'''simple docstring'''
from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
a=	2_0

# Time between time steps in seconds
a=	INTERVAL / 1_0_0_0






class       __lowercase		:







     """simple docstring"""






     def __init__(		self  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase = 1.0  ,      _lowerCamelCase = 1.0  ,      _lowerCamelCase = "blue"  ,      ):
         __UpperCamelCase						:						Tuple		     =	position_x
         __UpperCamelCase						:						Optional[Any]		     =	position_y
         __UpperCamelCase						:						str		     =	velocity_x
         __UpperCamelCase						:						int		     =	velocity_y
         __UpperCamelCase						:						int		     =	mass
         __UpperCamelCase						:						Any		     =	size
         __UpperCamelCase						:						str		     =	color







     @property
     def lowerCAmelCase  (		self     ):
         return self.position_x, self.position_y







     @property
     def lowerCAmelCase  (		self     ):
         return self.velocity_x, self.velocity_y







     def lowerCAmelCase  (		self  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase     ):
         self.velocity_x += force_x * delta_time
         self.velocity_y += force_y * delta_time







     def lowerCAmelCase  (		self  ,      _lowerCamelCase     ):
         self.position_x += self.velocity_x * delta_time
         self.position_y += self.velocity_y * delta_time






class       __lowercase		:







     """simple docstring"""






     def __init__(		self  ,      _lowerCamelCase  ,      _lowerCamelCase = 1.0  ,      _lowerCamelCase = 1.0  ,      _lowerCamelCase = 0.0  ,      ):
         __UpperCamelCase						:						Dict		     =	bodies
         __UpperCamelCase						:						Dict		     =	gravitation_constant
         __UpperCamelCase						:						Union[str, Any]		     =	time_factor
         __UpperCamelCase						:						List[Any]		     =	softening_factor







     def __len__(		self     ):
         return len(self.bodies     )







     def lowerCAmelCase  (		self  ,      _lowerCamelCase     ):
         for bodya in self.bodies:
             __UpperCamelCase						:						Tuple		     =	0.0
             __UpperCamelCase						:						int		     =	0.0
             for bodya in self.bodies:
                 if bodya != bodya:
                     __UpperCamelCase						:						List[Any]		     =	bodya.position_x - bodya.position_x
                     __UpperCamelCase						:						Dict		     =	bodya.position_y - bodya.position_y

                     # Calculation of the distance using Pythagoras's theorem
                     # Extra factor due to the softening technique
                     __UpperCamelCase						:						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(a__  ,      a__  ,      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 			_UpperCamelCase			(  _a						:						int					,  _a						:						Optional[int]					,  _a						:						Union[str, Any]      ):




    """simple docstring"""



    body_system.update_system(_a      )

    # Update the positions of the patches
    for patch, body in zip(_a					,  body_system.bodies      ):
        __UpperCamelCase						:						str		     =	(body.position_x, body.position_y)







def 			_UpperCamelCase			(  _a						:						Union[str, Any]					,  _a						:						List[Any]					,  _a						:						List[str] = -1					,  _a						:						List[str] = 1					,  _a						:						List[Any] = -1					,  _a						:						str = 1					,  ):




    """simple docstring"""



    __UpperCamelCase						:						Any		     =	plt.figure()
    fig.canvas.set_window_title(_a      )
    __UpperCamelCase						:						int		     =	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						:						Union[str, Any]		     =	[
        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(_a      )

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

    __UpperCamelCase						:						Any		     =	animation.FuncAnimation(  # noqa: F841
        _a					,  _a					,  interval=_a					,  blit=_a      )

    plt.show()







def 			_UpperCamelCase			(  ):




    """simple docstring"""



    __UpperCamelCase						:						Optional[Any]		     =	0.9700436
    __UpperCamelCase						:						int		     =	-0.24308753
    __UpperCamelCase						:						Optional[int]		     =	0.466203685
    __UpperCamelCase						:						str		     =	0.43236573

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







def 			_UpperCamelCase			(  ):




    """simple docstring"""



    __UpperCamelCase						:						Tuple		     =	7.3_476E22
    __UpperCamelCase						:						Any		     =	5.972E24
    __UpperCamelCase						:						Dict		     =	1_0_2_2
    __UpperCamelCase						:						int		     =	3_8_4_3_9_9_0_0_0
    __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						:						Any		     =	earth_mass * velocity_dif / (earth_mass + moon_mass)
    __UpperCamelCase						:						Dict		     =	moon_velocity - velocity_dif

    __UpperCamelCase						:						List[str]		     =	Body(-earth_moon_distance					,  0					,  0					,  _a					,  _a					,  1_0_0_0_0_0_0_0					,  'grey'      )
    __UpperCamelCase						:						Tuple		     =	Body(0					,  0					,  0					,  _a					,  _a					,  5_0_0_0_0_0_0_0					,  'blue'      )
    return BodySystem([earth, moon]					,  _a					,  time_factor=1_0_0_0_0_0_0      )







def 			_UpperCamelCase			(  ):




