

from __future__ import annotations

from scipy.special import comb  # type: ignore



class   __lowercase    :




			"""simple docstring"""







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



			def 	_SCREAMING_SNAKE_CASE      (			self  :					List[str]       ,						lowerCAmelCase__  :					float):
									assert 0 <= t <= 1, "Time t must be between 0 and 1."
									SCREAMING_SNAKE_CASE_:			list[float]  		=	[]
									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 	_SCREAMING_SNAKE_CASE      (			self  :					List[Any]       ,						lowerCAmelCase__  :					float):
									assert 0 <= t <= 1, "Time t must be between 0 and 1."

									SCREAMING_SNAKE_CASE_:			List[str]  		=	self.basis_function(lowercase_)
									SCREAMING_SNAKE_CASE_:			Tuple  		=	0.0
									SCREAMING_SNAKE_CASE_:			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 	_SCREAMING_SNAKE_CASE      (			self  :					Optional[Any]       ,						lowerCAmelCase__  :					float = 0.01):
									from matplotlib import pyplot as plt  # type: ignore

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

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

									SCREAMING_SNAKE_CASE_:			Any  		=	[i[0] for i in self.list_of_points]
									SCREAMING_SNAKE_CASE_:			List[str]  		=	[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








from __future__ import annotations

from collections import deque
from collections.abc import Iterator
from dataclasses import dataclass



@dataclass
class   __lowercase    :




			"""simple docstring"""







			_UpperCAmelCase       :							int
			_UpperCAmelCase       :							int







class   __lowercase    :




			"""simple docstring"""







			def __init__(			self  :					Any       ,						lowerCAmelCase__  :					int):
									SCREAMING_SNAKE_CASE_:			list[list[Edge]]  		=	[[] for _ in range(lowerCAmelCase__)]
									SCREAMING_SNAKE_CASE_:			Dict  		=	size



			def __getitem__(			self  :					Dict       ,						lowerCAmelCase__  :					int):
									return iter(self._graph[vertex])



			@property
			def 	_SCREAMING_SNAKE_CASE      (			self  :					Tuple):
									return self._size



			def 	_SCREAMING_SNAKE_CASE      (			self  :					Dict       ,						lowerCAmelCase__  :					int       ,						lowerCAmelCase__  :					int       ,						lowerCAmelCase__  :					int):
									if weight not in (0, 1):
															raise ValueError("Edge weight must be either 0 or 1.")

									if to_vertex < 0 or to_vertex >= self.size:
															raise ValueError("Vertex indexes must be in [0; size).")

									self._graph[from_vertex].append(Edge(lowerCAmelCase__       ,						lowerCAmelCase__))




			def 	_SCREAMING_SNAKE_CASE      (			self  :					List[Any]       ,						lowerCAmelCase__  :					int       ,						lowerCAmelCase__  :					int):
									SCREAMING_SNAKE_CASE_:			Optional[int]  		=	deque([start_vertex])
									SCREAMING_SNAKE_CASE_:			list[int | None]  		=	[None] * self.size
									SCREAMING_SNAKE_CASE_:			List[Any]  		=	0

									while queue:
															SCREAMING_SNAKE_CASE_:			int  		=	queue.popleft()
															SCREAMING_SNAKE_CASE_:			str  		=	distances[current_vertex]
															if current_distance is None:
																					continue

															for edge in self[current_vertex]:
																					SCREAMING_SNAKE_CASE_:			Optional[int]  		=	current_distance + edge.weight
																					SCREAMING_SNAKE_CASE_:			str  		=	distances[edge.destination_vertex]
																					if (
																					    isinstance(lowerCAmelCase__       ,						lowerCAmelCase__)
																					    and new_distance >= dest_vertex_distance
																					):
																											continue
																					SCREAMING_SNAKE_CASE_:			Any  		=	new_distance
																					if edge.weight == 0:
																											queue.appendleft(edge.destination_vertex)
																					else:
																											queue.append(edge.destination_vertex)

									if distances[finish_vertex] is None:
															raise ValueError("No path from start_vertex to finish_vertex.")

									return distances[finish_vertex]


if __name__ == "__main__":
						import doctest

						doctest.testmod()






