
'''simple docstring'''






from __future__ import annotations

from scipy.special import comb  # type: ignore

class 			UpperCAmelCase__    :



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



    def 	lowerCamelCase_	(						self   :							Optional[int],__A   :							float  ):
          assert 0 <= t <= 1, "Time t must be between 0 and 1."
          _lowerCamelCase					: list[float]		    = []
          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 	lowerCamelCase_	(						self   :							int,__A   :							float  ):
          assert 0 <= t <= 1, "Time t must be between 0 and 1."

          _lowerCamelCase					: List[Any]		    = self.basis_function(__A  )
          _lowerCamelCase					: str		    = 0.0
          _lowerCamelCase					: str		    = 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 	lowerCamelCase_	(						self   :							Optional[Any],__A   :							float = 0.01  ):
          from matplotlib import pyplot as plt  # type: ignore

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

          _lowerCamelCase					: Tuple		    = 0.0
          while t <= 1:
                _lowerCamelCase					: str		    = self.bezier_curve_function(__A  )
                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					: Union[str, Any]		    = [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




import unittest

from knapsack import knapsack as k


class 				_a						(       unittest.TestCase			):





							'''simple docstring'''

							def 		_A	(							self				):







											"""simple docstring"""



											a__	:							List[str]      						= 0
											a__	:							Union[str, Any]      						= [0]
											a__	:							Optional[Any]      						= [0]
											a__	:							Tuple      						= len(__UpperCAmelCase				)
											self.assertEqual(k.knapsack(__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				) ,					0				)

											a__	:							Optional[Any]      						= [60]
											a__	:							Tuple      						= [10]
											a__	:							Optional[Any]      						= len(__UpperCAmelCase				)
											self.assertEqual(k.knapsack(__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				) ,					0				)



							def 		_A	(							self				):







											"""simple docstring"""



											a__	:							Dict      						= 3
											a__	:							Optional[int]      						= [1, 2, 3]
											a__	:							List[Any]      						= [3, 2, 1]
											a__	:							List[Any]      						= len(__UpperCAmelCase				)
											self.assertEqual(k.knapsack(__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				) ,					5				)




							def 		_A	(							self				):







											"""simple docstring"""



											a__	:							List[Any]      						= 50
											a__	:							Union[str, Any]      						= [60, 100, 120]
											a__	:							str      						= [10, 20, 30]
											a__	:							Union[str, Any]      						= len(__UpperCAmelCase				)
											self.assertEqual(k.knapsack(__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				) ,					220				)


if __name__ == "__main__":
						unittest.main()


