


'''simple docstring'''






import random


def       _snake_case     (  A				,					A )		->					tuple:
							lowerCAmelCase__     ,      lowerCAmelCase__     ,      lowerCAmelCase__      =			[], [], []
							for element in data:
														if element < pivot:
																					less.append(A )
														elif element > pivot:
																					greater.append(A )
														else:
																					equal.append(A )
							return less, equal, greater






def       _snake_case     (  A				,					A )		->					Tuple:
							# index = len(items) // 2 when trying to find the median
							#   (value of index when items is sorted)

							# invalid input
							if index >= len(A ) or index < 0:
														return None

							lowerCAmelCase__      =			items[random.randint(0				,					len(A ) - 1 )]
							lowerCAmelCase__      =			0
							lowerCAmelCase__     ,      lowerCAmelCase__     ,      lowerCAmelCase__      =			_partition(A				,					A )
							lowerCAmelCase__      =			len(A )
							lowerCAmelCase__      =			len(A )

							# index is the pivot
							if m <= index < m + count:
														return pivot
							# must be in smaller
							elif m > index:
														return quick_select(A				,					A )
							# must be in larger
							else:
														return quick_select(A				,					index - (m + count) )



'''simple docstring'''






import doctest
from collections import deque

import numpy as np




class 	a__       :





							'''simple docstring'''






							def __init__(	self     ) ->							None:
														lowerCAmelCase__      =			[2, 1, 2, -1]
														lowerCAmelCase__      =			[1, 2, 3, 4]







							def 						__SCREAMING_SNAKE_CASE							(	self     ) ->							list[float]:
														lowerCAmelCase__      =			len(self.first_signal     )
														lowerCAmelCase__      =			len(self.second_signal     )

														lowerCAmelCase__      =			max(lowerCamelCase_      ,					lowerCamelCase_     )

														# create a zero matrix of max_length x max_length
														lowerCAmelCase__      =			[[0] * max_length for i in range(lowerCamelCase_     )]

														# fills the smaller signal with zeros to make both signals of same length
														if length_first_signal < length_second_signal:
																					self.first_signal += [0] * (max_length - length_first_signal)
														elif length_first_signal > length_second_signal:
																					self.second_signal += [0] * (max_length - length_second_signal)
														for i in range(lowerCamelCase_     ):
																					lowerCAmelCase__      =			deque(self.second_signal     )
																					rotated_signal.rotate(lowerCamelCase_     )
																					for j, item in enumerate(lowerCamelCase_     ):
																												matrix[i][j] += item

        # multiply the matrix with the first signal
														lowerCAmelCase__      =			np.matmul(np.transpose(lowerCamelCase_     )      ,					np.transpose(self.first_signal     )     )

														# rounding-off to two decimal places
														return [round(lowerCamelCase_      ,					2     ) for i in final_signal]


if __name__ == "__main__":
		doctest.testmod()