




from __future__ import annotations

lowercase__    :					Dict					=						[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]
class 		UpperCAmelCase       :







						'''simple docstring'''





						def __init__(						self							:					Tuple	,     __lowercase							:					int						):






							"""simple docstring"""






							snake_case_		   =					-1
							snake_case_		   =					-1
							snake_case_		   =					[-1] * length
							snake_case_		   =					None
							snake_case_		   =					None






						def __repr__(						self							:					int						):






							"""simple docstring"""






							return f"Node(min_value={self.minn} max_value={self.maxx})"







def 						lowerCamelCase__   (		_A							):







	'''simple docstring'''





	snake_case_		   =					Node(len(_A							)							)
	snake_case_   ,				snake_case_		   =					min(_A							), max(_A							)
	# Leaf node case where the node contains only one unique value
	if root.minn == root.maxx:
		return root
	snake_case_		   =					(root.minn + root.maxx) // 2

	snake_case_		   =					[]
	snake_case_		   =					[]

	for index, num in enumerate(_A							):
		if num <= pivot:
			left_arr.append(_A							)
		else:
			right_arr.append(_A							)
		snake_case_		   =					len(_A							)
	snake_case_		   =					build_tree(_A							)
	snake_case_		   =					build_tree(_A							)
	return root


def 						lowerCamelCase__   (		_A					,     _A					,     _A							):







	'''simple docstring'''





	if index < 0 or node is None:
		return 0
	# Leaf node cases
	if node.minn == node.maxx:
		return index + 1 if node.minn == num else 0
	snake_case_		   =					(node.minn + node.maxx) // 2
	if num <= pivot:
		# go the left subtree and map index to the left subtree
		return rank_till_index(node.left					,     _A					,     node.map_left[index] - 1							)
	else:
		# go to the right subtree and map index to the right subtree
		return rank_till_index(node.right					,     _A					,     index - node.map_left[index]							)


def 						lowerCamelCase__   (		_A					,     _A					,     _A					,     _A							):







	'''simple docstring'''





	if start > end:
		return 0
	snake_case_		   =					rank_till_index(_A					,     _A					,     _A							)
	snake_case_		   =					rank_till_index(_A					,     _A					,     start - 1							)
	return rank_till_end - rank_before_start


def 						lowerCamelCase__   (		_A					,     _A					,     _A					,     _A							):







	'''simple docstring'''





	if index > (end - start) or start > end or node is None:
		return -1
	# Leaf node case
	if node.minn == node.maxx:
		return node.minn
	# Number of elements in the left subtree in interval [start, end]
	snake_case_		   =					node.map_left[end] - (
	    node.map_left[start - 1] if start else 0
	)
	if num_elements_in_left_tree > index:
		return quantile(
		    node.left					,     _A					,     (node.map_left[start - 1] if start else 0)					,     node.map_left[end] - 1					,     )
	else:
		return quantile(
		    node.right					,     index - num_elements_in_left_tree					,     start - (node.map_left[start - 1] if start else 0)					,     end - node.map_left[end]					,     )


def 						lowerCamelCase__   (		_A					,     _A					,     _A					,     _A					,     _A							):







	'''simple docstring'''





	if (
	    start > end
	    or node is None
	    or start_num > end_num
	    or node.minn > end_num
	    or node.maxx < start_num
	):
		return 0
	if start_num <= node.minn and node.maxx <= end_num:
		return end - start + 1
	snake_case_		   =					range_counting(
	    node.left					,     (node.map_left[start - 1] if start else 0)					,     node.map_left[end] - 1					,     _A					,     _A					,     )
	snake_case_		   =					range_counting(
	    node.right					,     start - (node.map_left[start - 1] if start else 0)					,     end - node.map_left[end]					,     _A					,     _A					,     )
	return left + right


if __name__ == "__main__":
		import doctest

		doctest.testmod()






import unittest
from functools import partial

import torch

from accelerate import Accelerator, debug_launcher
from accelerate.state import AcceleratorState, GradientState
from accelerate.test_utils import require_cpu, require_huggingface_suite
from accelerate.utils import GradientAccumulationPlugin


def 						lowerCamelCase__   (		_A=2					,     _A=True					,     _A=False							):







	'''simple docstring'''





	snake_case_		   =					Accelerator(step_scheduler_with_optimizer=_A					,     split_batches=_A							)
	snake_case_		   =					torch.nn.Linear(2					,     4							)
	snake_case_		   =					torch.optim.AdamW(model.parameters()					,     lr=1.0							)
	snake_case_		   =					torch.optim.lr_scheduler.OneCycleLR(_A					,     max_lr=0.01					,     steps_per_epoch=2					,     epochs=1							)
	snake_case_   ,				snake_case_   ,				snake_case_		   =					accelerator.prepare(_A					,     _A					,     _A							)

	# Optimizer has stepped
	scheduler.step()
	if step_scheduler_with_optimizer or (num_processes == 1):
		assert (
		    scheduler.scheduler.last_epoch == num_processes
		), f"Last Epoch ({scheduler.scheduler.last_epoch}) != Num Processes ({num_processes})"
	else:
		assert (
		    scheduler.scheduler.last_epoch != num_processes
		), f"Last Epoch ({scheduler.scheduler.last_epoch}) == Num Processes ({num_processes})"


def 						lowerCamelCase__   (		_A=2					,     _A=True					,     _A=False							):







