

"""simple docstring"""




from dataclasses import dataclass, field
from typing import TYPE_CHECKING, Any, ClassVar, Dict, List, Optional, Union

import pyarrow as pa


if TYPE_CHECKING:
						from .features import FeatureType





@dataclass
class       lowerCamelCase  :
			lowerCamelCase__      :						List[str]
			lowerCamelCase__      :						Optional[str]    						=							None
			# Automatically constructed
			lowerCamelCase__      :						ClassVar[str]    						=							"dict"
			lowerCamelCase__      :						ClassVar[Any]    						=							None
			lowerCamelCase__      :						str    						=							field(default='Translation'	,init=_UpperCamelCase	,repr=_UpperCamelCase	)

			def __call__(    self :  Any				)      ->			Union[str, Any]:
						return pa.struct({lang: pa.string() for lang in sorted(self.languages				)}				)





			def     SCREAMING_SNAKE_CASE (    self :  Union[str, Any]				)      ->			Union["FeatureType", Dict[str, "FeatureType"]]:
						from .features import Value

						return {k: Value("""string"""				) for k in sorted(self.languages				)}





@dataclass
class       lowerCamelCase  :
			lowerCamelCase__      :						Optional[List]    						=							None
			lowerCamelCase__      :						Optional[int]    						=							None
			lowerCamelCase__      :						Optional[str]    						=							None
			# Automatically constructed
			lowerCamelCase__      :						ClassVar[str]    						=							"dict"
			lowerCamelCase__      :						ClassVar[Any]    						=							None
			lowerCamelCase__      :						str    						=							field(default='TranslationVariableLanguages'	,init=_UpperCamelCase	,repr=_UpperCamelCase	)

			def     SCREAMING_SNAKE_CASE (    self :  int				)      ->			List[Any]:
						SCREAMING_SNAKE_CASE__									=					sorted(set(self.languages				)				) if self.languages else None
						SCREAMING_SNAKE_CASE__									=					len(self.languages				) if self.languages else None

			def __call__(    self :  str				)      ->			Dict:
						return pa.struct({"""language""": pa.list_(pa.string()				), """translation""": pa.list_(pa.string()				)}				)

			def     SCREAMING_SNAKE_CASE (    self :  int			, __UpperCAmelCase :  Tuple				)      ->			Dict:
						SCREAMING_SNAKE_CASE__									=					set(self.languages				)
						if self.languages and set(__lowerCamelCase				) - lang_set:
									raise ValueError(
									    F"""Some languages in example ({", ".join(sorted(set(__lowerCamelCase				) - lang_set				)				)}) are not in valid set ({", ".join(__lowerCamelCase				)})."""				)

						# Convert dictionary into tuples, splitting out cases where there are
						# multiple translations for a single language.
						SCREAMING_SNAKE_CASE__									=					[]
						for lang, text in translation_dict.items():
									if isinstance(__lowerCamelCase			, __lowerCamelCase				):
												translation_tuples.append((lang, text)				)
									else:
												translation_tuples.extend([(lang, el) for el in text]				)

        # Ensure translations are in ascending order by language code.
						SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__									=					zip(*sorted(__lowerCamelCase				)				)

						return {"language": languages, "translation": translations}





			def     SCREAMING_SNAKE_CASE (    self :  List[Any]				)      ->			Union["FeatureType", Dict[str, "FeatureType"]]:
						from .features import Sequence, Value

						return {
						    "language": Sequence(Value("""string"""				)				),
						    "translation": Sequence(Value("""string"""				)				),
						}








from __future__ import annotations

from scipy.special import comb  # type: ignore




class     snake_case__							:
				"""simple docstring"""



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





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

							a    =			self.basis_function(__lowerCamelCase							)
							a    =			0.0
							a    =			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				:     Optional[Any]					,      __lowerCamelCase				:     float = 0.01							)					->     List[str]:
							from matplotlib import pyplot as plt  # type: ignore

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

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

							a    =			[i[0] for i in self.list_of_points]
							a    =			[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






