





'''simple docstring'''




from __future__ import annotations

from collections.abc import MutableSequence


class  SCREAMING_SNAKE_CASE    :


     def __init__(						self						,	_UpperCAmelCase						,	_UpperCAmelCase):

          '''simple docstring'''






          if len(_UpperCAmelCase) != degree + 1:
               raise ValueError(
                   'The number of coefficients should be equal to the degree + 1.')

          __A						: list[float]      =       list(_UpperCAmelCase)
          __A						: Tuple      =       degree


     def __add__(						self						,	_UpperCAmelCase):

          '''simple docstring'''






          if self.degree > polynomial_a.degree:
               __A						: Dict      =       self.coefficients[:]
               for i in range(polynomial_a.degree + 1):
                    coefficients[i] += polynomial_a.coefficients[i]
               return Polynomial(self.degree						,	_UpperCAmelCase)
          else:
               __A						: Dict      =       polynomial_a.coefficients[:]
               for i in range(self.degree + 1):
                    coefficients[i] += self.coefficients[i]
               return Polynomial(polynomial_a.degree						,	_UpperCAmelCase)


     def __sub__(						self						,	_UpperCAmelCase):

          '''simple docstring'''






          return self + polynomial_a * Polynomial(0						,	[-1])


     def __neg__(						self):

          '''simple docstring'''






          return Polynomial(self.degree						,	[-c for c in self.coefficients])


     def __mul__(						self						,	_UpperCAmelCase):

          '''simple docstring'''






          __A						: list[float]      =       [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						,	_UpperCAmelCase)


     def 							SCREAMING_SNAKE_CASE  (						self						,	_UpperCAmelCase):

          '''simple docstring'''






          __A						: int | float      =       0
          for i in range(self.degree + 1):
               result += self.coefficients[i] * (substitution**i)
          return result


     def __str__(						self):

          '''simple docstring'''






          __A						: List[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(_UpperCAmelCase)

          return polynomial


     def __repr__(						self):

          '''simple docstring'''






          return self.__str__()


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          __A						: list[float]      =       [0] * self.degree
          for i in range(self.degree):
               __A						: str      =       self.coefficients[i + 1] * (i + 1)
          return Polynomial(self.degree - 1						,	_UpperCAmelCase)


     def 							SCREAMING_SNAKE_CASE  (						self						,	_UpperCAmelCase = 0):

          '''simple docstring'''






          __A						: list[float]      =       [0] * (self.degree + 2)
          __A						: List[str]      =       constant
          for i in range(self.degree + 1):
               __A						: Union[str, Any]      =       self.coefficients[i] / (i + 1)
          return Polynomial(self.degree + 1						,	_UpperCAmelCase)


     def __eq__(						self						,	_UpperCAmelCase):

          '''simple docstring'''






          if not isinstance(_UpperCAmelCase						,	_UpperCAmelCase):
               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						,	_UpperCAmelCase):

          '''simple docstring'''






          return not self.__eq__(_UpperCAmelCase)






'''simple docstring'''




import random






def        _lowerCAmelCase			(  __snake_case  : int ,							__snake_case  : float ,							__snake_case  : bool = False			)     ->     dict:
     __A						: dict      =       {i: [] for i in range(__snake_case			)}

     # if probability is greater or equal than 1, then generate a complete graph
     if probability >= 1:
          return complete_graph(__snake_case			)
     # if probability is lower or equal than 0, then return a graph without edges
     if probability <= 0:
          return graph

     # for each couple of nodes, add an edge from u to v
     # if the number randomly generated is greater than probability probability
     for i in range(__snake_case			):
          for j in range(i + 1 ,							__snake_case			):
               if random.random() < probability:
                    graph[i].append(__snake_case			)
                    if not directed:
                         # if the graph is undirected, add an edge in from j to i, either
                         graph[j].append(__snake_case			)
     return graph






def        _lowerCAmelCase			(  __snake_case  : int			)     ->     dict:
     return {
         i: [j for j in range(__snake_case			) if i != j] for i in range(__snake_case			)
     }


if __name__ == "__main__":
  import doctest

  doctest.testmod()