

from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
_SCREAMING_SNAKE_CASE          = 2_0

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


class     lowerCamelCase_   :




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




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




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




 def 						a					( self     ,     _UpperCAmelCase     ,     _UpperCAmelCase     ,     _UpperCAmelCase       ):
   self.velocity_x += force_x * delta_time
   self.velocity_y += force_y * delta_time




 def 						a					( self     ,     _UpperCAmelCase       ):
   self.position_x += self.velocity_x * delta_time
   self.position_y += self.velocity_y * delta_time



class     lowerCamelCase_   :




 def __init__( self     ,     _UpperCAmelCase     ,     _UpperCAmelCase = 1.0     ,     _UpperCAmelCase = 1.0     ,     _UpperCAmelCase = 0.0     ,     ):
   __UpperCAmelCase  :     Any		=    bodies
   __UpperCAmelCase  :     str		=    gravitation_constant
   __UpperCAmelCase  :     List[Any]		=    time_factor
   __UpperCAmelCase  :     List[Any]		=    softening_factor




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




 def 						a					( self     ,     _UpperCAmelCase       ):
   for bodya in self.bodies:
     __UpperCAmelCase  :     int		=    0.0
     __UpperCAmelCase  :     Union[str, Any]		=    0.0
     for bodya in self.bodies:
       if bodya != bodya:
         __UpperCAmelCase  :     Optional[int]		=    bodya.position_x - bodya.position_x
         __UpperCAmelCase  :     Tuple		=    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    _snake_case		(snake_case_				:    BodySystem						,					snake_case_				:    float						,					snake_case_				:    list[plt.Circle]     )       ->		None:
  body_system.update_system(snake_case_     )

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





def    _snake_case		(snake_case_				:    str						,					snake_case_				:    BodySystem						,					snake_case_				:    float = -1						,					snake_case_				:    float = 1						,					snake_case_				:    float = -1						,					snake_case_				:    float = 1						,					)       ->		None:
  __UpperCAmelCase  :     Tuple		=    plt.figure()
  fig.canvas.set_window_title(snake_case_     )
  __UpperCAmelCase  :     List[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  :     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(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  :     Union[str, Any]		=    animation.FuncAnimation(  # noqa: F841
      snake_case_						,					snake_case_						,					interval=snake_case_						,					blit=snake_case_     )

  plt.show()





def    _snake_case		()       ->		BodySystem:
  __UpperCAmelCase  :     Optional[int]		=    0.9700436
  __UpperCAmelCase  :     int		=    -0.24308753
  __UpperCAmelCase  :     Union[str, Any]		=    0.466203685
  __UpperCAmelCase  :     Dict		=    0.43236573

  __UpperCAmelCase  :     str		=    [
      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    _snake_case		()       ->		BodySystem:
  __UpperCAmelCase  :     int		=    7.34_76e22
  __UpperCAmelCase  :     Tuple		=    5.9_72e24
  __UpperCAmelCase  :     Optional[int]		=    1022
  __UpperCAmelCase  :     Dict		=    3_8439_9000
  __UpperCAmelCase  :     Union[str, Any]		=    6.6_74e-11

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

  __UpperCAmelCase  :     List[str]		=    Body(-earth_moon_distance						,					0						,					0						,					snake_case_						,					snake_case_						,					1000_0000						,					'grey'     )
  __UpperCAmelCase  :     List[str]		=    Body(0						,					0						,					0						,					snake_case_						,					snake_case_						,					5000_0000						,					'blue'     )
  return BodySystem([earth, moon]						,					snake_case_						,					time_factor=100_0000     )





def    _snake_case		()       ->		BodySystem:
  __UpperCAmelCase  :     Optional[Any]		=    []
  for _ in range(10     ):
    __UpperCAmelCase  :     Optional[int]		=    random.uniform(-0.5						,					0.5     )
    __UpperCAmelCase  :     List[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     )						,					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_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)








def    _snake_case		(snake_case_				:    list						,					snake_case_				:    list     )       ->		list:
  __UpperCAmelCase  :     int		=    len(snake_case_     )
  __UpperCAmelCase  :     int		=    len(snake_case_     )
  __UpperCAmelCase  :     int		=    (
      first_input_list_length
      if first_input_list_length > second_input_list_length
      else second_input_list_length
  )
  __UpperCAmelCase  :     list		=    []
  for char_count in range(snake_case_     ):
    if char_count < first_input_list_length:
      output_result_list.append(first_input_list[char_count]     )
    if char_count < second_input_list_length:
      output_result_list.append(second_input_list[char_count]     )

  return output_result_list


if __name__ == "__main__":
      print(alternative_list_arrange(['''A''', '''B''', '''C'''], [1, 2, 3, 4, 5]), end=''' ''')





