






from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
__UpperCAmelCase										=		20

# Time between time steps in seconds
__UpperCAmelCase										=		INTERVAL / 1000



class 						lowerCamelCase   :







		'''simple docstring'''



		def __init__(							self       ,	_UpperCamelCase       ,	_UpperCamelCase       ,	_UpperCamelCase       ,	_UpperCamelCase       ,	_UpperCamelCase = 1.0       ,	_UpperCamelCase = 1.0       ,	_UpperCamelCase = "blue"       ,	)			->							None:
							UpperCAmelCase_					:   Optional[Any]   =		position_x
							UpperCAmelCase_					:   Optional[Any]   =		position_y
							UpperCAmelCase_					:   int   =		velocity_x
							UpperCAmelCase_					:   str   =		velocity_y
							UpperCAmelCase_					:   List[Any]   =		mass
							UpperCAmelCase_					:   Union[str, Any]   =		size
							UpperCAmelCase_					:   Tuple   =		color



		@property
		def       __UpperCAmelCase    (							self     )			->							tuple[float, float]:
							return self.position_x, self.position_y



		@property
		def       __UpperCAmelCase    (							self     )			->							tuple[float, float]:
							return self.velocity_x, self.velocity_y



		def       __UpperCAmelCase    (							self       ,	_UpperCamelCase       ,	_UpperCamelCase       ,	_UpperCamelCase     )			->							None:
							self.velocity_x += force_x * delta_time
							self.velocity_y += force_y * delta_time



		def       __UpperCAmelCase    (							self       ,	_UpperCamelCase     )			->							None:
							self.position_x += self.velocity_x * delta_time
							self.position_y += self.velocity_y * delta_time





class 						lowerCamelCase   :







		'''simple docstring'''



		def __init__(							self       ,	_UpperCamelCase       ,	_UpperCamelCase = 1.0       ,	_UpperCamelCase = 1.0       ,	_UpperCamelCase = 0.0       ,	)			->							None:
							UpperCAmelCase_					:   List[str]   =		bodies
							UpperCAmelCase_					:   Tuple   =		gravitation_constant
							UpperCAmelCase_					:   List[Any]   =		time_factor
							UpperCAmelCase_					:   str   =		softening_factor



		def __len__(							self     )			->							int:
							return len(self.bodies     )



		def       __UpperCAmelCase    (							self       ,	_UpperCamelCase     )			->							None:
							for bodya in self.bodies:
												UpperCAmelCase_					:   Dict   =		0.0
												UpperCAmelCase_					:   Dict   =		0.0
												for bodya in self.bodies:
																	if bodya != bodya:
																						UpperCAmelCase_					:   List[Any]   =		bodya.position_x - bodya.position_x
																						UpperCAmelCase_					:   Union[str, Any]   =		bodya.position_y - bodya.position_y

																						# Calculation of the distance using Pythagoras's theorem
																						# Extra factor due to the softening technique
																						UpperCAmelCase_					:   Optional[Any]   =		(dif_x**2 + dif_y**2 + self.softening_factor) ** (
																						    1 / 2
																						)

																						# Newton's law of universal gravitation.
																						force_x += (
																						    self.gravitation_constant * bodya.mass * dif_x / distance**3
																						)
																						force_y += (
																						    self.gravitation_constant * bodya.mass * dif_y / distance**3
																						)

            # Update the body's velocity once all the force components have been added
												bodya.update_velocity(_UpperCamelCase       ,	_UpperCamelCase       ,	delta_time * self.time_factor     )

							# Update the positions only after all the velocities have been updated
							for body in self.bodies:
												body.update_position(delta_time * self.time_factor     )





def   lowercase__   (  __snake_case					:							BodySystem  , __snake_case					:							float  , __snake_case					:							list[plt.Circle]						):


					'''simple docstring'''


					body_system.update_system(__snake_case						)

					# Update the positions of the patches
					for patch, body in zip(__snake_case  , body_system.bodies						):
										UpperCAmelCase_					:   List[Any]   =		(body.position_x, body.position_y)




def   lowercase__   (  __snake_case					:							str  , __snake_case					:							BodySystem  , __snake_case					:							float = -1  , __snake_case					:							float = 1  , __snake_case					:							float = -1  , __snake_case					:							float = 1  , ):


					'''simple docstring'''


					UpperCAmelCase_					:   Any   =		plt.figure()
					fig.canvas.set_window_title(__snake_case						)
					UpperCAmelCase_					:   str   =		plt.axes(
					    xlim=(x_start, x_end)  , ylim=(y_start, y_end)						)  # Set section to be plotted
					plt.gca().set_aspect('equal'						)  # Fix aspect ratio

					# Each body is drawn as a patch by the plt-function
					UpperCAmelCase_					:   Tuple   =		[
					    plt.Circle((body.position_x, body.position_y)  , body.size  , fc=body.color						)
					    for body in body_system.bodies
					]

					for patch in patches:
										ax.add_patch(__snake_case						)

					# Function called at each step of the animation
					def update(__snake_case					:							int						) -> list[plt.Circle]:
										update_step(__snake_case  , __snake_case  , __snake_case						)
										return patches

