

'''simple docstring'''





from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
lowerCAmelCase						:   int										=    20

# Time between time steps in seconds
lowerCAmelCase						:   Optional[int]										=    INTERVAL / 1000
class     SCREAMING_SNAKE_CASE__     :





       '''simple docstring'''




       def __init__(						self       :						Optional[Any]    ,		lowerCAmelCase__       :						float    ,		lowerCAmelCase__       :						float    ,		lowerCAmelCase__       :						float    ,		lowerCAmelCase__       :						float    ,		lowerCAmelCase__       :						float = 1.0    ,		lowerCAmelCase__       :						float = 1.0    ,		lowerCAmelCase__       :						str = "blue"    ,		)			->    None:
             snake_case__					=   position_x
             snake_case__					=   position_y
             snake_case__					=   velocity_x
             snake_case__					=   velocity_y
             snake_case__					=   mass
             snake_case__					=   size
             snake_case__					=   color

       @property
       def UpperCAmelCase_						(						self       :						List[str]							)			->    tuple[float, float]:
             return self.position_x, self.position_y

       @property
       def UpperCAmelCase_						(						self       :						List[str]							)			->    tuple[float, float]:
             return self.velocity_x, self.velocity_y

       def UpperCAmelCase_						(						self       :						int    ,		lowerCAmelCase__       :						float    ,		lowerCAmelCase__       :						float    ,		lowerCAmelCase__       :						float							)			->    None:
             self.velocity_x += force_x * delta_time
             self.velocity_y += force_y * delta_time

       def UpperCAmelCase_						(						self       :						List[Any]    ,		lowerCAmelCase__       :						float							)			->    None:
             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       :						List[str]    ,		lowerCAmelCase__       :						list[Body]    ,		lowerCAmelCase__       :						float = 1.0    ,		lowerCAmelCase__       :						float = 1.0    ,		lowerCAmelCase__       :						float = 0.0    ,		)			->    None:
             snake_case__					=   bodies
             snake_case__					=   gravitation_constant
             snake_case__					=   time_factor
             snake_case__					=   softening_factor

       def __len__(						self       :						Optional[Any]							)			->    int:
             return len(self.bodies							)

       def UpperCAmelCase_						(						self       :						Union[str, Any]    ,		lowerCAmelCase__       :						float							)			->    None:
             for bodya in self.bodies:
                   snake_case__					=   0.0
                   snake_case__					=   0.0
                   for bodya in self.bodies:
                         if bodya != bodya:
                               snake_case__					=   bodya.position_x - bodya.position_x
                               snake_case__					=   bodya.position_y - bodya.position_y

                               # Calculation of the distance using Pythagoras's theorem
                               # Extra factor due to the softening technique
                               snake_case__					=   (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 			_lowercase    (      __UpperCamelCase     :		BodySystem   ,       __UpperCamelCase     :		float   ,       __UpperCamelCase     :		list[plt.Circle] ):
      body_system.update_system(__UpperCamelCase )

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





def 			_lowercase    (      __UpperCamelCase     :		str   ,       __UpperCamelCase     :		BodySystem   ,       __UpperCamelCase     :		float = -1   ,       __UpperCamelCase     :		float = 1   ,       __UpperCamelCase     :		float = -1   ,       __UpperCamelCase     :		float = 1   ,       ):
      snake_case__					=   plt.figure()
      fig.canvas.set_window_title(__UpperCamelCase )
      snake_case__					=   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
      snake_case__					=   [
          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(__UpperCamelCase )

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

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

      plt.show()





def 			_lowercase    (      ):
      snake_case__					=   0.9_7_0_0_4_3_6
      snake_case__					=   -0.2_4_3_0_8_7_5_3
      snake_case__					=   0.4_6_6_2_0_3_6_8_5
      snake_case__					=   0.4_3_2_3_6_5_7_3

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





def 			_lowercase    (      ):
      snake_case__					=   7.3476E22
      snake_case__					=   5.972E24
      snake_case__					=   1022
      snake_case__					=   3_8439_9000
      snake_case__					=   6.674E-11

