




"""simple docstring"""







from __future__ import annotations

from scipy.special import comb  # type: ignore

class 				snake_case_			:







   """simple docstring"""




   def __init__(		self       ,					lowerCamelCase_)				->   Optional[Any]:
       UpperCamelCase              =	list_of_points
       # Degree determines the flexibility of the curve.
       # Degree = 1 will produce a straight line.
       UpperCamelCase              =	len(lowerCamelCase_) - 1







   def   UpperCAmelCase__			(		self       ,					lowerCamelCase_)				->   list[float]:
       assert 0 <= t <= 1, "Time t must be between 0 and 1."
       UpperCamelCase              =	[]
       for i in range(len(self.list_of_points)):
           # basis function for each i
           output_values.append(
               comb(self.degree       ,					lowerCamelCase_) * ((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(lowerCamelCase_)       ,					5) == 1
       return output_values







   def   UpperCAmelCase__			(		self       ,					lowerCamelCase_)				->   tuple[float, float]:
       assert 0 <= t <= 1, "Time t must be between 0 and 1."

       UpperCamelCase              =	self.basis_function(lowerCamelCase_)
       UpperCamelCase              =	0.0
       UpperCamelCase              =	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   UpperCAmelCase__			(		self       ,					lowerCamelCase_ = 0.01)				->   List[Any]:
       from matplotlib import pyplot as plt  # type: ignore

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

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

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

       plt.plot(
           lowerCamelCase_       ,					lowerCamelCase_       ,					color='''blue'''       ,					label='''Curve of Degree ''' + str(self.degree)       ,					)
       plt.scatter(lowerCamelCase_       ,					lowerCamelCase_       ,					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

'''simple docstring'''
from __future__ import annotations

lowerCAmelCase					:    Union[str, Any]           = [-10, -5, 0, 5, 5.1, 11, 13, 21, 3, 4, -21, -10, -5, -1, 0]
lowerCAmelCase					:    List[str]           = [-5, 0, 5, 5.1, 11, 13, 21, -1, 4, -1, -10, -5, -1, 0, -1]







def 		A_(     A						:		list[float]):
							UpperCamelCase   			=     []
							UpperCamelCase   			=     len(A)

							for i in range(A):
														UpperCamelCase   			=     -1
														for j in range(i + 1		,     A):
																					if arr[i] < arr[j]:
																												UpperCamelCase   			=     arr[j]
																												break
														result.append(A)
							return result







def 		A_(     A						:		list[float]):
							UpperCamelCase   			=     []
							for i, outer in enumerate(A):
														UpperCamelCase   			=     -1
														for inner in arr[i + 1 :]:
																					if outer < inner:
																												UpperCamelCase   			=     inner
																												break
														result.append(A)
							return result







def 		A_(     A						:		list[float]):
							UpperCamelCase   			=     len(A)
							UpperCamelCase   			=     []
							UpperCamelCase   			=     [-1] * arr_size

							for index in reversed(range(A)):
														if stack:
																					while stack[-1] <= arr[index]:
																												stack.pop()
																												if not stack:
																																			break
														if stack:
																					UpperCamelCase   			=     stack[-1]
														stack.append(arr[index])
							return result


if __name__ == "__main__":
						from doctest import testmod
						from timeit import timeit

						testmod()
						print(next_greatest_element_slow(arr))
						print(next_greatest_element_fast(arr))
						print(next_greatest_element(arr))

						lowerCAmelCase					:    Optional[Any]           = (
						    'from __main__ import arr, next_greatest_element_slow, '
						    'next_greatest_element_fast, next_greatest_element'
						)
						print(
						    'next_greatest_element_slow():',
						    timeit('next_greatest_element_slow(arr)', setup=setup),
						)
						print(
						    'next_greatest_element_fast():',
						    timeit('next_greatest_element_fast(arr)', setup=setup),
						)
						print(
						    '     next_greatest_element():',
						    timeit('next_greatest_element(arr)', setup=setup),
						)




