


"""simple docstring"""






from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
__snake_case												=							20

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


class      __lowerCamelCase	:

     '''simple docstring'''


     def __init__(   self     ,					__UpperCAmelCase     ,					__UpperCAmelCase     ,					__UpperCAmelCase     ,					__UpperCAmelCase     ,					__UpperCAmelCase = 1.0     ,					__UpperCAmelCase = 1.0     ,					__UpperCAmelCase = "blue"     ,					)							->				None:
          _a     						=					position_x
          _a     						=					position_y
          _a     						=					velocity_x
          _a     						=					velocity_y
          _a     						=					mass
          _a     						=					size
          _a     						=					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:
          _a     						=					bodies
          _a     						=					gravitation_constant
          _a     						=					time_factor
          _a     						=					softening_factor


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





     def 				_UpperCAmelCase   (   self     ,					__UpperCAmelCase				)							->				None:
          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(_SCREAMING_SNAKE_CASE     ,					_SCREAMING_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    A_ ( _lowerCAmelCase  :       BodySystem,  _lowerCAmelCase  :       float,  _lowerCAmelCase  :       list[plt.Circle]							):






     """simple docstring"""

     body_system.update_system(_A							)

     # Update the positions of the patches
     for patch, body in zip(_A,  body_system.bodies							):
          _a     						=					(body.position_x, body.position_y)
def    A_ ( _lowerCAmelCase  :       str,  _lowerCAmelCase  :       BodySystem,  _lowerCAmelCase  :       float = -1,  _lowerCAmelCase  :       float = 1,  _lowerCAmelCase  :       float = -1,  _lowerCAmelCase  :       float = 1,  ):






     """simple docstring"""

     _a     						=					plt.figure()
     fig.canvas.set_window_title(_A							)
     _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(_A							)

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

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

     plt.show()
def    A_ ( ):






     """simple docstring"""

     _a     						=					0.9_7_0_0_4_3_6
     _a     						=					-0.2_4_3_0_8_7_5_3
     _a     						=					0.4_6_6_2_0_3_6_8_5
     _a     						=					0.4_3_2_3_6_5_7_3

     _a     						=					[
         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    A_ ( ):






     """simple docstring"""

     _a     						=					7.3_4_7_6e2_2
     _a     						=					5.9_7_2e2_4
     _a     						=					10_22
     _a     						=					3_84_39_90_00
     _a     						=					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
     _a     						=					earth_mass * velocity_dif / (earth_mass + moon_mass)
     _a     						=					moon_velocity - velocity_dif

     _a     						=					Body(-earth_moon_distance,  0,  0,  _A,  _A,  10_00_00_00,  '''grey'''							)
     _a     						=					Body(0,  0,  0,  _A,  _A,  50_00_00_00,  '''blue'''							)
     return BodySystem([earth, moon],  _A,  time_factor=1_00_00_00							)
def    A_ ( ):






     """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							),  _A,  _A,  size=0.0_5,  )							)
          bodies.append(
              Body(
                  random.uniform(-0.5,  0.5							),  random.uniform(-0.5,  0.5							),  -velocity_x,  -velocity_y,  size=0.0_5,  )							)
     return BodySystem(_A,  0.0_1,  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 sklearn.neural_network import MLPClassifier

__A	:   Tuple	=					[[0.0, 0.0], [1.0, 1.0], [1.0, 0.0], [0.0, 1.0]]
__A	:   Optional[int]	=					[0, 1, 0, 0]


__A	:   int	=					MLPClassifier(
    solver='lbfgs', alpha=1E-5, hidden_layer_sizes=(5, 2), random_state=1
)

clf.fit(X, y)


__A	:   str	=					[[0.0, 0.0], [0.0, 1.0], [1.0, 1.0]]
__A	:   str	=					clf.predict(test)




def        __UpperCamelCase     (      _A					:							int		)				->Union[str, Any]:



							"""simple docstring"""
							return list(_A		)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