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

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





def 			_lowercase    (      ):
      snake_case__					=   []
      for _ in range(10 ):
            snake_case__					=   random.uniform(-0.5   ,       0.5 )
            snake_case__					=   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 )   ,       __UpperCamelCase   ,       __UpperCamelCase   ,       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(__UpperCamelCase   ,       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(),
           -4_3000_0000,
           4_3000_0000,
           -4_3000_0000,
           4_3000_0000,
       )
       plot('''Random system with many bodies''', example_a(), -1.5, 1.5, -1.5, 1.5)









import os
from shutil import copyfile
from typing import Optional, Tuple

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import is_sentencepiece_available, logging


if is_sentencepiece_available():
       from .tokenization_reformer import ReformerTokenizer
else:
       lowerCAmelCase						:   Union[str, Any]										=    None


lowerCAmelCase						:   str										=    logging.get_logger(__name__)


lowerCAmelCase						:   Any										=    '''▁'''

lowerCAmelCase						:   Tuple										=    {'''vocab_file''': '''spiece.model''', '''tokenizer_file''': '''tokenizer.json'''}

lowerCAmelCase						:   Optional[Any]										=    {
    '''vocab_file''': {
        '''google/reformer-crime-and-punishment''': (
            '''https://huggingface.co/google/reformer-crime-and-punishment/resolve/main/spiece.model'''
        )
    },
    '''tokenizer_file''': {
        '''google/reformer-crime-and-punishment''': (
            '''https://huggingface.co/google/reformer-crime-and-punishment/resolve/main/tokenizer.json'''
        )
    },
}

lowerCAmelCase						:   Union[str, Any]										=    {
    '''google/reformer-crime-and-punishment''': 52_4288,
}
class     SCREAMING_SNAKE_CASE__     (						__a		):





       '''simple docstring'''




       UpperCamelCase__ :     Union[str, Any]				    =       VOCAB_FILES_NAMES
       UpperCamelCase__ :     str				    =       PRETRAINED_VOCAB_FILES_MAP
       UpperCamelCase__ :     str				    =       PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
       UpperCamelCase__ :     str				    =       ['''input_ids''', '''attention_mask''']
       UpperCamelCase__ :     Optional[Any]				    =       ReformerTokenizer

       def __init__(						self       :						List[str]    ,		lowerCAmelCase__       :						Tuple=None    ,		lowerCAmelCase__       :						Optional[Any]=None    ,		lowerCAmelCase__       :						Dict="</s>"    ,		lowerCAmelCase__       :						Tuple="<unk>"    ,		lowerCAmelCase__       :						Dict=[]    ,		**lowerCAmelCase__       :						Optional[Any]    ,		)			->    Dict:
             super().__init__(
                 lowerCAmelCase__    ,		tokenizer_file=lowerCAmelCase__    ,		eos_token=lowerCAmelCase__    ,		unk_token=lowerCAmelCase__    ,		additional_special_tokens=lowerCAmelCase__    ,		**lowerCAmelCase__    ,		)

             snake_case__					=   vocab_file
             snake_case__					=   False if not self.vocab_file else True

       def UpperCAmelCase_						(						self       :						int    ,		lowerCAmelCase__       :						str    ,		lowerCAmelCase__       :						Optional[str] = None							)			->    Tuple[str]:
             if not self.can_save_slow_tokenizer:
                   raise ValueError(
                       """Your fast tokenizer does not have the necessary information to save the vocabulary for a slow """
                       """tokenizer."""							)

             if not os.path.isdir(lowerCAmelCase__							):
                   logger.error(f'''Vocabulary path ({save_directory}) should be a directory'''							)
                   return
             snake_case__					=   os.path.join(
                 lowerCAmelCase__    ,		(filename_prefix + """-""" if filename_prefix else """""") + VOCAB_FILES_NAMES["""vocab_file"""]							)

             if os.path.abspath(self.vocab_file							) != os.path.abspath(lowerCAmelCase__							):
                   copyfile(self.vocab_file    ,		lowerCAmelCase__							)

             return (out_vocab_file,)






