protocol, TypeVar
  
  
  
  
  class      lowercase_						(						UpperCamelCase_		):
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  	@abstractmethod
  	def __lt__(							self	,    __SCREAMING_SNAKE_CASE       )		->bool:
  								pass
  
  
  	@abstractmethod
  	def __gt__(							self	,    __SCREAMING_SNAKE_CASE       )		->bool:
  								pass
  
  
  
  
  	@abstractmethod
  	def __eq__(							self	,    __SCREAMING_SNAKE_CASE       )		->bool:
  								pass
  lowercase__    :       Tuple						=			TypeVar('''T''', bound=Comparable)
  
  
  
  
  class      lowercase_						(						Generic[T]		):
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  	def __init__(							self       )		->None:
  								lowerCAmelCase				=	[]
  								lowerCAmelCase				=	0
  
  
  	def __repr__(							self       )		->str:
  								return str(self.h       )
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE       )		->int | None:
  								if child_idx > 0:
  															return (child_idx - 1) // 2
  								return None
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE       )		->int | None:
  								lowerCAmelCase				=	2 * parent_idx + 1
  								if left_child_index < self.heap_size:
  															return left_child_index
  								return None
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE       )		->int | None:
  								lowerCAmelCase				=	2 * parent_idx + 2
  								if right_child_index < self.heap_size:
  															return right_child_index
  								return None
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE       )		->None:
  								if index < self.heap_size:
  															lowerCAmelCase				=	index
  															lowerCAmelCase				=	self.left_child_idx(__SCREAMING_SNAKE_CASE       )
  															lowerCAmelCase				=	self.right_child_idx(__SCREAMING_SNAKE_CASE       )
  															# check which child is larger than its parent
  															if left_child is not None and self.h[left_child] > self.h[violation]:
  																						lowerCAmelCase				=	left_child
  															if right_child is not None and self.h[right_child] > self.h[violation]:
  																						lowerCAmelCase				=	right_child
  															# if violation indeed exists
  															if violation != index:
  																						# swap to fix the violation
  																						lowerCAmelCase	,   lowerCAmelCase				=	self.h[index], self.h[violation]
  																						# fix the subsequent violation recursively if any
  																						self.max_heapify(__SCREAMING_SNAKE_CASE       )
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE       )		->None:
  								lowerCAmelCase				=	list(__SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	len(self.h       )
  								if self.heap_size > 1:
  															# max_heapify from right to left but exclude leaves (last level)
  															for i in range(self.heap_size // 2 - 1	,    -1	,    -1       ):
  																						self.max_heapify(__SCREAMING_SNAKE_CASE       )
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self       )		->T:
  								if self.heap_size >= 2:
  															lowerCAmelCase				=	self.h[0]
  															lowerCAmelCase				=	self.h.pop(-1       )
  															self.heap_size -= 1
  															self.max_heapify(0       )
  															return me
  								elif self.heap_size == 1:
  															self.heap_size -= 1
  															return self.h.pop(-1       )
  								else:
  															raise Exception('''Empty heap'''       )
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE       )		->None:
  								self.h.append(__SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	(self.heap_size - 1) // 2
  								self.heap_size += 1
  								while idx >= 0:
  															self.max_heapify(__SCREAMING_SNAKE_CASE       )
  															lowerCAmelCase				=	(idx - 1) // 2
  
  
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self       )		->None:
  								lowerCAmelCase				=	self.heap_size
  								for j in range(size - 1	,    0	,    -1       ):
  															lowerCAmelCase	,   lowerCAmelCase				=	self.h[j], self.h[0]
  															self.heap_size -= 1
  															self.max_heapify(0       )
  								lowerCAmelCase				=	size
  
  
  if __name__ == "__main__":
  	import doctest
  
  	# run doc test
  	doctest.testmod()
  
  	# demo
  	for unsorted in [
  	    [0],
  	    [2],
  	    [3, 5],
  	    [5, 3],
  	    [5, 5],
  	    [0, 0, 0, 0],
  	    [1, 1, 1, 1],
  	    [2, 2, 3, 5],
  	    [0, 2, 2, 3, 5],
  	    [2, 5, 3, 0, 2, 3, 0, 3],
  	    [6, 1, 2, 7, 9, 3, 4, 5, 1_0, 8],
  	    [1_0_3, 9, 1, 7, 1_1, 1_5, 2_5, 2_0_1, 2_0_9, 1_0_7, 5],
  	    [-4_5, -2, -5],
  	]:
  		print(f'unsorted array: {unsorted}')
  
  		lowercase__    :       Heap[int]						=			Heap()
  		heap.build_max_heap(unsorted)
  		print(f'after build heap: {heap}')
  
  		print(f'max value: {heap.extract_max()}')
  		print(f'after max value removed: {heap}')
  
  		heap.insert(1_0_0)
  		print(f'after new value 100 inserted: {heap}')
  
  		heap.heap_sort()
  		print(f'heap-sorted array: {heap}\n')
  