	'''simple docstring'''





	snake_case_		   =					Accelerator(step_scheduler_with_optimizer=_A					,     split_batches=_A							)
	snake_case_		   =					torch.nn.Linear(2					,     4							)
	snake_case_		   =					torch.optim.AdamW(model.parameters()					,     lr=1.0							)
	snake_case_		   =					torch.optim.lr_scheduler.LambdaLR(_A					,     lr_lambda=lambda _A							: 1 - n / 10							)
	snake_case_   ,				snake_case_   ,				snake_case_		   =					accelerator.prepare(_A					,     _A					,     _A							)

	# Optimizer has stepped
	snake_case_		   =					False
	scheduler.step()
	snake_case_		   =					1 - (num_processes if (step_scheduler_with_optimizer and not split_batches) else 1) / 10
	assert (
	    scheduler.get_last_lr()[0] == expected_lr
	), f"Wrong lr found at first step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}"

	# Optimizer has not stepped
	snake_case_		   =					True
	scheduler.step()
	if not step_scheduler_with_optimizer:
		snake_case_		   =					1 - 2 / 10
	assert (
	    scheduler.get_last_lr()[0] == expected_lr
	), f"Wrong lr found at second step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}"


def 						lowerCamelCase__   (		_A = 2							):







	'''simple docstring'''





	from transformers import get_linear_schedule_with_warmup

	snake_case_		   =					[1, 2, 4]
	for num_steps in steps:
		snake_case_		   =					GradientAccumulationPlugin(num_steps=_A					,     adjust_scheduler=num_steps > 1							)
		snake_case_		   =					Accelerator(gradient_accumulation_plugin=_A							)
		snake_case_		   =					torch.nn.Linear(2					,     4							)
		snake_case_		   =					torch.optim.AdamW(model.parameters()					,     lr=10.0							)
		snake_case_		   =					get_linear_schedule_with_warmup(optimizer=_A					,     num_warmup_steps=0					,     num_training_steps=20							)

		snake_case_   ,				snake_case_   ,				snake_case_		   =					accelerator.prepare(_A					,     _A					,     _A							)

		for i in range(10 * num_steps							):
			with accelerator.accumulate(_A							):
				optimizer.step()
				scheduler.step()

			if i == (10 * num_steps - 2):
				assert (
				    scheduler.get_last_lr()[0] != 0
				), f"Wrong lr found at second-to-last step, expected non-zero, got {scheduler.get_last_lr()[0]}. num_steps: {num_steps}"
		assert (
		    scheduler.get_last_lr()[0] == 0
		), f"Wrong lr found at last step, expected 0, got {scheduler.get_last_lr()[0]}"
		GradientState._reset_state()






@require_cpu
class 		UpperCAmelCase       (    unittest.TestCase      ):







						'''simple docstring'''





						def 	snake_case__						(						self							:					Tuple						):






							"""simple docstring"""






							debug_launcher(partial(__lowercase	,     num_processes=1						)	,     num_processes=1						)
							debug_launcher(partial(__lowercase	,     num_processes=1	,     split_batches=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					int						):






							"""simple docstring"""






							debug_launcher(partial(__lowercase	,     num_processes=1						)	,     num_processes=1						)
							debug_launcher(partial(__lowercase	,     num_processes=1	,     split_batches=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					Dict						):






							"""simple docstring"""






							debug_launcher(partial(__lowercase	,     num_processes=1	,     step_scheduler_with_optimizer=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					Union[str, Any]						):






							"""simple docstring"""






							debug_launcher(partial(__lowercase	,     num_processes=1	,     step_scheduler_with_optimizer=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					List[Any]						):






							"""simple docstring"""






							AcceleratorState._reset_state(__lowercase						)
							debug_launcher(__lowercase						)
							debug_launcher(partial(__lowercase	,     num_processes=1	,     split_batches=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					Dict						):






							"""simple docstring"""






							AcceleratorState._reset_state(__lowercase						)
							debug_launcher(__lowercase						)
							debug_launcher(partial(__lowercase	,     num_processes=1	,     split_batches=__lowercase						)	,     num_processes=1						)






						def 	snake_case__						(						self							:					List[str]						):






							"""simple docstring"""






							AcceleratorState._reset_state(__lowercase						)
							debug_launcher(partial(__lowercase	,     step_scheduler_with_optimizer=__lowercase						)						)






						def 	snake_case__						(						self							:					Optional[Any]						):






							"""simple docstring"""






							AcceleratorState._reset_state(__lowercase						)
							debug_launcher(partial(__lowercase	,     step_scheduler_with_optimizer=__lowercase						)						)






						@require_huggingface_suite
						def 	snake_case__						(						self							:					Optional[Any]						):






							"""simple docstring"""






							AcceleratorState._reset_state(__lowercase						)
							debug_launcher(partial(__lowercase	,     num_processes=1						)						)
							debug_launcher(__lowercase						)
