






from __future__ import annotations

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

# initial triangle of Koch snowflake
UpperCAmelCase__				   =		numpy.array([0, 0])
UpperCAmelCase__				   =		numpy.array([0.5, 0.866_0254])
UpperCAmelCase__				   =		numpy.array([1, 0])
UpperCAmelCase__				   =		[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]
def 						_a    (      a :list[numpy.ndarray]	,							a :int )							->			list[numpy.ndarray]:
 a		  =      initial_vectors
 for _ in range(a ):
  a		  =      iteration_step(a )
 return vectors
def 						_a    (      a :list[numpy.ndarray] )							->			list[numpy.ndarray]:
 a		  =      []
 for i, start_vector in enumerate(vectors[:-1] ):
  a		  =      vectors[i + 1]
  new_vectors.append(a )
  a		  =      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    (      a :numpy.ndarray	,							a :float )							->			numpy.ndarray:
 a		  =      numpy.radians(a )
 a  ,     a		  =      numpy.cos(a ), numpy.sin(a )
 a		  =      numpy.array(((c, -s), (s, c)) )
 return numpy.dot(a	,							a )
def 						_a    (      a :list[numpy.ndarray] )							->			None:
 a		  =      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()
 a  ,     a		  =      zip(*a )
 plt.plot(a	,							a )
 plt.show()


if __name__ == "__main__":
     import doctest

     doctest.testmod()

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










def 						_a    (      a :int )							->			list:

 # bit count represents no. of bits in the gray code
 if bit_count < 0:
  raise ValueError('''The given input must be positive''' )

 # get the generated string sequence
 a		  =      gray_code_sequence_string(a )
 #
 # convert them to integers
 for i in range(len(a ) ):
  a		  =      int(sequence[i]	,							2 )

 return sequence
def 						_a    (      a :int )							->			list:

 # The approach is a recursive one
 # Base case achieved when either n = 0 or n=1
 if bit_count == 0:
  return ["0"]

 if bit_count == 1:
  return ["0", "1"]

 a		  =      1 << bit_count  # defines the length of the sequence
 # 1<< n is equivalent to 2^n

 # recursive answer will generate answer for n-1 bits
 a		  =      gray_code_sequence_string(bit_count - 1 )

 a		  =      []

 # append 0 to first half of the smaller sequence generated
 for i in range(seq_len // 2 ):
  a		  =      '''0''' + smaller_sequence[i]
  sequence.append(a )

 # append 1 to second half ... start from the end of the list
 for i in reversed(range(seq_len // 2 ) ):
  a		  =      '''1''' + smaller_sequence[i]
  sequence.append(a )

 return sequence


if __name__ == "__main__":
     import doctest

     doctest.testmod()