  
  
  
style_context: import argparse
  import os
  import re
  
  import numpy as np
  import PIL
  import torch
  from timm import create_model
  from torch.optim.lr_scheduler import OneCycleLR
  from torch.utils.data import DataLoader, Dataset
  from torchvision.transforms import Compose, RandomResizedCrop, Resize, ToTensor
  
  from accelerate import Accelerator
  
  def      SCREAMING_SNAKE_CASE_  (		snake_case__							)  ->			Optional[Any]:
  							lowerCAmelCase				=	fname.split(os.path.sep							)[-1]
  							return re.search(R'''^(.*)_\d+\.jpg$'''     ,						snake_case__							).groups()[0]
  
  
  
  
  class      lowercase_						(						UpperCamelCase_		):
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  	def __init__(							self	,    __SCREAMING_SNAKE_CASE	,    __SCREAMING_SNAKE_CASE=None	,    __SCREAMING_SNAKE_CASE=None       )		->Optional[Any]:
  								lowerCAmelCase				=	file_names
  								lowerCAmelCase				=	image_transform
  								lowerCAmelCase				=	label_to_id
  
  
  	def __len__(							self       )		->Optional[int]:
  								return len(self.file_names       )
  
  
  
  
  	def __getitem__(							self	,    __SCREAMING_SNAKE_CASE       )		->int:
  								lowerCAmelCase				=	self.file_names[idx]
  								lowerCAmelCase				=	PIL.Image.open(__SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	raw_image.convert('''RGB'''       )
  								if self.image_transform is not None:
  															lowerCAmelCase				=	self.image_transform(__SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	extract_label(__SCREAMING_SNAKE_CASE       )
  								if self.label_to_id is not None:
  															lowerCAmelCase				=	self.label_to_id[label]
  								return {"image": image, "label": label}
  
  def      SCREAMING_SNAKE_CASE_  (		snake_case__     ,						snake_case__							)  ->			Any:
  							# Initialize accelerator
  							lowerCAmelCase				=	Accelerator(cpu=args.cpu     ,						mixed_precision=args.mixed_precision							)
  
  							# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
  							lowerCAmelCase				=	config['''lr''']
  							lowerCAmelCase				=	int(config['''num_epochs''']							)
  							lowerCAmelCase				=	int(config['''seed''']							)
  							lowerCAmelCase				=	int(config['''batch_size''']							)
  							lowerCAmelCase				=	config['''image_size''']
  							if not isinstance(snake_case__     ,						(list, tuple)							):
  														lowerCAmelCase				=	(image_size, image_size)
  
  							# Grab all the image filenames
  							lowerCAmelCase				=	[os.path.join(args.data_dir     ,						snake_case__							) for fname in os.listdir(args.data_dir							) if fname.endswith('''.jpg'''							)]
  
  							# Build the label correspondences
  							lowerCAmelCase				=	[extract_label(snake_case__							) for fname in file_names]
  							lowerCAmelCase				=	list(set(snake_case__							)							)
  							id_to_label.sort()
  							lowerCAmelCase				=	{lbl: i for i, lbl in enumerate(snake_case__							)}
  
  							# Set the seed before splitting the data.
  							np.random.seed(snake_case__							)
  							torch.manual_seed(snake_case__							)
  							torch.cuda.manual_seed_all(snake_case__							)
  
  							# Split our filenames between train and validation
  							lowerCAmelCase				=	np.random.permutation(len(snake_case__							)							)
  							lowerCAmelCase				=	int(0.8 * len(snake_case__							)							)
  							lowerCAmelCase				=	random_perm[:cut]
  							lowerCAmelCase				=	random_perm[cut:]
  
  							# For training we use a simple RandomResizedCrop
  							lowerCAmelCase				=	Compose([RandomResizedCrop(snake_case__     ,						scale=(0.5, 1.0)							), ToTensor()]							)
  							lowerCAmelCase				=	PetsDataset(
  							    [file_names[i] for i in train_split]     ,						image_transform=snake_case__     ,						label_to_id=snake_case__							)
  
  							# For evaluation, we use a deterministic Resize
  							lowerCAmelCase				=	Compose([Resize(snake_case__							), ToTensor()]							)
  							lowerCAmelCase				=	PetsDataset([file_names[i] for i in eval_split]     ,						image_transform=snake_case__     ,						label_to_id=snake_case__							)
  
  							# Instantiate dataloaders.
  							lowerCAmelCase				=	DataLoader(snake_case__     ,						shuffle=snake_case__     ,						batch_size=snake_case__     ,						num_workers=4							)
  							lowerCAmelCase				=	DataLoader(snake_case__     ,						shuffle=snake_case__     ,						batch_size=snake_case__     ,						num_workers=4							)
  
  							# Instantiate the model (we build the model here so that the seed also control new weights initialization)
  							lowerCAmelCase				=	create_model('''resnet50d'''     ,						pretrained=snake_case__     ,						num_classes=len(snake_case__							)							)
  
