


'''simple docstring'''
from __future__ import annotations

import math

import numpy as np
from numpy.linalg import norm


def     a   (    __a				,      __a     )						->			float:



					'''simple docstring'''






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


def     a   (    __a				,      __a     )						->			list[list[list[float] | float]]:



					'''simple docstring'''






					if dataset.ndim != value_array.ndim:
										UpperCamelCase__     :int							      =				(
										    '''Wrong input data\'s dimensions... '''
										    f'''dataset : {dataset.ndim}, value_array : {value_array.ndim}'''
										)
										raise ValueError(__a     )

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

					if dataset.dtype != value_array.dtype:
										UpperCamelCase__     :List[Any]							      =				(
										    '''Input data have different datatype... '''
										    f'''dataset : {dataset.dtype}, value_array : {value_array.dtype}'''
										)
										raise TypeError(__a     )

					UpperCamelCase__     :Union[str, Any]							      =				[]

					for value in value_array:
										UpperCamelCase__     :Optional[Any]							      =				euclidean(__a				,      dataset[0]     )
										UpperCamelCase__     :Tuple							      =				dataset[0].tolist()

										for dataset_value in dataset[1:]:
															UpperCamelCase__     :Tuple							      =				euclidean(__a				,      __a     )

															if dist > temp_dist:
																				UpperCamelCase__     :Union[str, Any]							      =				temp_dist
																				UpperCamelCase__     :Optional[Any]							      =				dataset_value.tolist()

										answer.append([vector, dist]     )

					return answer


def     a   (    __a				,      __a     )						->			float:



					'''simple docstring'''






					return np.dot(__a				,      __a     ) / (norm(__a     ) * norm(__a     ))


if __name__ == "__main__":
						import doctest

						doctest.testmod()



'''simple docstring'''
import numpy as np


def     a   (    __a				,      __a				,      __a				,      __a				,      __a     )						->			Union[str, Any]:



					'''simple docstring'''






					UpperCamelCase__     :Tuple							      =				int(np.ceil((x_end - xa) / h     )     )
					UpperCamelCase__     :Optional[int]							      =				np.zeros((n + 1,)     )
					UpperCamelCase__     :List[str]							      =				ya
					UpperCamelCase__     :Tuple							      =				xa

					for k in range(__a     ):
										UpperCamelCase__     :Dict							      =				f(__a				,      y[k]     )
										UpperCamelCase__     :List[Any]							      =				f(x + 0.5 * h				,      y[k] + 0.5 * h * ka     )
										UpperCamelCase__     :Dict							      =				f(x + 0.5 * h				,      y[k] + 0.5 * h * ka     )
										UpperCamelCase__     :List[Any]							      =				f(x + h				,      y[k] + h * ka     )
										UpperCamelCase__     :List[str]							      =				y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
										x += h

					return y


if __name__ == "__main__":
		import doctest

		doctest.testmod()