

from __future__ import annotations

from scipy.special import comb  # type: ignore

class 				__UpperCamelCase				:







	def __init__(   self: Dict  , __UpperCamelCase: Union[str, Any]      ):

						'''simple docstring'''





						__magic_name__							=    list_of_points
						# Degree determines the flexibility of the curve.
						# Degree = 1 will produce a straight line.
						__magic_name__							=    len(__UpperCamelCase      ) - 1







	def 	_SCREAMING_SNAKE_CASE							(   self: Optional[int]  , __UpperCamelCase: int      ):

						'''simple docstring'''





						assert 0 <= t <= 1, "Time t must be between 0 and 1."
						__magic_name__							=    []
						for i in range(len(self.list_of_points      )      ):
											# basis function for each i
											output_values.append(
											    comb(self.degree  , __UpperCamelCase      ) * ((1 - t) ** (self.degree - i)) * (t**i)      )
						# the basis must sum up to 1 for it to produce a valid Bezier curve.
						assert round(sum(__UpperCamelCase      )  , 5      ) == 1
						return output_values







	def 	_SCREAMING_SNAKE_CASE							(   self: Optional[int]  , __UpperCamelCase: Optional[int]      ):

						'''simple docstring'''





						assert 0 <= t <= 1, "Time t must be between 0 and 1."

						__magic_name__							=    self.basis_function(__UpperCamelCase      )
						__magic_name__							=    0.0
						__magic_name__							=    0.0
						for i in range(len(self.list_of_points      )      ):
											# For all points, sum up the product of i-th basis function and i-th point.
											x += basis_function[i] * self.list_of_points[i][0]
											y += basis_function[i] * self.list_of_points[i][1]
						return (x, y)







	def 	_SCREAMING_SNAKE_CASE							(   self: Any  , __UpperCamelCase: List[Any] = 0.01      ):

						'''simple docstring'''





						from matplotlib import pyplot as plt  # type: ignore

						__magic_name__							=    []  # x coordinates of points to plot
						__magic_name__							=    []  # y coordinates of points to plot

						__magic_name__							=    0.0
						while t <= 1:
											__magic_name__							=    self.bezier_curve_function(__UpperCamelCase      )
											to_plot_x.append(value[0]      )
											to_plot_y.append(value[1]      )
											t += step_size

						__magic_name__							=    [i[0] for i in self.list_of_points]
						__magic_name__							=    [i[1] for i in self.list_of_points]

						plt.plot(
						    __UpperCamelCase  , __UpperCamelCase  , color='blue'  , label='Curve of Degree ' + str(self.degree      )  , )
						plt.scatter(__UpperCamelCase  , __UpperCamelCase  , color='red'  , label='Control Points'      )
						plt.legend()
						plt.show()


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
						BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
						BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3



from __future__ import annotations




def 					_lowercase     (				a_				:					list[int]				)				->	int:




					'''simple docstring'''







					if not nums:
										return 0
					__magic_name__							=    nums[0]
					__magic_name__							=    0
					for num in nums[1:]:
										__magic_name__,	__magic_name__							=    (
										    max_excluding + num,
										    max(a_					,a_				),
										)
					return max(a_					,a_				)


if __name__ == "__main__":
						import doctest

						doctest.testmod()




