from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst




def    lowerCAmelCase_ (     )     ->				str:







      '''simple docstring'''


      UpperCAmelCase__		,      UpperCAmelCase__								=  9, 14  # noqa: F841
      UpperCAmelCase__								=  [
          [0, 1, 4],
          [0, 7, 8],
          [1, 2, 8],
          [7, 8, 7],
          [7, 6, 1],
          [2, 8, 2],
          [8, 6, 6],
          [2, 3, 7],
          [2, 5, 4],
          [6, 5, 2],
          [3, 5, 14],
          [3, 4, 9],
          [5, 4, 10],
          [1, 7, 11],
      ]

      UpperCAmelCase__								=  defaultdict(__A							)
      for nodea, nodea, cost in edges:
            adjancency[nodea].append([nodea, cost]							)
            adjancency[nodea].append([nodea, cost]							)

      UpperCAmelCase__								=  mst(__A							)

      UpperCAmelCase__								=  [
          [7, 6, 1],
          [2, 8, 2],
          [6, 5, 2],
          [0, 1, 4],
          [2, 5, 4],
          [2, 3, 7],
          [0, 7, 8],
          [3, 4, 9],
      ]

      for answer in expected:
            UpperCAmelCase__								=  tuple(answer[:2]							)
            UpperCAmelCase__								=  tuple(edge[::-1]							)
            assert edge in result or reverse in result




from __future__ import annotations

from scipy.special import comb  # type: ignore





class      A							:


   def __init__(self     :						List[Any]       ,  __UpperCAmelCase     :						list[tuple[float, float]]		)						->				List[str]:
         """simple docstring"""



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


   def 			lowercase_      (self     :						int       ,  __UpperCAmelCase     :						float		)						->				list[float]:
         """simple docstring"""



         assert 0 <= t <= 1, "Time t must be between 0 and 1."
         UpperCAmelCase__								=  []
         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 			lowercase_      (self     :						Dict       ,  __UpperCAmelCase     :						float		)						->				tuple[float, float]:
         """simple docstring"""



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

         UpperCAmelCase__								=  self.basis_function(__UpperCAmelCase		)
         UpperCAmelCase__								=  0.0
         UpperCAmelCase__								=  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     :						Optional[int]       ,  __UpperCAmelCase     :						float = 0.01		)						->				Optional[int]:
         """simple docstring"""



         from matplotlib import pyplot as plt  # type: ignore

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

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

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



