

from __future__ import annotations

import math
from collections.abc import Callable






def        UpperCamelCase_(							_snake_case   :  Any       ,     _snake_case   :  Optional[Any]       ,     _snake_case   :  str       ,     _snake_case   :  List[Any] = 100       ,     ):




			"""simple docstring"""






			__a        =x_start
			__a        =fnc(lowercase__	)
			__a        =0.0

			for _ in range(lowercase__	):
						# Approximates curve as a sequence of linear lines and sums their length
						__a        =(x_end - x_start) / steps + xa
						__a        =fnc(lowercase__	)
						length += math.hypot(xa - xa       ,     fxa - fxa	)

						# Increment step
						__a        =xa
						__a        =fxa

			return length


if __name__ == "__main__":






						def        UpperCamelCase_(							_snake_case   :  Any	):




									"""simple docstring"""






									return math.sin(10 * x	)

						print("f(x) = sin(10 * x)")
						print("The length of the curve from x = -10 to x = 10 is:")
						_lowerCAmelCase					:			Optional[int]  				=			10
						while i <= 100_000:
												print(f'''With {i} steps: {line_length(f, -10, 10, i)}''')
												i *= 10












"""simple docstring"""






from __future__ import annotations

import math

import numpy as np
from numpy.linalg import norm







def      _snake_case			(				lowercase__							,    lowercase__		):
				return math.sqrt(sum(pow(a - b							,    2		) for a, b in zip(lowercase__							,    lowercase__		)		)		)







def      _snake_case			(				lowercase__							,    lowercase__		):

				if dataset.ndim != value_array.ndim:
								_lowerCamelCase     :			Tuple    =    (
								    'Wrong input data\'s dimensions... '
								    f'''dataset : {dataset.ndim}, value_array : {value_array.ndim}'''
								)
								raise ValueError(lowercase__		)

				try:
								if dataset.shape[1] != value_array.shape[1]:
												_lowerCamelCase     :			Optional[int]    =    (
												    'Wrong input data\'s shape... '
												    f'''dataset : {dataset.shape[1]}, value_array : {value_array.shape[1]}'''
												)
												raise ValueError(lowercase__		)
				except IndexError:
								if dataset.ndim != value_array.ndim:
												raise TypeError('Wrong shape'		)

				if dataset.dtype != value_array.dtype:
								_lowerCamelCase     :			int    =    (
								    'Input data have different datatype... '
								    f'''dataset : {dataset.dtype}, value_array : {value_array.dtype}'''
								)
								raise TypeError(lowercase__		)

				_lowerCamelCase     :			Optional[int]    =    []

				for value in value_array:
								_lowerCamelCase     :			Tuple    =    euclidean(lowercase__							,    dataset[0]		)
								_lowerCamelCase     :			Union[str, Any]    =    dataset[0].tolist()

								for dataset_value in dataset[1:]:
												_lowerCamelCase     :			Optional[Any]    =    euclidean(lowercase__							,    lowercase__		)

												if dist > temp_dist:
																_lowerCamelCase     :			List[Any]    =    temp_dist
																_lowerCamelCase     :			List[str]    =    dataset_value.tolist()

								answer.append([vector, dist]		)

				return answer







def      _snake_case			(				lowercase__							,    lowercase__		):
				return np.dot(lowercase__							,    lowercase__		) / (norm(lowercase__		) * norm(lowercase__		))


if __name__ == "__main__":
			import doctest

			doctest.testmod()