






"""simple docstring"""
import numpy as np

def 				snake_case      (   A__						):
			return 1 / (1 + np.exp(-vector						))

def 				snake_case      (   A__						):
			return vector * sigmoid(A__						)


if __name__ == "__main__":
			import doctest

			doctest.testmod()











"""simple docstring"""
from __future__ import annotations

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

from matplotlib import pyplot as plt

def 				snake_case      (   A__	,A__	,A__						):
			if not arr:
						return None, None, 0
			if low == high:
						return low, high, arr[low]

			UpperCAmelCase_     : Dict			     =					(low + high) // 2
			UpperCAmelCase_     ,	UpperCAmelCase_     ,	UpperCAmelCase_     : Any			     =					max_subarray(A__	,A__	,A__						)
			UpperCAmelCase_     ,	UpperCAmelCase_     ,	UpperCAmelCase_     : Union[str, Any]			     =					max_subarray(A__	,mid + 1	,A__						)
			UpperCAmelCase_     ,	UpperCAmelCase_     ,	UpperCAmelCase_     : Optional[Any]			     =					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 				snake_case      (   A__	,A__	,A__	,A__						):
			UpperCAmelCase_     ,	UpperCAmelCase_     : str			     =					float("-inf"						), -1
			UpperCAmelCase_     ,	UpperCAmelCase_     : Optional[Any]			     =					float("-inf"						), -1

			UpperCAmelCase_     : int | float			     =					0
			for i in range(A__	,low - 1	,-1						):
						summ += arr[i]
						if summ > left_sum:
									UpperCAmelCase_     : str			     =					summ
									UpperCAmelCase_     : Any			     =					i

			UpperCAmelCase_     : Dict			     =					0
			for i in range(mid + 1	,high + 1						):
						summ += arr[i]
						if summ > right_sum:
									UpperCAmelCase_     : List[Any]			     =					summ
									UpperCAmelCase_     : Optional[Any]			     =					i

			return max_left, max_right, (left_sum + right_sum)

def 				snake_case      (   A__						):
			UpperCAmelCase_     : str			     =					[randint(1	,A__						) for _ in range(A__						)]
			UpperCAmelCase_     : str			     =					time.time()
			max_subarray(A__	,0	,input_size - 1						)
			UpperCAmelCase_     : int			     =					time.time()
			return end - start

def 				snake_case      (   ):
			UpperCAmelCase_     : int			     =					[10, 1_00, 10_00, 1_00_00, 5_00_00, 10_00_00, 20_00_00, 30_00_00, 40_00_00, 50_00_00]
			UpperCAmelCase_     : List[str]			     =					[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()



