






"""simple docstring"""


from __future__ import annotations

from scipy.special import comb  # type: ignore






class 						snake_case  :





    def __init__(							self     : Optional[int]    ,		A     : list[tuple[float, float]]      ):


      '''simple docstring'''




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





    def     lowerCamelCase__				(							self     : Optional[int]    ,		A     : float      ):


      '''simple docstring'''




      assert 0 <= t <= 1, "Time t must be between 0 and 1."
      a					:      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     : List[Any]    ,		A     : float      ):


      '''simple docstring'''




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

      a					:      Optional[Any]    =       self.basis_function(A      )
      a					:      Tuple    =       0.0
      a					:      Dict    =       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     : Union[str, Any]    ,		A     : float = 0.01      ):


      '''simple docstring'''




      from matplotlib import pyplot as plt  # type: ignore

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

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

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












"""simple docstring"""


def       snake_case  (A_				:list[int]     ,      A_				:str				):







  '''simple docstring'''

  a					:      Optional[int]    =       int(A_				)

  # Initialize Result
  a					:      int    =       []

  # Traverse through all denomination
  for denomination in reversed(A_				):
    # Find denominations
    while int(A_				) >= int(A_				):
      total_value -= int(A_				)
      answer.append(A_				)  # Append the "answers" array

  return answer


# Driver Code
if __name__ == "__main__":
   _UpperCamelCase    :   Dict   			=						[]
   _UpperCamelCase    :   str   			=						'0'

   if (
       input('Do you want to enter your denominations ? (yY/n): ').strip().lower()
       == "y"
   ):
      _UpperCamelCase    :   Dict   			=						int(input('Enter the number of denominations you want to add: ').strip())

      for i in range(0, n):
         denominations.append(int(input(f'''Denomination {i}: ''').strip()))
      _UpperCamelCase    :   Optional[int]   			=						input('Enter the change you want to make in Indian Currency: ').strip()
   else:
      # All denominations of Indian Currency if user does not enter
      _UpperCamelCase    :   Union[str, Any]   			=						[1, 2, 5, 10, 20, 50, 100, 500, 2000]
      _UpperCamelCase    :   Dict   			=						input('Enter the change you want to make: ').strip()

   if int(value) == 0 or int(value) < 0:
      print('The total value cannot be zero or negative.')

   else:
      print(f'''Following is minimal change for {value}: ''')
      _UpperCamelCase    :   Tuple   			=						find_minimum_change(denominations, value)
      # Print result
      for i in range(len(answer)):
         print(answer[i], end=' ')




