

'''simple docstring'''
from __future__ import annotations







class 							A__    :





  def __init__(		self      :	int							,					_a      :	int )	->    None:





       '''simple docstring'''






       _SCREAMING_SNAKE_CASE							    =order

       # a_{0} ... a_{k}
       _SCREAMING_SNAKE_CASE							    =[1.0] + [0.0] * order
       # b_{0} ... b_{k}
       _SCREAMING_SNAKE_CASE							    =[1.0] + [0.0] * order

       # x[n-1] ... x[n-k]
       _SCREAMING_SNAKE_CASE							    =[0.0] * self.order
       # y[n-1] ... y[n-k]
       _SCREAMING_SNAKE_CASE							    =[0.0] * self.order





  def 						A  (		self      :	Dict							,					_a      :	list[float]							,					_a      :	list[float] )	->    None:





       '''simple docstring'''






       if len(_a ) < self.order:
            _SCREAMING_SNAKE_CASE							    =[1.0, *a_coeffs]

       if len(_a ) != self.order + 1:
            _SCREAMING_SNAKE_CASE							    =(
                f"Expected a_coeffs to have {self.order + 1} elements "
                f"for {self.order}-order filter, got {len(_a )}"
            )
            raise ValueError(_a )

       if len(_a ) != self.order + 1:
            _SCREAMING_SNAKE_CASE							    =(
                f"Expected b_coeffs to have {self.order + 1} elements "
                f"for {self.order}-order filter, got {len(_a )}"
            )
            raise ValueError(_a )

       _SCREAMING_SNAKE_CASE							    =a_coeffs
       _SCREAMING_SNAKE_CASE							    =b_coeffs





  def 						A  (		self      :	Union[str, Any]							,					_a      :	float )	->    float:





       '''simple docstring'''






       _SCREAMING_SNAKE_CASE							    =0.0

       # Start at index 1 and do index 0 at the end.
       for i in range(1							,					self.order + 1 ):
            result += (
                self.b_coeffs[i] * self.input_history[i - 1]
                - self.a_coeffs[i] * self.output_history[i - 1]
            )

       _SCREAMING_SNAKE_CASE							    =(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

       _SCREAMING_SNAKE_CASE							    =self.input_history[:-1]
       _SCREAMING_SNAKE_CASE							    =self.output_history[:-1]

       _SCREAMING_SNAKE_CASE							    =sample
       _SCREAMING_SNAKE_CASE							    =result

       return result








"""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()