					UpperCAmelCase_					:   Optional[int]   =		animation.FuncAnimation(  # noqa: F841
					    __snake_case  , __snake_case  , interval=__snake_case  , blit=__snake_case						)

					plt.show()




def   lowercase__   (  ):


					'''simple docstring'''


					UpperCAmelCase_					:   List[str]   =		0.9700436
					UpperCAmelCase_					:   Union[str, Any]   =		-0.24308753
					UpperCAmelCase_					:   Dict   =		0.466203685
					UpperCAmelCase_					:   int   =		0.43236573

					UpperCAmelCase_					:   Optional[Any]   =		[
					    Body(__snake_case  , __snake_case  , __snake_case  , __snake_case  , size=0.2  , color='red'						),
					    Body(-position_x  , -position_y  , __snake_case  , __snake_case  , size=0.2  , color='green'						),
					    Body(0  , 0  , -2 * velocity_x  , -2 * velocity_y  , size=0.2  , color='blue'						),
					]
					return BodySystem(__snake_case  , time_factor=3						)




def   lowercase__   (  ):


					'''simple docstring'''


					UpperCAmelCase_					:   List[str]   =		7.3476E22
					UpperCAmelCase_					:   List[str]   =		5.972E24
					UpperCAmelCase_					:   Dict   =		1_022
					UpperCAmelCase_					:   Any   =		384_399_000
					UpperCAmelCase_					:   List[str]   =		6.674E-11

					# Calculation of the respective velocities so that total impulse is zero,
					# i.e. the two bodies together don't move
					UpperCAmelCase_					:   str   =		earth_mass * velocity_dif / (earth_mass + moon_mass)
					UpperCAmelCase_					:   int   =		moon_velocity - velocity_dif

					UpperCAmelCase_					:   Optional[int]   =		Body(-earth_moon_distance  , 0  , 0  , __snake_case  , __snake_case  , 10_000_000  , 'grey'						)
					UpperCAmelCase_					:   Optional[Any]   =		Body(0  , 0  , 0  , __snake_case  , __snake_case  , 50_000_000  , 'blue'						)
					return BodySystem([earth, moon]  , __snake_case  , time_factor=1_000_000						)




def   lowercase__   (  ):


					'''simple docstring'''


					UpperCAmelCase_					:   Optional[int]   =		[]
					for _ in range(10						):
										UpperCAmelCase_					:   int   =		random.uniform(-0.5  , 0.5						)
										UpperCAmelCase_					:   str   =		random.uniform(-0.5  , 0.5						)

										# Bodies are created pairwise with opposite velocities so that the
										# total impulse remains zero
										bodies.append(
										    Body(
										        random.uniform(-0.5  , 0.5						)  , random.uniform(-0.5  , 0.5						)  , __snake_case  , __snake_case  , size=0.05  , )						)
										bodies.append(
										    Body(
										        random.uniform(-0.5  , 0.5						)  , random.uniform(-0.5  , 0.5						)  , -velocity_x  , -velocity_y  , size=0.05  , )						)
					return BodySystem(__snake_case  , 0.01  , 10  , 0.1						)


if __name__ == "__main__":
		plot('Figure-8 solution to the 3-body-problem', example_a(), -2, 2, -2, 2)
		plot(
		    'Moon\'s orbit around the earth',
		    example_a(),
		    -430000000,
		    430000000,
		    -430000000,
		    430000000,
		)
		plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)














from __future__ import annotations



class 						lowerCamelCase   :







		'''simple docstring'''



		def __init__(							self       ,	_UpperCamelCase = 0     )			->							None:
							UpperCAmelCase_					:   int   =		value
							UpperCAmelCase_					:   Node | None   =		None
							UpperCAmelCase_					:   Node | None   =		None





def   lowercase__   (  __snake_case					:							Node | None  , __snake_case					:							Node | None						):


					'''simple docstring'''


					if treea is None:
										return treea
					if treea is None:
										return treea

					UpperCAmelCase_					:   List[Any]   =		treea.value + treea.value
					UpperCAmelCase_					:   Dict   =		merge_two_binary_trees(treea.left  , treea.left						)
					UpperCAmelCase_					:   str   =		merge_two_binary_trees(treea.right  , treea.right						)
					return treea




def   lowercase__   (  __snake_case					:							Node | None						):


					'''simple docstring'''


					if root:
										print(root.value						)
										print_preorder(root.left						)
										print_preorder(root.right						)


if __name__ == "__main__":
		__UpperCAmelCase										=		Node(1)
		__UpperCAmelCase										=		Node(2)
		__UpperCAmelCase										=		Node(3)
		__UpperCAmelCase										=		Node(4)

		__UpperCAmelCase										=		Node(2)
		__UpperCAmelCase										=		Node(4)
		__UpperCAmelCase										=		Node(6)
		__UpperCAmelCase										=		Node(9)
		__UpperCAmelCase										=		Node(5)

		print('Tree1 is: ')
		print_preorder(treea)
		print('Tree2 is: ')
		print_preorder(treea)
		__UpperCAmelCase										=		merge_two_binary_trees(treea, treea)
		print('Merged Tree is: ')
		print_preorder(merged_tree)






