



"""simple docstring"""







from __future__ import annotations

from scipy.special import comb  # type: ignore

class       _a  :



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



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



			def 				__lowercase					(			self							:				Union[str, Any]   ,	_lowercase							:				float		)							->					tuple[float, float]:
									assert 0 <= t <= 1, "Time t must be between 0 and 1."

									snake_case   :			Optional[int]						    = self.basis_function(_lowercase		)
									snake_case   :			Tuple						    = 0.0
									snake_case   :			Optional[Any]						    = 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 				__lowercase					(			self							:				Tuple   ,	_lowercase							:				float = 0.01		)							->					Optional[Any]:
									from matplotlib import pyplot as plt  # type: ignore

									snake_case   :			list[float]						    = []  # x coordinates of points to plot
									snake_case   :			list[float]						    = []  # y coordinates of points to plot

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

									snake_case   :			Any						    = [i[0] for i in self.list_of_points]
									snake_case   :			Tuple						    = [i[1] for i in self.list_of_points]

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

A		=						'#'

class       _a  :



			def __init__(			self							:				List[Any]		)							->					None:
									snake_case   :			dict						    = {}



			def 				__lowercase					(			self							:				str   ,	_lowercase							:				str		)							->					None:
									snake_case   :			Optional[int]						    = self._trie
									for char in text:
															if char not in trie:
																					snake_case   :			str						    = {}
															snake_case   :			Optional[Any]						    = trie[char]
									snake_case   :			str						    = True



			def 				__lowercase					(			self							:				List[Any]   ,	_lowercase							:				str		)							->					tuple | list:
									snake_case   :			Dict						    = self._trie
									for char in prefix:
															if char in trie:
																					snake_case   :			Tuple						    = trie[char]
															else:
																					return []
									return self._elements(_lowercase		)



			def 				__lowercase					(			self							:				Optional[int]   ,	_lowercase							:				dict		)							->					tuple:
									snake_case   :			int						    = []
									for c, v in d.items():
															snake_case   :			int						    = [" "] if c == END else [(c + s) for s in self._elements(_lowercase		)]
															result.extend(_lowercase		)
									return tuple(_lowercase		)



A		=						Trie()
A		=						('depart', 'detergent', 'daring', 'dog', 'deer', 'deal')
for word in words:
			trie.insert_word(word)

def  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							str ):
						"""simple docstring"""






						snake_case   :			Optional[int]						    = trie.find_word(lowerCamelCase_ )
						return tuple(string + word for word in suffixes )

def  __SCREAMING_SNAKE_CASE		(			):
						"""simple docstring"""






						print(autocomplete_using_trie("de" ) )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			main()



