


'''simple docstring'''







from __future__ import annotations

from scipy.special import comb  # type: ignore
class 						UpperCamelCase__       :



     """simple docstring"""






     def __init__(			self   ,						snake_case__ ):

            '''simple docstring'''

            _lowerCAmelCase     :				List[str]       =							list_of_points
            # Degree determines the flexibility of the curve.
            # Degree = 1 will produce a straight line.
            _lowerCAmelCase     :				int       =							len(UpperCAmelCase_ ) - 1







     def a						(			self   ,						snake_case__ ):

            '''simple docstring'''

            assert 0 <= t <= 1, "Time t must be between 0 and 1."
            _lowerCAmelCase     :				Optional[Any]       =							[]
            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 a						(			self   ,						snake_case__ ):

            '''simple docstring'''

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

            _lowerCAmelCase     :				Tuple       =							self.basis_function(UpperCAmelCase_ )
            _lowerCAmelCase     :				int       =							0.0
            _lowerCAmelCase     :				Optional[int]       =							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 a						(			self   ,						snake_case__ = 0.01 ):

            '''simple docstring'''

            from matplotlib import pyplot as plt  # type: ignore

            _lowerCAmelCase     :				Optional[Any]       =							[]  # x coordinates of points to plot
            _lowerCAmelCase     :				Tuple       =							[]  # y coordinates of points to plot

            _lowerCAmelCase     :				List[Any]       =							0.0
            while t <= 1:
                   _lowerCAmelCase     :				Dict       =							self.bezier_curve_function(UpperCAmelCase_ )
                   to_plot_x.append(value[0] )
                   to_plot_y.append(value[1] )
                   t += step_size

            _lowerCAmelCase     :				List[str]       =							[i[0] for i in self.list_of_points]
            _lowerCAmelCase     :				Any       =							[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






'''simple docstring'''





import json
from typing import Iterator, List, Union

from tokenizers import AddedToken, Regex, Tokenizer, decoders, normalizers, pre_tokenizers, trainers
from tokenizers.implementations.base_tokenizer import BaseTokenizer
from tokenizers.models import Unigram
from tokenizers.processors import TemplateProcessing


class 					snake_case			(UpperCamelCase ):



       def __init__(					self  ,UpperCAmelCase_ = "▁"  ,UpperCAmelCase_ = True  ,UpperCAmelCase_ = "<unk>"  ,UpperCAmelCase_ = "</s>"  ,UpperCAmelCase_ = "<pad>"  ,)	->				Optional[int]:
           lowercase__									=    {
               "pad": {"id": 0, "token": pad_token},
               "eos": {"id": 1, "token": eos_token},
               "unk": {"id": 2, "token": unk_token},
           }

           lowercase__									=    [None] * len(self.special_tokens   )
           for token_dict in self.special_tokens.values():
               lowercase__									=    token_dict["token"]

           lowercase__									=    Tokenizer(Unigram()   )

           lowercase__									=    normalizers.Sequence(
               [
                   normalizers.Nmt(),
                   normalizers.NFKC(),
                   normalizers.Replace(Regex(" {2,}"   )  ," "   ),
                   normalizers.Lowercase(),
               ]   )
           lowercase__									=    pre_tokenizers.Sequence(
               [
                   pre_tokenizers.Metaspace(replacement=UpperCAmelCase_  ,add_prefix_space=UpperCAmelCase_   ),
                   pre_tokenizers.Digits(individual_digits=UpperCAmelCase_   ),
                   pre_tokenizers.Punctuation(),
               ]   )
           lowercase__									=    decoders.Metaspace(replacement=UpperCAmelCase_  ,add_prefix_space=UpperCAmelCase_   )

           lowercase__									=    TemplateProcessing(
               single=F'''$A {self.special_tokens['eos']['token']}'''  ,special_tokens=[(self.special_tokens["eos"]["token"], self.special_tokens["eos"]["id"])]  ,)

           lowercase__									=    {
               "model": "SentencePieceUnigram",
               "replacement": replacement,
               "add_prefix_space": add_prefix_space,
           }

           super().__init__(UpperCAmelCase_  ,UpperCAmelCase_   )



       def 				_a   (					self  ,UpperCAmelCase_  ,UpperCAmelCase_ = 8_000  ,UpperCAmelCase_ = True  ,)	->				List[str]:
           lowercase__									=    trainers.UnigramTrainer(
               vocab_size=UpperCAmelCase_  ,special_tokens=self.special_tokens_list  ,show_progress=UpperCAmelCase_  ,)

           if isinstance(UpperCAmelCase_  ,UpperCAmelCase_   ):
               lowercase__									=    [files]
           self._tokenizer.train(UpperCAmelCase_  ,trainer=UpperCAmelCase_   )

           self.add_unk_id()



       def 				_a   (					self  ,UpperCAmelCase_  ,UpperCAmelCase_ = 8_000  ,UpperCAmelCase_ = True  ,)	->				Union[str, Any]:
           lowercase__									=    trainers.UnigramTrainer(
               vocab_size=UpperCAmelCase_  ,special_tokens=self.special_tokens_list  ,show_progress=UpperCAmelCase_  ,)

           self._tokenizer.train_from_iterator(UpperCAmelCase_  ,trainer=UpperCAmelCase_   )

           self.add_unk_id()







       def 				_a   (					self   )	->				str:
           lowercase__									=    json.loads(self._tokenizer.to_str()   )

           lowercase__									=    self.special_tokens["unk"]["id"]

           lowercase__									=    Tokenizer.from_str(json.dumps(UpperCAmelCase_   )   )




