
from __future__ import annotations

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

# initial triangle of Koch snowflake
A     :	Any    = numpy.array([0, 0])
A     :	int    = numpy.array([0.5, 0.8660254])
A     :	int    = numpy.array([1, 0])
A     :	Optional[int]    = [VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]


def     __lowerCAmelCase			(			a__						,    a__  )       ->  list[numpy.ndarray]:
				__a										=    initial_vectors
				for _ in range(a__  ):
								__a										=    iteration_step(a__  )
				return vectors


def     __lowerCAmelCase			(			a__  )       ->  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     __lowerCAmelCase			(			a__						,    a__  )       ->  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     __lowerCAmelCase			(			a__  )       ->  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()

					A     :	Dict    = iterate(INITIAL_VECTORS, 5)
					plot(processed_vectors)



'''simple docstring'''
# Algorithm for the pigeonhole sorting







def 					a__       (					lowerCAmelCase__						)    ->	Optional[Any]:
    UpperCAmelCase__			:		Any													=				min(lowerCAmelCase__						)  # min() finds the minimum value
    UpperCAmelCase__			:		Optional[int]													=				max(lowerCAmelCase__						)  # max() finds the maximum value

    UpperCAmelCase__			:		int													=				max_val - min_val + 1  # size is difference of max and min values plus one

    # list of pigeonholes of size equal to the variable size
    UpperCAmelCase__			:		Any													=				[0] * size

    # Populate the pigeonholes.
    for x in a:
        assert isinstance(lowerCAmelCase__  ,					lowerCAmelCase__						), "integers only please"
        holes[x - min_val] += 1

    # Putting the elements back into the array in an order.
    UpperCAmelCase__			:		Optional[int]													=				0
    for count in range(lowerCAmelCase__						):
        while holes[count] > 0:
            holes[count] -= 1
            UpperCAmelCase__			:		Dict													=				count + min_val
            i += 1





def 					a__       (					)    ->	Union[str, Any]:
    UpperCAmelCase__			:		List[str]													=				[8, 3, 2, 7, 4, 6, 8]
    pigeonhole_sort(lowerCAmelCase__						)
    print('''Sorted order is:'''  ,					''' '''.join(lowerCAmelCase__						)						)


if __name__ == "__main__":
  main()
