



'''simple docstring'''

from __future__ import annotations

from scipy.special import comb  # type: ignore



class 		lowerCamelCase__      :




					'''simple docstring'''



					def __init__(  self				:	Optional[Any]     ,  UpperCamelCase_				:	Tuple					)  ->       List[Any]:



						'''simple docstring'''





						_lowercase					:       List[Any]       =		list_of_points
						# Degree determines the flexibility of the curve.
						# Degree = 1 will produce a straight line.
						_lowercase					:       Optional[int]       =		len(A__					) - 1




					def 						__UpperCAmelCase     (  self				:	Dict     ,  UpperCamelCase_				:	str					)  ->       list[float]:



						'''simple docstring'''





						assert 0 <= t <= 1, "Time t must be between 0 and 1."
						_lowercase					:       Optional[Any]       =		[]
						for i in range(len(self.list_of_points					)					):
							# basis function for each i
							output_values.append(
							    comb(self.degree     ,  A__					) * ((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(A__					)     ,  5					) == 1
						return output_values




					def 						__UpperCAmelCase     (  self				:	Optional[Any]     ,  UpperCamelCase_				:	int					)  ->       tuple[float, float]:



						'''simple docstring'''





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

						_lowercase					:       str       =		self.basis_function(A__					)
						_lowercase					:       str       =		0.0
						_lowercase					:       Dict       =		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				:	Union[str, Any]     ,  UpperCamelCase_				:	List[str] = 0.01					)  ->       str:



						'''simple docstring'''





						from matplotlib import pyplot as plt  # type: ignore

						_lowercase					:       int       =		[]  # x coordinates of points to plot
						_lowercase					:       Union[str, Any]       =		[]  # y coordinates of points to plot

						_lowercase					:       List[str]       =		0.0
						while t <= 1:
							_lowercase					:       List[Any]       =		self.bezier_curve_function(A__					)
							to_plot_x.append(value[0]					)
							to_plot_y.append(value[1]					)
							t += step_size

						_lowercase					:       Optional[Any]       =		[i[0] for i in self.list_of_points]
						_lowercase					:       List[str]       =		[i[1] for i in self.list_of_points]

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

import os
from collections.abc import Iterator







def 						__UpperCamelCase				(							_lowercase = "."					) ->			Iterator[str]:
	for dir_path, dir_names, filenames in os.walk(_lowercase					):
		_lowercase					:       Optional[int]       =		[d for d in dir_names if d != 'scripts' and d[0] not in '._']
		for filename in filenames:
			if filename == "__init__.py":
				continue
			if os.path.splitext(_lowercase					)[1] in (".py", ".ipynb"):
				yield os.path.join(_lowercase,				_lowercase					).lstrip('./'					)







def 						__UpperCamelCase				(							_lowercase					) ->			List[str]:
	return f'''{i * "  "}*''' if i else "\n##"







def 						__UpperCamelCase				(							_lowercase,				_lowercase					) ->			str:
	_lowercase					:       Optional[Any]       =		old_path.split(os.sep					)
	for i, new_part in enumerate(new_path.split(os.sep					)					):
		if (i + 1 > len(_lowercase					) or old_parts[i] != new_part) and new_part:
			print(f'''{md_prefix(_lowercase					)} {new_part.replace("_",				" "					).title()}'''					)
	return new_path







def 						__UpperCamelCase				(							_lowercase = "."					) ->			None:
	_lowercase					:       Dict       =		''
	for filepath in sorted(good_file_paths(_lowercase					)					):
		_lowercase  ,    _lowercase					:       Optional[Any]       =		os.path.split(_lowercase					)
		if filepath != old_path:
			_lowercase					:       Dict       =		print_path(_lowercase,				_lowercase					)
		_lowercase					:       Optional[int]       =		(filepath.count(os.sep					) + 1) if filepath else 0
		_lowercase					:       Dict       =		f'''{filepath}/{filename}'''.replace(' ',				'%20'					)
		_lowercase					:       Optional[int]       =		os.path.splitext(filename.replace('_',				' '					).title()					)[0]
		print(f'''{md_prefix(_lowercase					)} [{filename}]({url})'''					)


if __name__ == "__main__":
		print_directory_md('''.''')
