



"""simple docstring"""







from __future__ import annotations

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

# initial triangle of Koch snowflake
A    =			numpy.array([0, 0])
A    =			numpy.array([0.5, 0.866_0254])
A    =			numpy.array([1, 0])
A    =			[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							list[numpy.ndarray]:
							A         =					initial_vectors
							for _ in range(lowerCamelCase__			):
														A         =					iteration_step(lowerCamelCase__			)
							return vectors

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							list[numpy.ndarray]:
							A         =					[]
							for i, start_vector in enumerate(vectors[:-1]			):
														A         =					vectors[i + 1]
														new_vectors.append(lowerCamelCase__			)
														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__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							numpy.ndarray:
							A         =					numpy.radians(lowerCamelCase__			)
							A      ,  A         =					numpy.cos(lowerCamelCase__			), numpy.sin(lowerCamelCase__			)
							A         =					numpy.array(((c, -s), (s, c))			)
							return numpy.dot(lowerCamelCase__				,      lowerCamelCase__			)

def   lowerCAmelCase__			(     lowerCamelCase__			) ->							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(*lowerCamelCase__			)
							plt.plot(lowerCamelCase__				,      lowerCamelCase__			)
							plt.show()


if __name__ == "__main__":
							import doctest

							doctest.testmod()

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








"""simple docstring"""







def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__			) ->							float:

							def get_matched_characters(lowerCamelCase__				,      lowerCamelCase__			) -> str:
														A         =					[]
														A         =					min(len(_stra			)				,      len(_stra			)			) // 2
														for i, l in enumerate(_stra			):
																					A         =					int(max(0				,      i - limit			)			)
																					A         =					int(min(i + limit + 1				,      len(_stra			)			)			)
																					if l in _stra[left:right]:
																												matched.append(lowerCamelCase__			)
																												A         =					f"""{_stra[0:_stra.index(lowerCamelCase__			)]} {_stra[_stra.index(lowerCamelCase__			) + 1:]}"""

														return "".join(lowerCamelCase__			)

							# matching characters
							A         =					get_matched_characters(lowerCamelCase__				,      lowerCamelCase__			)
							A         =					get_matched_characters(lowerCamelCase__				,      lowerCamelCase__			)
							A         =					len(lowerCamelCase__			)

							# transposition
							A         =					(
							    len([(ca, ca) for ca, ca in zip(lowerCamelCase__				,      lowerCamelCase__			) if ca != ca]			) // 2
							)

							if not match_count:
														A         =					0.0
							else:
														A         =					(
														    1
														    / 3
														    * (
														        match_count / len(lowerCamelCase__			)
														        + match_count / len(lowerCamelCase__			)
														        + (match_count - transpositions) / match_count
														    )
														)

							# common prefix up to 4 characters
							A         =					0
							for ca, ca in zip(stra[:4]				,      stra[:4]			):
														if ca == ca:
																					prefix_len += 1
														else:
																					break

							return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(jaro_winkler('hello', 'world'))



