
from __future__ import annotations

import math

import numpy as np
from numpy.linalg import norm




def 	A_ (							snake_case							:   np.ndarray ,      snake_case							:   np.ndarray )      ->    float:



						'''simple docstring'''

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




def 	A_ (							snake_case							:   np.ndarray ,      snake_case							:   np.ndarray )      ->    list[list[list[float] | float]]:



						'''simple docstring'''

						if dataset.ndim != value_array.ndim:
												__UpperCamelCase       =			(
												    '''Wrong input data\'s dimensions... '''
												    f"dataset : {dataset.ndim}, value_array : {value_array.ndim}"
												)
												raise ValueError(snake_case )

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

						if dataset.dtype != value_array.dtype:
												__UpperCamelCase       =			(
												    '''Input data have different datatype... '''
												    f"dataset : {dataset.dtype}, value_array : {value_array.dtype}"
												)
												raise TypeError(snake_case )

						__UpperCamelCase       =			[]

						for value in value_array:
												__UpperCamelCase       =			euclidean(snake_case ,      dataset[0] )
												__UpperCamelCase       =			dataset[0].tolist()

												for dataset_value in dataset[1:]:
																		__UpperCamelCase       =			euclidean(snake_case ,      snake_case )

																		if dist > temp_dist:
																								__UpperCamelCase       =			temp_dist
																								__UpperCamelCase       =			dataset_value.tolist()

												answer.append([vector, dist] )

						return answer




def 	A_ (							snake_case							:   np.ndarray ,      snake_case							:   np.ndarray )      ->    float:



						'''simple docstring'''

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


if __name__ == "__main__":
					import doctest

					doctest.testmod()






from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean




def 	A_ (							snake_case							:   int )      ->    int:



						'''simple docstring'''

						def is_in_circle(snake_case							:   float ,      snake_case							:   float ) -> bool:
												__UpperCamelCase       =			sqrt((x**2) + (y**2) )
												# Our circle has a radius of 1, so a distance
												# greater than 1 would land outside the circle.
												return distance_from_centre <= 1

						# The proportion of guesses that landed in the circle
						__UpperCamelCase       =			mean(
						    int(is_in_circle(uniform(-1.0 ,      1.0 ) ,      uniform(-1.0 ,      1.0 ) ) )
						    for _ in range(snake_case ) )
						# The ratio of the area for circle to square is pi/4.
						__UpperCamelCase       =			proportion * 4
						print(f"The estimated value of pi is {pi_estimate}" )
						print(f"The numpy value of pi is {pi}" )
						print(f"The total error is {abs(pi - pi_estimate )}" )




def 	A_ (							snake_case							:   int ,      snake_case							:   Callable[[float], float] ,      snake_case							:   float = 0.0 ,      snake_case							:   float = 1.0 ,      )      ->    float:



						'''simple docstring'''

						return mean(
						    function_to_integrate(uniform(snake_case ,      snake_case ) ) for _ in range(snake_case ) ) * (max_value - min_value)




def 	A_ (							snake_case							:   int ,      snake_case							:   float = 0.0 ,      snake_case							:   float = 1.0 )      ->    None:



						'''simple docstring'''

						def identity_function(snake_case							:   float ) -> float:
												return x

						__UpperCamelCase       =			area_under_curve_estimator(
						    snake_case ,      snake_case ,      snake_case ,      snake_case )
						__UpperCamelCase       =			(max_value * max_value - min_value * min_value) / 2

						print('''******************''' )
						print(f"Estimating area under y=x where x varies from {min_value} to {max_value}" )
						print(f"Estimated value is {estimated_value}" )
						print(f"Expected value is {expected_value}" )
						print(f"Total error is {abs(estimated_value - expected_value )}" )
						print('''******************''' )




def 	A_ (							snake_case							:   int )      ->    None:



						'''simple docstring'''

						def function_to_integrate(snake_case							:   float ) -> float:
												return sqrt(4.0 - x * x )

						__UpperCamelCase       =			area_under_curve_estimator(
						    snake_case ,      snake_case ,      0.0 ,      2.0 )

						print('''******************''' )
						print('''Estimating pi using area_under_curve_estimator''' )
						print(f"Estimated value is {estimated_value}" )
						print(f"Expected value is {pi}" )
						print(f"Total error is {abs(estimated_value - pi )}" )
						print('''******************''' )


if __name__ == "__main__":
				import doctest

				doctest.testmod()




