




from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
lowercase_			:       List[str]						       =				20

# Time between time steps in seconds
lowercase_			:       List[Any]						       =				INTERVAL / 10_00






class 					__lowerCAmelCase				:







			def __init__( self					:    List[Any]					,					snake_case__					:    float					,					snake_case__					:    float					,					snake_case__					:    float					,					snake_case__					:    float					,					snake_case__					:    float = 1.0					,					snake_case__					:    float = 1.0					,					snake_case__					:    str = "blue"					,					):




									"""simple docstring"""


									_UpperCAmelCase									=  position_x
									_UpperCAmelCase									=  position_y
									_UpperCAmelCase									=  velocity_x
									_UpperCAmelCase									=  velocity_y
									_UpperCAmelCase									=  mass
									_UpperCAmelCase									=  size
									_UpperCAmelCase									=  color







			@property
			def UpperCamelCase    ( self					:    Union[str, Any]   ):




									"""simple docstring"""


									return self.position_x, self.position_y







			@property
			def UpperCamelCase    ( self					:    Dict   ):




									"""simple docstring"""


									return self.velocity_x, self.velocity_y







			def UpperCamelCase    ( self					:    List[str]					,					snake_case__					:    float					,					snake_case__					:    float					,					snake_case__					:    float   ):




									"""simple docstring"""


									self.velocity_x += force_x * delta_time
									self.velocity_y += force_y * delta_time







			def UpperCamelCase    ( self					:    Union[str, Any]					,					snake_case__					:    float   ):




									"""simple docstring"""


									self.position_x += self.velocity_x * delta_time
									self.position_y += self.velocity_y * delta_time






class 					__lowerCAmelCase				:







			def __init__( self					:    List[Any]					,					snake_case__					:    list[Body]					,					snake_case__					:    float = 1.0					,					snake_case__					:    float = 1.0					,					snake_case__					:    float = 0.0					,					):




									"""simple docstring"""


									_UpperCAmelCase									=  bodies
									_UpperCAmelCase									=  gravitation_constant
									_UpperCAmelCase									=  time_factor
									_UpperCAmelCase									=  softening_factor







			def __len__( self					:    Optional[Any]   ):




									"""simple docstring"""


									return len(self.bodies   )







			def UpperCamelCase    ( self					:    str					,					snake_case__					:    float   ):




									"""simple docstring"""


									for bodya in self.bodies:
															_UpperCAmelCase									=  0.0
															_UpperCAmelCase									=  0.0
															for bodya in self.bodies:
																					if bodya != bodya:
																											_UpperCAmelCase									=  bodya.position_x - bodya.position_x
																											_UpperCAmelCase									=  bodya.position_y - bodya.position_y

																											# Calculation of the distance using Pythagoras's theorem
																											# Extra factor due to the softening technique
																											_UpperCAmelCase									=  (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(snake_case__					,					snake_case__					,					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 							__SCREAMING_SNAKE_CASE						(    snake_case_			,					snake_case_			,					snake_case_		):

						'''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									=  (body.position_x, body.position_y)


def 							__SCREAMING_SNAKE_CASE						(    snake_case_			,					snake_case_			,					snake_case_ = -1			,					snake_case_ = 1			,					snake_case_ = -1			,					snake_case_ = 1			,					):

						'''simple docstring'''


						_UpperCAmelCase									=  plt.figure()
						fig.canvas.set_window_title(snake_case_		)
						_UpperCAmelCase									=  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									=  [
						    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_		) -> list[plt.Circle]:
												update_step(snake_case_			,					snake_case_			,					snake_case_		)
												return patches

						_UpperCAmelCase									=  animation.FuncAnimation(  # noqa: F841
						    snake_case_			,					snake_case_			,					interval=snake_case_			,					blit=snake_case_		)

						plt.show()


def 							__SCREAMING_SNAKE_CASE						(    ):

						'''simple docstring'''


						_UpperCAmelCase									=  0.9700436
						_UpperCAmelCase									=  -0.24308753
						_UpperCAmelCase									=  0.466203685
						_UpperCAmelCase									=  0.43236573

						_UpperCAmelCase									=  [
						    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 							__SCREAMING_SNAKE_CASE						(    ):

						'''simple docstring'''


						_UpperCAmelCase									=  7.3_4_7_6e2_2
						_UpperCAmelCase									=  5.9_7_2e2_4
						_UpperCAmelCase									=  1022
						_UpperCAmelCase									=  3_8439_9000
						_UpperCAmelCase									=  6.6_7_4e-1_1

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

						_UpperCAmelCase									=  Body(-earth_moon_distance			,					0			,					0			,					snake_case_			,					snake_case_			,					1000_0000			,					"grey"		)
						_UpperCAmelCase									=  Body(0			,					0			,					0			,					snake_case_			,					snake_case_			,					5000_0000			,					"blue"		)
						return BodySystem([earth, moon]			,					snake_case_			,					time_factor=100_0000		)


def 							__SCREAMING_SNAKE_CASE						(    ):

						'''simple docstring'''


						_UpperCAmelCase									=  []
						for _ in range(10		):
												_UpperCAmelCase									=  random.uniform(-0.5			,					0.5		)
												_UpperCAmelCase									=  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(),
				    -4_30_00_00_00,
				    4_30_00_00_00,
				    -4_30_00_00_00,
				    4_30_00_00_00,
				)
				plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)










def 							__SCREAMING_SNAKE_CASE						(    snake_case_ = 99_8001		):

						'''simple docstring'''


						for number in range(n - 1			,					9999			,					-1		):
												_UpperCAmelCase									=  str(snake_case_		)

												# checks whether 'str_number' is a palindrome.
												if str_number == str_number[::-1]:
																		_UpperCAmelCase									=  999

																		# if 'number' is a product of two 3-digit numbers
																		# then number is the answer otherwise fetch next number.
																		while divisor != 99:
																								if (number % divisor == 0) and (len(str(number // divisor		)		) == 3.0):
																														return number
																								divisor -= 1
						raise ValueError("That number is larger than our acceptable range."		)


if __name__ == "__main__":
				print(f"""{solution() = }""")