  							# We could avoid this line since the accelerator is set with `device_placement=True` (default value).
  							# Note that if you are placing tensors on devices manually, this line absolutely needs to be before the optimizer
  							# creation otherwise training will not work on TPU (`accelerate` will kindly throw an error to make us aware of that).
  							lowerCAmelCase				=	model.to(accelerator.device							)
  
  							# Freezing the base model
  							for param in model.parameters():
  														lowerCAmelCase				=	False
  							for param in model.get_classifier().parameters():
  														lowerCAmelCase				=	True
  
  							# We normalize the batches of images to be a bit faster.
  							lowerCAmelCase				=	torch.tensor(model.default_cfg['''mean''']							)[None, :, None, None].to(accelerator.device							)
  							lowerCAmelCase				=	torch.tensor(model.default_cfg['''std''']							)[None, :, None, None].to(accelerator.device							)
  
  							# Instantiate optimizer
  							lowerCAmelCase				=	torch.optim.Adam(params=model.parameters()     ,						lr=lr / 2_5							)
  
  							# Instantiate learning rate scheduler
  							lowerCAmelCase				=	OneCycleLR(optimizer=snake_case__     ,						max_lr=snake_case__     ,						epochs=snake_case__     ,						steps_per_epoch=len(snake_case__							)							)
  
  							# Prepare everything
  							# There is no specific order to remember, we just need to unpack the objects in the same order we gave them to the
  							# prepare method.
  							lowerCAmelCase	,   lowerCAmelCase	,   lowerCAmelCase	,   lowerCAmelCase	,   lowerCAmelCase				=	accelerator.prepare(
  							    snake_case__     ,						snake_case__     ,						snake_case__     ,						snake_case__     ,						snake_case__							)
  
  							# Now we train the model
  							for epoch in range(snake_case__							):
  														model.train()
  														for step, batch in enumerate(snake_case__							):
  																					# We could avoid this line since we set the accelerator with `device_placement=True`.
  																					lowerCAmelCase				=	{k: v.to(accelerator.device							) for k, v in batch.items()}
  																					lowerCAmelCase				=	(batch['''image'''] - mean) / std
  																					lowerCAmelCase				=	model(snake_case__							)
  																					lowerCAmelCase				=	torch.nn.functional.cross_entropy(snake_case__     ,						batch['''label''']							)
  																					accelerator.backward(snake_case__							)
  																					optimizer.step()
  																					lr_scheduler.step()
  																					optimizer.zero_grad()
  
  														model.eval()
  														lowerCAmelCase				=	0
  														lowerCAmelCase				=	0
  														for _, batch in enumerate(snake_case__							):
  																					# We could avoid this line since we set the accelerator with `device_placement=True`.
  																					lowerCAmelCase				=	{k: v.to(accelerator.device							) for k, v in batch.items()}
  																					lowerCAmelCase				=	(batch['''image'''] - mean) / std
  																					with torch.no_grad():
  																												lowerCAmelCase				=	model(snake_case__							)
  																					lowerCAmelCase				=	outputs.argmax(dim=-1							)
  																					lowerCAmelCase	,   lowerCAmelCase				=	accelerator.gather_for_metrics((predictions, batch['''label'''])							)
  																					lowerCAmelCase				=	predictions == references
  																					num_elems += accurate_preds.shape[0]
  																					accurate += accurate_preds.long().sum()
  
  														lowerCAmelCase				=	accurate.item() / num_elems
  														# Use accelerator.print to print only on the main process.
  														accelerator.print(f"epoch {epoch}: {1_0_0 * eval_metric:.2f}"							)
  
  def      SCREAMING_SNAKE_CASE_  (		)  ->			List[str]:
  							lowerCAmelCase				=	argparse.ArgumentParser(description='''Simple example of training script.'''							)
  							parser.add_argument('''--data_dir'''     ,						required=snake_case__     ,						help='''The data folder on disk.'''							)
  							parser.add_argument(
  							    '''--mixed_precision'''     ,						type=snake_case__     ,						default=snake_case__     ,						choices=['''no''', '''fp16''', '''bf16''', '''fp8''']     ,						help='''Whether to use mixed precision. Choose'''
  							    '''between fp16 and bf16 (bfloat16). Bf16 requires PyTorch >= 1.10.'''
  							    '''and an Nvidia Ampere GPU.'''     ,						)
  							parser.add_argument(
  							    '''--checkpointing_steps'''     ,						type=snake_case__     ,						default=snake_case__     ,						help='''Whether the various states should be saved at the end of every n steps, or \'epoch\' for each epoch.'''     ,						)
  							parser.add_argument('''--cpu'''     ,						action='''store_true'''     ,						help='''If passed, will train on the CPU.'''							)
  							lowerCAmelCase				=	parser.parse_args()
  							lowerCAmelCase				=	{'''lr''': 3E-2, '''num_epochs''': 3, '''seed''': 4_2, '''batch_size''': 6_4, '''image_size''': 2_2_4}
  							training_function(snake_case__     ,						snake_case__							)
  
  
  if __name__ == "__main__":
  	main()
  
  
  
  