




from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt


def 		lowerCamelCase__       (						_A	,      _A	,      _A				):







	'''simple docstring'''





	if not arr:
		return None, None, 0
	if low == high:
		return low, high, arr[low]

	snake_case_						       =	(low + high) // 2
	snake_case_       , snake_case_       , snake_case_						       =	max_subarray(_A	,      _A	,      _A				)
	snake_case_       , snake_case_       , snake_case_						       =	max_subarray(_A	,      mid + 1	,      _A				)
	snake_case_       , snake_case_       , snake_case_						       =	max_cross_sum(_A	,      _A	,      _A	,      _A				)
	if left_sum >= right_sum and left_sum >= cross_sum:
		return left_low, left_high, left_sum
	elif right_sum >= left_sum and right_sum >= cross_sum:
		return right_low, right_high, right_sum
	return cross_left, cross_right, cross_sum


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







	'''simple docstring'''





	snake_case_       , snake_case_						       =	float("-inf"				), -1
	snake_case_       , snake_case_						       =	float("-inf"				), -1

	snake_case_						       =	0
	for i in range(_A	,      low - 1	,      -1				):
		summ += arr[i]
		if summ > left_sum:
			snake_case_						       =	summ
			snake_case_						       =	i

	snake_case_						       =	0
	for i in range(mid + 1	,      high + 1				):
		summ += arr[i]
		if summ > right_sum:
			snake_case_						       =	summ
			snake_case_						       =	i

	return max_left, max_right, (left_sum + right_sum)


def 		lowerCamelCase__       (						_A				):







	'''simple docstring'''





	snake_case_						       =	[randint(1	,      _A				) for _ in range(_A				)]
	snake_case_						       =	time.time()
	max_subarray(_A	,      0	,      input_size - 1				)
	snake_case_						       =	time.time()
	return end - start


def 		lowerCamelCase__       (						):







	'''simple docstring'''





	snake_case_						       =	[10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
	snake_case_						       =	[time_max_subarray(_A				) for input_size in input_sizes]
	print("No of Inputs\t\tTime Taken"				)
	for input_size, runtime in zip(_A	,      _A				):
		print(_A	,      "\t\t"	,      _A				)
	plt.plot(_A	,      _A				)
	plt.xlabel("Number of Inputs"				)
	plt.ylabel("Time taken in seconds"				)
	plt.show()


if __name__ == "__main__":
		from doctest import testmod

		testmod()






import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import TaBlock, TaConfig, TaLayerNorm

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin
class 						UpperCAmelCase  (							UpperCAmelCase__			,  UpperCAmelCase__			,  UpperCAmelCase__     ):







						'''simple docstring'''





						@register_to_config
						def __init__(		self				:	Tuple			,      __lowercase				:	int			,      __lowercase				:	int			,      __lowercase				:	int			,      __lowercase				:	float			,      __lowercase				:	int			,      __lowercase				:	int			,      __lowercase				:	int			,      __lowercase				:	int			,      __lowercase				:	str			,      __lowercase				:	bool = False			,      ):






							"""simple docstring"""






							super().__init__()

							snake_case_						       =	nn.Embedding(__lowercase			,      __lowercase		)

							snake_case_						       =	nn.Embedding(__lowercase			,      __lowercase		)
							snake_case_						       =	False

							snake_case_						       =	nn.Dropout(p=__lowercase		)

							snake_case_						       =	TaConfig(
							    vocab_size=__lowercase			,      d_model=__lowercase			,      num_heads=__lowercase			,      d_kv=__lowercase			,      d_ff=__lowercase			,      dropout_rate=__lowercase			,      feed_forward_proj=__lowercase			,      is_decoder=__lowercase			,      is_encoder_decoder=__lowercase			,      )

							snake_case_						       =	nn.ModuleList()
							for lyr_num in range(__lowercase		):
								snake_case_						       =	TaBlock(__lowercase		)
								self.encoders.append(__lowercase		)

							snake_case_						       =	TaLayerNorm(__lowercase		)
							snake_case_						       =	nn.Dropout(p=__lowercase		)






						def 			snake_case__		(		self				:	str			,      __lowercase				:	Dict			,      __lowercase				:	str		):






							"""simple docstring"""






							snake_case_						       =	self.token_embedder(__lowercase		)

							snake_case_						       =	encoder_input_tokens.shape[1]
							snake_case_						       =	torch.arange(__lowercase			,      device=encoder_input_tokens.device		)
							x += self.position_encoding(__lowercase		)

							snake_case_						       =	self.dropout_pre(__lowercase		)

							# inverted the attention mask
							snake_case_						       =	encoder_input_tokens.size()
							snake_case_						       =	self.get_extended_attention_mask(__lowercase			,      __lowercase		)

							for lyr in self.encoders:
								snake_case_						       =	lyr(__lowercase			,      __lowercase		)[0]
							snake_case_						       =	self.layer_norm(__lowercase		)

							return self.dropout_post(__lowercase		), encoder_inputs_mask
