





"""simple docstring"""
from __future__ import annotations

from scipy.special import comb  # type: ignore






class 					_UpperCAmelCase   :


					def __init__(					self			:Dict     ,       __UpperCamelCase			:list[tuple[float, float]]		):
												A		=  list_of_points
												# Degree determines the flexibility of the curve.
												# Degree = 1 will produce a straight line.
												A		=  len(__UpperCamelCase		) - 1


					def 	lowerCamelCase       (					self			:Dict     ,       __UpperCamelCase			:float		):
												assert 0 <= t <= 1, "Time t must be between 0 and 1."
												A		=  []
												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 	lowerCamelCase       (					self			:Any     ,       __UpperCamelCase			:float		):
												assert 0 <= t <= 1, "Time t must be between 0 and 1."

												A		=  self.basis_function(__UpperCamelCase		)
												A		=  0.0
												A		=  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			:str     ,       __UpperCamelCase			:float = 0.01		):
												from matplotlib import pyplot as plt  # type: ignore

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

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

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









"""simple docstring"""
class 					_UpperCAmelCase   :


					def __init__(					self			:List[str]     ,       __UpperCamelCase			:Union[str, Any]     ,       __UpperCamelCase			:Tuple		):
												A		=  name
												A		=  val


					def __str__(					self			:str		):
												return f"{self.__class__.__name__}({self.name}, {self.val})"


					def __lt__(					self			:List[Any]     ,       __UpperCamelCase			:Union[str, Any]		):
												return self.val < other.val







class 					_UpperCAmelCase   :


					def __init__(					self			:List[str]     ,       __UpperCamelCase			:Optional[Any]		):
												A		=  {}
												A		=  {}
												A		=  self.build_heap(__UpperCamelCase		)


					def __getitem__(					self			:int     ,       __UpperCamelCase			:Optional[int]		):
												return self.get_value(__UpperCamelCase		)


					def 	lowerCamelCase       (					self			:List[Any]     ,       __UpperCamelCase			:str		):
												return (idx - 1) // 2


					def 	lowerCamelCase       (					self			:int     ,       __UpperCamelCase			:Optional[Any]		):
												return idx * 2 + 1


					def 	lowerCamelCase       (					self			:Union[str, Any]     ,       __UpperCamelCase			:Optional[int]		):
												return idx * 2 + 2


					def 	lowerCamelCase       (					self			:Optional[Any]     ,       __UpperCamelCase			:str		):
												return self.heap_dict[key]


					def 	lowerCamelCase       (					self			:int     ,       __UpperCamelCase			:Optional[Any]		):
												A		=  len(__UpperCamelCase		) - 1
												A		=  self.get_parent_idx(__UpperCamelCase		)

												for idx, i in enumerate(__UpperCamelCase		):
																			A		=  idx
																			A		=  i.val

												for i in range(__UpperCamelCase     ,       -1     ,       -1		):
																			self.sift_down(__UpperCamelCase     ,       __UpperCamelCase		)
												return array


					def 	lowerCamelCase       (					self			:str     ,       __UpperCamelCase			:Optional[Any]     ,       __UpperCamelCase			:Dict		):
												while True:
																			A		=  self.get_left_child_idx(__UpperCamelCase		)  # noqa: E741
																			A		=  self.get_right_child_idx(__UpperCamelCase		)

																			A		=  idx
																			if l < len(__UpperCamelCase		) and array[l] < array[idx]:
																										A		=  l
																			if r < len(__UpperCamelCase		) and array[r] < array[smallest]:
																										A		=  r

																			if smallest != idx:
																										A,	A		=  array[smallest], array[idx]
																										(
																										    (
																										    A
																										),	(
																										    A
																										),	
																										)		=  (
																										    self.idx_of_element[array[smallest]],
																										    self.idx_of_element[array[idx]],
																										)
																										A		=  smallest
																			else:
																										break


					def 	lowerCamelCase       (					self			:Optional[Any]     ,       __UpperCamelCase			:Optional[int]		):
												A		=  self.get_parent_idx(__UpperCamelCase		)
												while p >= 0 and self.heap[p] > self.heap[idx]:
																			A,	A		=  self.heap[idx], self.heap[p]
																			A,	A		=  (
																			    self.idx_of_element[self.heap[idx]],
																			    self.idx_of_element[self.heap[p]],
																			)
																			A		=  p
																			A		=  self.get_parent_idx(__UpperCamelCase		)


					def 	lowerCamelCase       (					self			:Any		):
												return self.heap[0]


					def 	lowerCamelCase       (					self			:Tuple		):
												A,	A		=  self.heap[-1], self.heap[0]
												A,	A		=  (
												    self.idx_of_element[self.heap[-1]],
												    self.idx_of_element[self.heap[0]],
												)

												A		=  self.heap.pop()
												del self.idx_of_element[x]
												self.sift_down(0     ,       self.heap		)
												return x


					def 	lowerCamelCase       (					self			:Optional[int]     ,       __UpperCamelCase			:Optional[int]		):
												self.heap.append(__UpperCamelCase		)
												A		=  len(self.heap		) - 1
												A		=  node.val
												self.sift_up(len(self.heap		) - 1		)


					def 	lowerCamelCase       (					self			:Tuple		):
												return len(self.heap		) == 0


					def 	lowerCamelCase       (					self			:Any     ,       __UpperCamelCase			:str     ,       __UpperCamelCase			:Dict		):
												assert (
												    self.heap[self.idx_of_element[node]].val > new_value
												), "newValue must be less that current value"
												A		=  new_value
												A		=  new_value
												self.sift_up(self.idx_of_element[node]		)







_snake_case     :		Optional[int]       						= Node('R', -1)
_snake_case     :		Tuple       						= Node('B', 6)
_snake_case     :		Tuple       						= Node('A', 3)
_snake_case     :		Optional[int]       						= Node('X', 1)
_snake_case     :		List[Any]       						= Node('E', 4)

# Use one of these two ways to generate Min-Heap

# Generating Min-Heap from array
_snake_case     :		Tuple       						= MinHeap([r, b, a, x, e])

# Generating Min-Heap by Insert method
# myMinHeap.insert(a)
# myMinHeap.insert(b)
# myMinHeap.insert(x)
# myMinHeap.insert(r)
# myMinHeap.insert(e)

# Before
print('Min Heap - before decrease key')
for i in my_min_heap.heap:
		print(i)

print('Min Heap - After decrease key of node [B -> -17]')
my_min_heap.decrease_key(b, -17)

# After
for i in my_min_heap.heap:
		print(i)

if __name__ == "__main__":
		import doctest

		doctest.testmod()


