


'''simple docstring'''







from __future__ import annotations

from scipy.special import comb  # type: ignore


class 			__lowerCamelCase			:
    """simple docstring"""


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


    def        A   (  self      :							Optional[Any]				,							SCREAMING_SNAKE_CASE      :							float):
           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				,							SCREAMING_SNAKE_CASE) * ((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(SCREAMING_SNAKE_CASE)				,							5) == 1
           return output_values


    def        A   (  self      :							str				,							SCREAMING_SNAKE_CASE      :							float):
           assert 0 <= t <= 1, "Time t must be between 0 and 1."

           _A					:     Tuple     = self.basis_function(SCREAMING_SNAKE_CASE)
           _A					:     List[str]     = 0.0
           _A					:     List[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        A   (  self      :							Any				,							SCREAMING_SNAKE_CASE      :							float = 0.01):
           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[int]     = 0.0
           while t <= 1:
                  _A					:     Union[str, Any]     = self.bezier_curve_function(SCREAMING_SNAKE_CASE)
                  to_plot_x.append(value[0])
                  to_plot_y.append(value[1])
                  t += step_size

           _A					:     List[str]     = [i[0] for i in self.list_of_points]
           _A					:     Union[str, Any]     = [i[1] for i in self.list_of_points]

           plt.plot(
               SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE				,							color='blue'				,							label='Curve of Degree ' + str(self.degree)				,							)
           plt.scatter(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE				,							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'''







class 			__lowerCamelCase			:  # Public class to implement a graph
    """simple docstring"""


    def __init__(  self      :							Optional[Any]				,							SCREAMING_SNAKE_CASE      :							int				,							SCREAMING_SNAKE_CASE      :							int				,							SCREAMING_SNAKE_CASE      :							list[list[bool]]):
           _A					:     List[Any]     = row
           _A					:     Union[str, Any]     = col
           _A					:     List[str]     = graph


    def        A   (  self      :							Any				,							SCREAMING_SNAKE_CASE      :							int				,							SCREAMING_SNAKE_CASE      :							int				,							SCREAMING_SNAKE_CASE      :							list[list[bool]]):
           return (
               0 <= i < self.ROW
               and 0 <= j < self.COL
               and not visited[i][j]
               and self.graph[i][j]
           )


    def        A   (  self      :							Tuple				,							SCREAMING_SNAKE_CASE      :							int				,							SCREAMING_SNAKE_CASE      :							int				,							SCREAMING_SNAKE_CASE      :							list[list[bool]]):
           # Checking all 8 elements surrounding nth element
           _A					:     Tuple     = [-1, -1, -1, 0, 0, 1, 1, 1]  # Coordinate order
           _A					:     Dict     = [-1, 0, 1, -1, 1, -1, 0, 1]
           _A					:     List[Any]     = True  # Make those cells visited
           for k in range(8):
                  if self.is_safe(i + row_nbr[k]				,							j + col_nbr[k]				,							SCREAMING_SNAKE_CASE):
                         self.diffs(i + row_nbr[k]				,							j + col_nbr[k]				,							SCREAMING_SNAKE_CASE)


    def        A   (  self      :							int):  # And finally, count all islands.
           _A					:     Dict     = [[False for j in range(self.COL)] for i in range(self.ROW)]
           _A					:     Union[str, Any]     = 0
           for i in range(self.ROW):
                  for j in range(self.COL):
                         if visited[i][j] is False and self.graph[i][j] == 1:
                                self.diffs(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE)
                                count += 1
           return count






