






'''simple docstring'''







from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
__lowerCAmelCase					   =       20

# Time between time steps in seconds
__lowerCAmelCase					   =       INTERVAL / 10_00




class      __SCREAMING_SNAKE_CASE					:


  """simple docstring"""


  def __init__( self      ,  UpperCamelCase__      ,  UpperCamelCase__      ,  UpperCamelCase__      ,  UpperCamelCase__      ,  UpperCamelCase__ = 1.0      ,  UpperCamelCase__ = 1.0      ,  UpperCamelCase__ = "blue"      ,  ):






         """simple docstring"""


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







  @property
  def       _a					( self  ):






         """simple docstring"""


         return self.position_x, self.position_y







  @property
  def       _a					( self  ):






         """simple docstring"""


         return self.velocity_x, self.velocity_y







  def       _a					( self      ,  UpperCamelCase__      ,  UpperCamelCase__      ,  UpperCamelCase__  ):






         """simple docstring"""


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







  def       _a					( self      ,  UpperCamelCase__  ):






         """simple docstring"""


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





class      __SCREAMING_SNAKE_CASE					:


  """simple docstring"""


  def __init__( self      ,  UpperCamelCase__      ,  UpperCamelCase__ = 1.0      ,  UpperCamelCase__ = 1.0      ,  UpperCamelCase__ = 0.0      ,  ):






         """simple docstring"""


         a_	    = bodies
         a_	    = gravitation_constant
         a_	    = time_factor
         a_	    = softening_factor







  def __len__( self  ):






         """simple docstring"""


         return len(self.bodies  )







  def       _a					( self      ,  UpperCamelCase__  ):






         """simple docstring"""


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

                              # Calculation of the distance using Pythagoras's theorem
                              # Extra factor due to the softening technique
                              a_	    = (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(lowerCamelCase__      ,  lowerCamelCase__      ,  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				(			lowercase_					:     Optional[Any]      ,					lowercase_					:     List[Any]      ,					lowercase_					:     Dict      ):
       """simple docstring"""




       body_system.update_system(lowercase_      )

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


def 			__UpperCamelCase				(			lowercase_					:     List[Any]      ,					lowercase_					:     Dict      ,					lowercase_					:     Dict = -1      ,					lowercase_					:     Union[str, Any] = 1      ,					lowercase_					:     Union[str, Any] = -1      ,					lowercase_					:     Optional[int] = 1      ,					):
       """simple docstring"""




       a_	    = plt.figure()
       fig.canvas.set_window_title(lowercase_      )
       a_	    = 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
       a_	    = [
           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(lowercase_      )

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

       a_	    = animation.FuncAnimation(  # noqa: F841
           lowercase_      ,					lowercase_      ,					interval=lowercase_      ,					blit=lowercase_      )

       plt.show()


def 			__UpperCamelCase				(			):
       """simple docstring"""




       a_	    = 0.970_0436
       a_	    = -0.2430_8753
       a_	    = 0.4_6620_3685
       a_	    = 0.4323_6573

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


def 			__UpperCamelCase				(			):
       """simple docstring"""




       a_	    = 7.3476E22
       a_	    = 5.972E24
       a_	    = 1_022
       a_	    = 384_399_000
       a_	    = 6.674E-11

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

       a_	    = Body(-earth_moon_distance      ,					0      ,					0      ,					lowercase_      ,					lowercase_      ,					10_000_000      ,					'grey'      )
       a_	    = Body(0      ,					0      ,					0      ,					lowercase_      ,					lowercase_      ,					50_000_000      ,					'blue'      )
       return BodySystem([earth, moon]      ,					lowercase_      ,					time_factor=1_000_000      )


def 			__UpperCamelCase				(			):
       """simple docstring"""




       a_	    = []
       for _ in range(10      ):
              a_	    = random.uniform(-0.5      ,					0.5      )
              a_	    = 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      )      ,					lowercase_      ,					lowercase_      ,					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(lowercase_      ,					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)












'''simple docstring'''







import re


def 			__UpperCamelCase				(			lowercase_					:     int      ):
       """simple docstring"""




       def docstring_decorator(lowercase_					:     int      ):
              a_	    = fn.__doc__
              a_	    = func_doc.split('\n'      )
              a_	    = 0
              while i < len(lowercase_      ) and re.search(R'^\s*Examples?:\s*$'      ,					lines[i]      ) is None:
                     i += 1
              if i < len(lowercase_      ):
                     a_	    = example_docstring
                     a_	    = '\n'.join(lowercase_      )
              else:
                     raise ValueError(
                         F'The function {fn} should have an empty \'Examples:\' in its docstring as placeholder, '
                         F'current docstring is:\n{func_doc}'      )
              a_	    = func_doc
              return fn

       return docstring_decorator




