

from __future__ import annotations

from typing import TypedDict


class 			A						(							_UpperCAmelCase			):







    """simple docstring"""





    lowerCamelCase		     =							42
    lowerCamelCase		     =							42




def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     str				)							->				list[str]:





    '''simple docstring'''






    if not isinstance(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				):
        raise TypeError('The parameter s type must be str.'				)

    return [s[i:] + s[:i] for i in range(len(SCREAMING_SNAKE_CASE__				)				)]
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     str				)							->				BWTTransformDict:





    '''simple docstring'''






    if not isinstance(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				):
        raise TypeError('The parameter s type must be str.'				)
    if not s:
        raise ValueError('The parameter s must not be empty.'				)

    A__   				=       all_rotations(SCREAMING_SNAKE_CASE__				)
    rotations.sort()  # sort the list of rotations in alphabetically order
    # make a string composed of the last char of each rotation
    A__   				=       {
        "bwt_string": "".join([word[-1] for word in rotations]				),
        "idx_original_string": rotations.index(SCREAMING_SNAKE_CASE__				),
    }
    return response
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     str   ,      SCREAMING_SNAKE_CASE__      :     int				)							->				str:





    '''simple docstring'''






    if not isinstance(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				):
        raise TypeError('The parameter bwt_string type must be str.'				)
    if not bwt_string:
        raise ValueError('The parameter bwt_string must not be empty.'				)
    try:
        A__   				=       int(SCREAMING_SNAKE_CASE__				)
    except ValueError:
        raise TypeError(
            'The parameter idx_original_string type must be int or passive'
            ' of cast to int.'				)
    if idx_original_string < 0:
        raise ValueError('The parameter idx_original_string must not be lower than 0.'				)
    if idx_original_string >= len(SCREAMING_SNAKE_CASE__				):
        raise ValueError(
            'The parameter idx_original_string must be lower than' ' len(bwt_string).'				)

    A__   				=       [''] * len(SCREAMING_SNAKE_CASE__				)
    for _ in range(len(SCREAMING_SNAKE_CASE__				)				):
        for i in range(len(SCREAMING_SNAKE_CASE__				)				):
            A__   				=       bwt_string[i] + ordered_rotations[i]
        ordered_rotations.sort()
    return ordered_rotations[idx_original_string]


if __name__ == "__main__":
     lowercase_			=  "Provide a string that I will generate its BWT transform: "
     lowercase_			=  input(entry_msg).strip()
     lowercase_			=  bwt_transform(s)
     print(
         f"""Burrows Wheeler transform for string '{s}' results """
         f"""in '{result["bwt_string"]}'"""
     )
     lowercase_			=  reverse_bwt(result["bwt_string"], result["idx_original_string"])
     print(
         f"""Reversing Burrows Wheeler transform for entry '{result["bwt_string"]}' """
         f"""we get original string '{original_string}'"""
     )




from __future__ import annotations

from scipy.special import comb  # type: ignore


class 			A						:







    """simple docstring"""





    def __init__(				self			:	Any,lowercase_			:	list[tuple[float, float]]		)->   Optional[int]:





        '''simple docstring'''







        A__   				=       list_of_points
        # Degree determines the flexibility of the curve.
        # Degree = 1 will produce a straight line.
        A__   				=       len(lowercase_		) - 1


    def 						snake_case__					(				self			:	List[Any],lowercase_			:	float		)->   list[float]:





        '''simple docstring'''







        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,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 						snake_case__					(				self			:	str,lowercase_			:	float		)->   tuple[float, float]:





        '''simple docstring'''







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

        A__   				=       self.basis_function(lowercase_		)
        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 						snake_case__					(				self			:	str,lowercase_			:	float = 0.01		)->   str:





        '''simple docstring'''







        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(lowercase_		)
            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(
            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

