

"""simple docstring"""





from __future__ import annotations

from collections.abc import MutableSequence







class 				SCREAMING_SNAKE_CASE					:






					"""simple docstring"""



					def __init__(       self			:				Dict   ,lowercase_			:				int   ,lowercase_			:				MutableSequence[float]		):
						if len(_lowerCamelCase		) != degree + 1:
							raise ValueError(
							    '''The number of coefficients should be equal to the degree + 1.'''		)

						lowerCAmelCase__	:						Optional[int]  				=	list(_lowerCamelCase		)
						lowerCAmelCase__	:						str  				=	degree







					def __add__(       self			:				List[Any]   ,lowercase_			:				Polynomial		):

						if self.degree > polynomial_a.degree:
							lowerCAmelCase__	:						str  				=	self.coefficients[:]
							for i in range(polynomial_a.degree + 1		):
								coefficients[i] += polynomial_a.coefficients[i]
							return Polynomial(self.degree   ,_lowerCamelCase		)
						else:
							lowerCAmelCase__	:						Any  				=	polynomial_a.coefficients[:]
							for i in range(self.degree + 1		):
								coefficients[i] += self.coefficients[i]
							return Polynomial(polynomial_a.degree   ,_lowerCamelCase		)







					def __sub__(       self			:				Optional[int]   ,lowercase_			:				Polynomial		):
						return self + polynomial_a * Polynomial(0   ,[-1]		)







					def __neg__(       self			:				Optional[int]		):
						return Polynomial(self.degree   ,[-c for c in self.coefficients]		)







					def __mul__(       self			:				List[Any]   ,lowercase_			:				Polynomial		):
						lowerCAmelCase__	:						str  				=	[0] * (self.degree + polynomial_a.degree + 1)
						for i in range(self.degree + 1		):
							for j in range(polynomial_a.degree + 1		):
								coefficients[i + j] += (
								    self.coefficients[i] * polynomial_a.coefficients[j]
								)

						return Polynomial(self.degree + polynomial_a.degree   ,_lowerCamelCase		)







					def        __lowerCAmelCase (       self			:				Union[str, Any]   ,lowercase_			:				int | float		):
						lowerCAmelCase__	:						int  				=	0
						for i in range(self.degree + 1		):
							result += self.coefficients[i] * (substitution**i)
						return result







					def __str__(       self			:				Tuple		):
						lowerCAmelCase__	:						str  				=	''''''
						for i in range(self.degree   ,-1   ,-1		):
							if self.coefficients[i] == 0:
								continue
							elif self.coefficients[i] > 0:
								if polynomial:
									polynomial += " + "
							else:
								polynomial += " - "

							if i == 0:
								polynomial += str(abs(self.coefficients[i]		)		)
							elif i == 1:
								polynomial += str(abs(self.coefficients[i]		)		) + "x"
							else:
								polynomial += str(abs(self.coefficients[i]		)		) + "x^" + str(_lowerCamelCase		)

						return polynomial







					def __repr__(       self			:				List[str]		):
						return self.__str__()







					def        __lowerCAmelCase (       self			:				Optional[int]		):
						lowerCAmelCase__	:						Dict  				=	[0] * self.degree
						for i in range(self.degree		):
							lowerCAmelCase__	:						int  				=	self.coefficients[i + 1] * (i + 1)
						return Polynomial(self.degree - 1   ,_lowerCamelCase		)







					def        __lowerCAmelCase (       self			:				List[str]   ,lowercase_			:				int | float = 0		):
						lowerCAmelCase__	:						Union[str, Any]  				=	[0] * (self.degree + 2)
						lowerCAmelCase__	:						Tuple  				=	constant
						for i in range(self.degree + 1		):
							lowerCAmelCase__	:						int  				=	self.coefficients[i] / (i + 1)
						return Polynomial(self.degree + 1   ,_lowerCamelCase		)







					def __eq__(       self			:				Optional[int]   ,lowercase_			:				object		):
						if not isinstance(_lowerCamelCase   ,_lowerCamelCase		):
							return False

						if self.degree != polynomial_a.degree:
							return False

						for i in range(self.degree + 1		):
							if self.coefficients[i] != polynomial_a.coefficients[i]:
								return False

						return True







					def __ne__(       self			:				List[Any]   ,lowercase_			:				object		):
						return not self.__eq__(_lowerCamelCase		)












"""simple docstring"""


from __future__ import annotations


class 					snake_case		:


   '''simple docstring'''

   def __init__(	self :     int,       _lowerCamelCase :     List[Any]=None  ):

     '''simple docstring'''
     __A									= data
     __A									= None






   def __repr__(	self :     Union[str, Any]  ):

     '''simple docstring'''
     __A									= []
     __A									= self
     while temp:
       string_rep.append(f'{temp.data}'  )
       __A									= temp.next
     return "->".join(_lowerCamelCase  )





def 					lowerCAmelCase				(    __UpperCamelCase ):




  """simple docstring"""







  if not elements_list:
    raise Exception('''The Elements List is empty''' )

  __A									= __A									= Node(elements_list[0] )
  for i in range(1		,       len(__UpperCamelCase ) ):
    __A									= Node(elements_list[i] )
    __A									= current.next
  return head



def 					lowerCAmelCase				(    __UpperCamelCase ):




  """simple docstring"""







  if head_node is not None and isinstance(__UpperCamelCase		,       __UpperCamelCase ):
    print_reverse(head_node.next )
    print(head_node.data )



def 					lowerCAmelCase				(    ):




  """simple docstring"""







  from doctest import testmod

  testmod()

  __A									= make_linked_list([1_4, 5_2, 1_4, 1_2, 4_3] )
  print('''Linked List:''' )
  print(__UpperCamelCase )
  print('''Elements in Reverse:''' )
  print_reverse(__UpperCamelCase )


if __name__ == "__main__":
       main()