    """simple docstring"""



    __UpperCamelCase						:						Union[str, Any]		     =	[]
    for _ in range(1_0      ):
        __UpperCamelCase						:						Dict		     =	random.uniform(-0.5					,  0.5      )
        __UpperCamelCase						:						Union[str, Any]		     =	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      )					,  _a					,  _a					,  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(_a					,  0.01					,  1_0					,  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_3_0_0_0_0_0_0_0,
      4_3_0_0_0_0_0_0_0,
      -4_3_0_0_0_0_0_0_0,
      4_3_0_0_0_0_0_0_0,
  )
  plot('''Random system with many bodies''', example_a(), -1.5, 1.5, -1.5, 1.5)





from __future__ import annotations

from collections.abc import Iterable
from dataclasses import dataclass
from typing import Any

class 		__magic_name__				:


  """simple docstring"""





  _UpperCamelCase						 = ("_front", "_back", "_len")

  @dataclass
  class 		__magic_name__				:


    """simple docstring"""





    _UpperCamelCase						 = None
    _UpperCamelCase						 = None
    _UpperCamelCase						 = None







  class 		__magic_name__				:


    """simple docstring"""





    _UpperCamelCase						 = ("_cur",)


    def __init__(					self	,		a__		):
      _lowerCamelCase      =						cur


    def __iter__(					self		):
      return self


    def     _UpperCAmelCase  (					self		):
      if self._cur is None:
        # finished iterating
        raise StopIteration
      _lowerCamelCase      =						self._cur.val
      _lowerCamelCase      =						self._cur.next_node

      return val







  def __init__(					self	,		a__ = None		):
    _lowerCamelCase      =						None
    _lowerCamelCase      =						None
    _lowerCamelCase      =						0

    if iterable is not None:
      # append every value to the deque
      for val in iterable:
        self.append(a__		)


  def     _UpperCAmelCase  (					self	,		a__		):
    _lowerCamelCase      =						self._Node(a__	,		a__	,		a__		)
    if self.is_empty():
      # front = back
      _lowerCamelCase      =						_lowerCamelCase      =						node
      _lowerCamelCase      =						1
    else:
      # connect nodes
      _lowerCamelCase      =						node
      _lowerCamelCase      =						self._back
      _lowerCamelCase      =						node  # assign new back to the new node

      self._len += 1

      # make sure there were no errors
      assert not self.is_empty(), "Error on appending value."


  def     _UpperCAmelCase  (					self	,		a__		):
    _lowerCamelCase      =						self._Node(a__	,		a__	,		a__		)
    if self.is_empty():
      # front = back
      _lowerCamelCase      =						_lowerCamelCase      =						node
      _lowerCamelCase      =						1
    else:
      # connect nodes
      _lowerCamelCase      =						self._front
      _lowerCamelCase      =						node
      _lowerCamelCase      =						node  # assign new front to the new node

      self._len += 1

      # make sure there were no errors
      assert not self.is_empty(), "Error on appending value."


  def     _UpperCAmelCase  (					self	,		a__		):
    for val in iterable:
      self.append(a__		)


  def     _UpperCAmelCase  (					self	,		a__		):
    for val in iterable:
      self.appendleft(a__		)


  def     _UpperCAmelCase  (					self		):
    assert not self.is_empty(), "Deque is empty."

    _lowerCamelCase      =						self._back
    _lowerCamelCase      =						self._back.prev_node  # set new back
    # drop the last node - python will deallocate memory automatically
    _lowerCamelCase      =						None

    self._len -= 1

    return topop.val


  def     _UpperCAmelCase  (					self		):
    assert not self.is_empty(), "Deque is empty."

    _lowerCamelCase      =						self._front
    _lowerCamelCase      =						self._front.next_node  # set new front and drop the first node
    _lowerCamelCase      =						None

    self._len -= 1

    return topop.val


  def     _UpperCAmelCase  (					self		):
    return self._front is None


  def __len__(					self		):
    return self._len


  def __eq__(					self	,		a__		):

    if not isinstance(a__	,		a__		):
      return NotImplemented

    _lowerCamelCase      =						self._front
    _lowerCamelCase      =						other._front

    # if the length of the dequeues are not the same, they are not equal
    if len(self		) != len(a__		):
      return False

    while me is not None and oth is not None:
      # compare every value
      if me.val != oth.val:
        return False
      _lowerCamelCase      =						me.next_node
      _lowerCamelCase      =						oth.next_node

    return True


  def __iter__(					self		):
    return Deque._Iterator(self._front		)


  def __repr__(					self		):
    _lowerCamelCase      =						[]
    _lowerCamelCase      =						self._front
    while aux is not None:
      # append the values in a list to display
      values_list.append(aux.val		)
      _lowerCamelCase      =						aux.next_node

    return f'''[{', '.join(repr(a__		) for val in values_list		)}]'''


if __name__ == "__main__":
  import doctest

  doctest.testmod()




