





from unittest import TestCase

from datasets import Sequence, Value
from datasets.arrow_dataset import Dataset





class 					A_					(   UpperCAmelCase						):







       """simple docstring"""





       def  __UpperCAmelCase			(     self						:						Tuple	)    ->       Optional[Any]:
         return [
             {"col_1": 3, "col_2": "a"},
             {"col_1": 2, "col_2": "b"},
             {"col_1": 1, "col_2": "c"},
             {"col_1": 0, "col_2": "d"},
         ]







       def  __UpperCAmelCase			(     self						:						List[str]	)    ->       Tuple:
         _lowercase						    =			{'col_1': [3, 2, 1, 0], 'col_2': ['a', 'b', 'c', 'd']}
         return Dataset.from_dict(__A	)







       def  __UpperCAmelCase			(     self						:						Optional[Any]	)    ->       Any:
         _lowercase						    =			self._create_example_records()
         _lowercase						    =			Dataset.from_list(__A	)
         self.assertListEqual(dset.column_names    ,['col_1', 'col_2']	)
         for i, r in enumerate(__A	):
           self.assertDictEqual(__A    ,example_records[i]	)







       def  __UpperCAmelCase			(     self						:						Union[str, Any]	)    ->       List[str]:
         _lowercase						    =			self._create_example_records()
         _lowercase						    =			Dataset.from_list(__A	)
         _lowercase						    =			Dataset.from_dict({k: [r[k] for r in example_records] for k in example_records[0]}	)
         self.assertEqual(dset.info    ,dset_from_dict.info	)







       def  __UpperCAmelCase			(     self						:						int	)    ->       Tuple:  # checks what happens with missing columns
         _lowercase						    =			[{'col_1': 1}, {'col_2': 'x'}]
         _lowercase						    =			Dataset.from_list(__A	)
         self.assertDictEqual(dset[0]    ,{'col_1': 1}	)
         self.assertDictEqual(dset[1]    ,{'col_1': None}	)  # NB: first record is used for columns







       def  __UpperCAmelCase			(     self						:						List[Any]	)    ->       List[Any]:  # checks if the type can be inferred from the second record
         _lowercase						    =			[{'col_1': []}, {'col_1': [1, 2]}]
         _lowercase						    =			Dataset.from_list(__A	)
         self.assertEqual(dset.info.features['col_1']    ,Sequence(Value('int64'	)	)	)







       def  __UpperCAmelCase			(     self						:						List[str]	)    ->       str:
         _lowercase						    =			Dataset.from_list([]	)
         self.assertEqual(len(__A	)    ,0	)
         self.assertListEqual(dset.column_names    ,[]	)


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



def 			_A	(      SCREAMING_SNAKE_CASE      ):

	# A local function to see if a dot lands in the circle.
	def is_in_circle(SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE      ) -> bool:
		UpperCAmelCase__:	Any									= 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__:	Optional[int]									= mean(
	    int(is_in_circle(uniform(-1.0	,1.0      )	,uniform(-1.0	,1.0      )      )      )
	    for _ in range(SCREAMING_SNAKE_CASE      )      )
	# The ratio of the area for circle to square is pi/4.
	UpperCAmelCase__:	Optional[int]									= 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	(      SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE = 0.0	,SCREAMING_SNAKE_CASE = 1.0	,):
	return mean(
	    function_to_integrate(uniform(SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE      )      ) for _ in range(SCREAMING_SNAKE_CASE      )      ) * (max_value - min_value)



def 			_A	(      SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE = 0.0	,SCREAMING_SNAKE_CASE = 1.0      ):

	def identity_function(SCREAMING_SNAKE_CASE      ) -> float:
		return x

	UpperCAmelCase__:	Tuple									= area_under_curve_estimator(
	    SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE      )
	UpperCAmelCase__:	Optional[Any]									= (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	(      SCREAMING_SNAKE_CASE      ):

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

	UpperCAmelCase__:	Union[str, Any]									= area_under_curve_estimator(
	    SCREAMING_SNAKE_CASE	,SCREAMING_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()