





from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
_snake_case           =			numpy.array([0, 0])
_snake_case           =			numpy.array([0.5, 0.8_66_02_54])
_snake_case           =			numpy.array([1, 0])
_snake_case           =			[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]


def _A       (   __magic_name__  , __magic_name__	):
   lowercase__			       =  initial_vectors
   for _ in range(lowerCAmelCase__	):
      lowercase__			       =  iteration_step(lowerCAmelCase__	)
   return vectors


def _A       (   __magic_name__	):
   lowercase__			       =  []
   for i, start_vector in enumerate(vectors[:-1]	):
      lowercase__			       =  vectors[i + 1]
      new_vectors.append(lowerCAmelCase__	)
      lowercase__			       =  end_vector - start_vector
      new_vectors.append(start_vector + difference_vector / 3	)
      new_vectors.append(
          start_vector + difference_vector / 3 + rotate(difference_vector / 3  , 60	)	)
      new_vectors.append(start_vector + difference_vector * 2 / 3	)
   new_vectors.append(vectors[-1]	)
   return new_vectors


def _A       (   __magic_name__  , __magic_name__	):
   lowercase__			       =  numpy.radians(lowerCAmelCase__	)
   lowercase__       ,							lowercase__			       =  numpy.cos(lowerCAmelCase__	), numpy.sin(lowerCAmelCase__	)
   lowercase__			       =  numpy.array(((c, -s), (s, c))	)
   return numpy.dot(lowerCAmelCase__  , lowerCAmelCase__	)


def _A       (   __magic_name__	):
   lowercase__			       =  plt.gca()
   axes.set_aspect("equal"	)

   # matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
   # y-coordinates as inputs, which are constructed from the vector-list using
   # zip()
   lowercase__       ,							lowercase__			       =  zip(*lowerCAmelCase__	)
   plt.plot(lowerCAmelCase__  , lowerCAmelCase__	)
   plt.show()


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  _snake_case           =			iterate(INITIAL_VECTORS, 5)
  plot(processed_vectors)













from abc import ABC, abstractmethod
from typing import Optional, Union

from .. import Dataset, DatasetDict, Features, IterableDataset, IterableDatasetDict, NamedSplit
from ..utils.typing import NestedDataStructureLike, PathLike





class  lowerCAmelCase							(       lowercase_ ):







  def __init__(      self  :str   ,							_lowercase  :Optional[NestedDataStructureLike[PathLike]] = None   ,							_lowercase  :Optional[NamedSplit] = None   ,							_lowercase  :Optional[Features] = None   ,							_lowercase  :str = None   ,							_lowercase  :bool = False   ,							_lowercase  :bool = False   ,							_lowercase  :Optional[int] = None   ,							**_lowercase  :Tuple   ,							):






     '''simple docstring'''





     lowercase__			       =  path_or_paths
     lowercase__			       =  split if split or isinstance(_lowercase   ,							_lowercase ) else "train"
     lowercase__			       =  features
     lowercase__			       =  cache_dir
     lowercase__			       =  keep_in_memory
     lowercase__			       =  streaming
     lowercase__			       =  num_proc
     lowercase__			       =  kwargs







  @abstractmethod
  def   UpperCAmelCase					(      self  :Any ):






     '''simple docstring'''





     pass





class  lowerCAmelCase							(       lowercase_ ):







  def __init__(      self  :List[Any]   ,							_lowercase  :Optional[Features] = None   ,							_lowercase  :str = None   ,							_lowercase  :bool = False   ,							_lowercase  :bool = False   ,							_lowercase  :Optional[int] = None   ,							**_lowercase  :Optional[int]   ,							):






     '''simple docstring'''





     lowercase__			       =  features
     lowercase__			       =  cache_dir
     lowercase__			       =  keep_in_memory
     lowercase__			       =  streaming
     lowercase__			       =  num_proc
     lowercase__			       =  kwargs







  @abstractmethod
  def   UpperCAmelCase					(      self  :int ):






     '''simple docstring'''





     pass






