


'''simple docstring'''


from __future__ import annotations

from collections.abc import MutableSequence






class 	lowerCAmelCase__			:




			def __init__(		self  :     List[Any]	,  lowerCamelCase__  :     Optional[Any]	,  lowerCamelCase__  :     Dict )   ->Optional[int]:



					'''simple docstring'''







					if len(_A ) != degree + 1:
							raise ValueError(
							    "The number of coefficients should be equal to the degree + 1." )

					_UpperCAmelCase		:       Union[str, Any]								=      list(_A )
					_UpperCAmelCase		:       str								=      degree




			def __add__(		self  :     Tuple	,  lowerCamelCase__  :     Optional[Any] )   ->List[str]:



					'''simple docstring'''







					if self.degree > polynomial_a.degree:
							_UpperCAmelCase		:       str								=      self.coefficients[:]
							for i in range(polynomial_a.degree + 1 ):
									coefficients[i] += polynomial_a.coefficients[i]
							return Polynomial(self.degree	,  _A )
					else:
							_UpperCAmelCase		:       str								=      polynomial_a.coefficients[:]
							for i in range(self.degree + 1 ):
									coefficients[i] += self.coefficients[i]
							return Polynomial(polynomial_a.degree	,  _A )




			def __sub__(		self  :     Optional[Any]	,  lowerCamelCase__  :     Optional[int] )   ->List[str]:



					'''simple docstring'''







					return self + polynomial_a * Polynomial(0	,  [-1] )




			def __neg__(		self  :     str )   ->List[str]:



					'''simple docstring'''







					return Polynomial(self.degree	,  [-c for c in self.coefficients] )




			def __mul__(		self  :     Any	,  lowerCamelCase__  :     List[Any] )   ->List[Any]:



					'''simple docstring'''







					_UpperCAmelCase		:       Optional[int]								=      [0] * (self.degree + polynomial_a.degree + 1)
					for i in range(self.degree + 1 ):
							for j in range(polynomial_a.degree + 1 ):
									coefficients[i + j] += (
									    self.coefficients[i] * polynomial_a.coefficients[j]
									)

					return Polynomial(self.degree + polynomial_a.degree	,  _A )




			def 							lowerCAmelCase__    (		self  :     List[Any]	,  lowerCamelCase__  :     Dict )   ->Optional[Any]:



					'''simple docstring'''







					_UpperCAmelCase		:       Tuple								=      0
					for i in range(self.degree + 1 ):
							result += self.coefficients[i] * (substitution**i)
					return result




			def __str__(		self  :     Optional[int] )   ->str:



					'''simple docstring'''







					_UpperCAmelCase		:       Tuple								=      ""
					for i in range(self.degree	,  -1	,  -1 ):
							if self.coefficients[i] == 0:
									continue
							elif self.coefficients[i] > 0:
									if polynomial:
											polynomial += " + "
							else:
									polynomial += " - "

							if i == 0:
									polynomial += str(abs(self.coefficients[i] ) )
							elif i == 1:
									polynomial += str(abs(self.coefficients[i] ) ) + "x"
							else:
									polynomial += str(abs(self.coefficients[i] ) ) + "x^" + str(_A )

					return polynomial




			def __repr__(		self  :     Optional[Any] )   ->Optional[int]:



					'''simple docstring'''







					return self.__str__()




			def 							lowerCAmelCase__    (		self  :     List[Any] )   ->List[str]:



					'''simple docstring'''







					_UpperCAmelCase		:       Tuple								=      [0] * self.degree
					for i in range(self.degree ):
							_UpperCAmelCase		:       Any								=      self.coefficients[i + 1] * (i + 1)
					return Polynomial(self.degree - 1	,  _A )




			def 							lowerCAmelCase__    (		self  :     List[Any]	,  lowerCamelCase__  :     List[str] = 0 )   ->Optional[Any]:



					'''simple docstring'''







					_UpperCAmelCase		:       Union[str, Any]								=      [0] * (self.degree + 2)
					_UpperCAmelCase		:       int								=      constant
					for i in range(self.degree + 1 ):
							_UpperCAmelCase		:       Union[str, Any]								=      self.coefficients[i] / (i + 1)
					return Polynomial(self.degree + 1	,  _A )




			def __eq__(		self  :     int	,  lowerCamelCase__  :     Any )   ->Any:



					'''simple docstring'''







					if not isinstance(_A	,  _A ):
							return False

					if self.degree != polynomial_a.degree:
							return False

					for i in range(self.degree + 1 ):
							if self.coefficients[i] != polynomial_a.coefficients[i]:
									return False

					return True






			def __ne__(		self  :     List[str]	,  lowerCamelCase__  :     Tuple )   ->Optional[Any]:



					'''simple docstring'''







					return not self.__eq__(_A )







'''simple docstring'''


from __future__ import annotations

import math

import numpy as np
from numpy.linalg import norm






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






def  __lowerCAmelCase (__lowerCAmelCase      , __lowerCAmelCase   ):

		if dataset.ndim != value_array.ndim:
				_UpperCAmelCase		:       Optional[Any]								=      (
				    "Wrong input data's dimensions... "
				    F"""dataset : {dataset.ndim}, value_array : {value_array.ndim}"""
				)
				raise ValueError(__lowerCAmelCase   )

		try:
				if dataset.shape[1] != value_array.shape[1]:
						_UpperCAmelCase		:       Optional[int]								=      (
						    "Wrong input data's shape... "
						    F"""dataset : {dataset.shape[1]}, value_array : {value_array.shape[1]}"""
						)
						raise ValueError(__lowerCAmelCase   )
		except IndexError:
				if dataset.ndim != value_array.ndim:
						raise TypeError("Wrong shape"   )

		if dataset.dtype != value_array.dtype:
				_UpperCAmelCase		:       Union[str, Any]								=      (
				    "Input data have different datatype... "
				    F"""dataset : {dataset.dtype}, value_array : {value_array.dtype}"""
				)
				raise TypeError(__lowerCAmelCase   )

		_UpperCAmelCase		:       Optional[int]								=      []

		for value in value_array:
				_UpperCAmelCase		:       List[str]								=      euclidean(__lowerCAmelCase      , dataset[0]   )
				_UpperCAmelCase		:       Dict								=      dataset[0].tolist()

				for dataset_value in dataset[1:]:
						_UpperCAmelCase		:       int								=      euclidean(__lowerCAmelCase      , __lowerCAmelCase   )

						if dist > temp_dist:
								_UpperCAmelCase		:       Tuple								=      temp_dist
								_UpperCAmelCase		:       Dict								=      dataset_value.tolist()

				answer.append([vector, dist]   )

		return answer






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


if __name__ == "__main__":
						import doctest

						doctest.testmod()



