





from __future__ import annotations

from scipy.special import comb  # type: ignore

class        __SCREAMING_SNAKE_CASE					:






							def __init__(						self  , __lowerCAmelCase  ):
														UpperCamelCase__				     =			list_of_points
														# Degree determines the flexibility of the curve.
														# Degree = 1 will produce a straight line.
														UpperCamelCase__				     =			len(__lowerCAmelCase  ) - 1






							def 				_lowerCamelCase		(						self  , __lowerCAmelCase  ):
														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  , __lowerCAmelCase  ) * ((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(__lowerCAmelCase  )  , 5  ) == 1
														return output_values






							def 				_lowerCamelCase		(						self  , __lowerCAmelCase  ):
														assert 0 <= t <= 1, "Time t must be between 0 and 1."

														UpperCamelCase__				     =			self.basis_function(__lowerCAmelCase  )
														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 				_lowerCamelCase		(						self  , __lowerCAmelCase = 0.01  ):
														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(__lowerCAmelCase  )
																					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(
														    __lowerCAmelCase  , __lowerCAmelCase  , color="""blue"""  , label="""Curve of Degree """ + str(self.degree  )  , )
														plt.scatter(__lowerCAmelCase  , __lowerCAmelCase  , 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 Sequence
from dataclasses import dataclass
from typing import Any

@dataclass
class        __SCREAMING_SNAKE_CASE					:
							snake_case     :      int
							snake_case     :      Node | None						     =       None
							snake_case     :      Node | None						     =       None






def     _UpperCamelCase     ():






							"""simple docstring"""





							UpperCamelCase__				     =			Node(1       )
							UpperCamelCase__				     =			Node(2       )
							UpperCamelCase__				     =			Node(3       )
							UpperCamelCase__				     =			Node(4       )
							UpperCamelCase__				     =			Node(5       )
							return tree





def     _UpperCamelCase     (a__   :Node | None       ):






							"""simple docstring"""





							return [root.data, *preorder(root.left       ), *preorder(root.right       )] if root else []





def     _UpperCamelCase     (a__   :Node | None       ):






							"""simple docstring"""





							return postorder(root.left       ) + postorder(root.right       ) + [root.data] if root else []





def     _UpperCamelCase     (a__   :Node | None       ):






							"""simple docstring"""





							return [*inorder(root.left       ), root.data, *inorder(root.right       )] if root else []





def     _UpperCamelCase     (a__   :Node | None       ):






							"""simple docstring"""





							return (max(height(root.left       )   ,			height(root.right       )       ) + 1) if root else 0





def     _UpperCamelCase     (a__   :Node | None       ):






							"""simple docstring"""





							UpperCamelCase__				     =			[]

							if root is None:
														return output

							UpperCamelCase__				     =			deque([root]       )

							while process_queue:
														UpperCamelCase__				     =			process_queue.popleft()
														output.append(node.data       )

														if node.left:
																					process_queue.append(node.left       )
														if node.right:
																					process_queue.append(node.right       )
							return output





def     _UpperCamelCase     (a__   :Node | None   ,			a__   :int       ):






							"""simple docstring"""





							UpperCamelCase__				     =			[]

							def populate_output(a__   :Node | None   ,			a__   :int       ) -> None:
														if not root:
																					return
														if level == 1:
																					output.append(root.data       )
														elif level > 1:
																					populate_output(root.left   ,			level - 1       )
																					populate_output(root.right   ,			level - 1       )

							populate_output(a__   ,			a__       )
							return output





def     _UpperCamelCase     (a__   :Node | None   ,			a__   :int       ):






							"""simple docstring"""





							UpperCamelCase__				     =			[]

							def populate_output(a__   :Node | None   ,			a__   :int       ) -> None:
														if root is None:
																					return
														if level == 1:
																					output.append(root.data       )
														elif level > 1:
																					populate_output(root.right   ,			level - 1       )
																					populate_output(root.left   ,			level - 1       )

							populate_output(a__   ,			a__       )
							return output





def     _UpperCamelCase     (a__   :Node | None       ):






							"""simple docstring"""





							if root is None:
														return []

							UpperCamelCase__				     =			[]

							UpperCamelCase__				     =			0
							UpperCamelCase__				     =			height(a__       )

							for h in range(1   ,			height_tree + 1       ):
														if not flag:
																					output.append(get_nodes_from_left_to_right(a__   ,			a__       )       )
																					UpperCamelCase__				     =			1
														else:
																					output.append(get_nodes_from_right_to_left(a__   ,			a__       )       )
																					UpperCamelCase__				     =			0

							return output





def     _UpperCamelCase     ():  # Main function for testing.






							"""simple docstring"""





							UpperCamelCase__				     =			make_tree()
							print(f"""In-order Traversal: {inorder(a__       )}"""       )
							print(f"""Pre-order Traversal: {preorder(a__       )}"""       )
							print(f"""Post-order Traversal: {postorder(a__       )}"""   ,			"""\n"""       )

							print(f"""Height of Tree: {height(a__       )}"""   ,			"""\n"""       )

							print("""Complete Level Order Traversal: """       )
							print(level_order(a__       )   ,			"""\n"""       )

							print("""Level-wise order Traversal: """       )

							for level in range(1   ,			height(a__       ) + 1       ):
														print(f"""Level {level}:"""   ,			get_nodes_from_left_to_right(a__   ,			level=a__       )       )

							print("""\nZigZag order Traversal: """       )
							print(zigzag(a__       )       )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()




