






def      lowercase__      (     __snake_case    :							Dict  ):


					'''simple docstring'''


					if not head:
										return True
					# split the list to two parts
					UpperCAmelCase_       ,  UpperCAmelCase_    :      Any            =						head.next, head
					while fast and fast.next:
										UpperCAmelCase_    :      str            =						fast.next.next
										UpperCAmelCase_    :      Union[str, Any]            =						slow.next
					UpperCAmelCase_    :      int            =						slow.next
					UpperCAmelCase_    :      List[Any]            =						None  # Don't forget here! But forget still works!
					# reverse the second part
					UpperCAmelCase_    :      Tuple            =						None
					while second:
										UpperCAmelCase_    :      int            =						second.next
										UpperCAmelCase_    :      Any            =						node
										UpperCAmelCase_    :      Optional[Any]            =						second
										UpperCAmelCase_    :      Tuple            =						nxt
					# compare two parts
					# second part has the same or one less node
					while node:
										if node.val != head.val:
															return False
										UpperCAmelCase_    :      Optional[Any]            =						node.next
										UpperCAmelCase_    :      Dict            =						head.next
					return True




def      lowercase__      (     __snake_case    :							Union[str, Any]  ):


					'''simple docstring'''


					if not head or not head.next:
										return True

					# 1. Get the midpoint (slow)
					UpperCAmelCase_    :      Any            =						head
					while fast and fast.next:
										UpperCAmelCase_       ,  UpperCAmelCase_    :      Tuple            =						fast.next.next, slow.next

					# 2. Push the second half into the stack
					UpperCAmelCase_    :      List[str]            =						[slow.val]
					while slow.next:
										UpperCAmelCase_    :      List[str]            =						slow.next
										stack.append(slow.val  )

					# 3. Comparison
					while stack:
										if stack.pop() != cur.val:
															return False
										UpperCAmelCase_    :      int            =						cur.next

					return True






def      lowercase__      (     __snake_case    :							Dict  ):


					'''simple docstring'''


					if not head or not head.next:
										return True
					UpperCAmelCase_    :      Tuple            =						{}
					UpperCAmelCase_    :      int            =						0
					while head:
										if head.val in d:
															d[head.val].append(__snake_case  )
										else:
															UpperCAmelCase_    :      List[Any]            =						[pos]
										UpperCAmelCase_    :      Any            =						head.next
										pos += 1
					UpperCAmelCase_    :      Dict            =						pos - 1
					UpperCAmelCase_    :      Optional[int]            =						0
					for v in d.values():
										if len(__snake_case  ) % 2 != 0:
															middle += 1
										else:
															UpperCAmelCase_    :      int            =						0
															for i in range(0     ,       len(__snake_case  )  ):
																				if v[i] + v[len(__snake_case  ) - 1 - step] != checksum:
																									return False
																				step += 1
										if middle > 1:
															return False
					return True







'''simple docstring'''

import doctest
from collections import deque

import numpy as np



class 			UpperCAmelCase  :





       '''simple docstring'''



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


       def _lowerCAmelCase(						self )  ->  list[float]:
        lowercase__				:    Optional[Any]  =					len(self.first_signal )
        lowercase__				:    Union[str, Any]  =					len(self.second_signal )

        lowercase__				:    int  =					max(__lowerCAmelCase	,   __lowerCAmelCase )

        # create a zero matrix of max_length x max_length
        lowercase__				:    List[str]  =					[[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 ):
         lowercase__				:    int  =					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
        lowercase__				:    Optional[int]  =					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()

