'''simple docstring'''





SCREAMING_SNAKE_CASE_:     Tuple  ={'a': ['c', 'b'], 'b': ['d', 'e'], 'c': [], 'd': [], 'e': []}
SCREAMING_SNAKE_CASE_:     List[str]  =['a', 'b', 'c', 'd', 'e']





def 	lowerCAmelCase_				(					snake_case_       : List[str]					,    snake_case_       : Optional[Any]					,    snake_case_       : Tuple			)    ->      Optional[int]:


     '''simple docstring'''




     UpperCAmelCase_           =   start
     # add current to visited
     visited.append(snake_case_			)
     UpperCAmelCase_           =   edges[current]
     for neighbor in neighbors:
          # if neighbor not in visited, visit
          if neighbor not in visited:
               UpperCAmelCase_           =   topological_sort(snake_case_					,    snake_case_					,    snake_case_			)
    # if all neighbors visited add current to sort
     sort.append(snake_case_			)
     # if all vertices haven't been visited select a new one to visit
     if len(snake_case_			) != len(snake_case_			):
          for vertice in vertices:
               if vertice not in visited:
                    UpperCAmelCase_           =   topological_sort(snake_case_					,    snake_case_					,    snake_case_			)
    # return sort
     return sort


if __name__ == "__main__":
    SCREAMING_SNAKE_CASE_:     List[Any]  =topological_sort('a', [], [])
    print(sort)











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



def A_	(		A__				)  ->		Tuple:

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



def A_	(		A__		,      A__ = 0.0		,      A__ = 1.0				)  ->		None:

       def identity_function(A__				) -> float:
              return x

       a__						:	List[Any] =				area_under_curve_estimator(
           A__		,      A__		,      A__		,      A__				)
       a__						:	Union[str, 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_	(		A__				)  ->		None:

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

       a__						:	Dict =				area_under_curve_estimator(
           A__		,      A__		,      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()


