
'''simple docstring'''







class 			lowerCAmelCase :




		def __init__(				self      ):
								_SCREAMING_SNAKE_CASE				= ""
								_SCREAMING_SNAKE_CASE				= ""
								_SCREAMING_SNAKE_CASE				= []




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase      ):
								if m == -1:
														return n + 1
								elif n == -1:
														return m + 1
								elif self.dp[m][n] > -1:
														return self.dp[m][n]
								else:
														if self.worda[m] == self.worda[n]:
																				_SCREAMING_SNAKE_CASE				= self.__min_dist_top_down_dp(m - 1					,						n - 1      )
														else:
																				_SCREAMING_SNAKE_CASE				= self.__min_dist_top_down_dp(UpperCamelCase					,						n - 1      )
																				_SCREAMING_SNAKE_CASE				= self.__min_dist_top_down_dp(m - 1					,						UpperCamelCase      )
																				_SCREAMING_SNAKE_CASE				= self.__min_dist_top_down_dp(m - 1					,						n - 1      )
																				_SCREAMING_SNAKE_CASE				= 1 + min(UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase      )

														return self.dp[m][n]




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase      ):
								_SCREAMING_SNAKE_CASE				= worda
								_SCREAMING_SNAKE_CASE				= worda
								_SCREAMING_SNAKE_CASE				= [[-1 for _ in range(len(UpperCamelCase      )      )] for _ in range(len(UpperCamelCase      )      )]

								return self.__min_dist_top_down_dp(len(UpperCamelCase      ) - 1					,						len(UpperCamelCase      ) - 1      )




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase      ):
								_SCREAMING_SNAKE_CASE				= worda
								_SCREAMING_SNAKE_CASE				= worda
								_SCREAMING_SNAKE_CASE				= len(UpperCamelCase      )
								_SCREAMING_SNAKE_CASE				= len(UpperCamelCase      )
								_SCREAMING_SNAKE_CASE				= [[0 for _ in range(n + 1      )] for _ in range(m + 1      )]

								for i in range(m + 1      ):
														for j in range(n + 1      ):
																				if i == 0:  # first string is empty
																										_SCREAMING_SNAKE_CASE				= j
																				elif j == 0:  # second string is empty
																										_SCREAMING_SNAKE_CASE				= i
																				elif worda[i - 1] == worda[j - 1]:  # last characters are equal
																										_SCREAMING_SNAKE_CASE				= self.dp[i - 1][j - 1]
																				else:
																										_SCREAMING_SNAKE_CASE				= self.dp[i][j - 1]
																										_SCREAMING_SNAKE_CASE				= self.dp[i - 1][j]
																										_SCREAMING_SNAKE_CASE				= self.dp[i - 1][j - 1]
																										_SCREAMING_SNAKE_CASE				= 1 + min(UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase      )
								return self.dp[m][n]


if __name__ == "__main__":
						_snake_case				:   Dict     =				EditDistance()

						print("""****************** Testing Edit Distance DP Algorithm ******************""")
						print()

						_snake_case				:   List[str]     =				input("""Enter the first string: """).strip()
						_snake_case				:   List[Any]     =				input("""Enter the second string: """).strip()

						print()
						print(F"The minimum edit distance is: {solver.min_dist_top_down(Sa, Sa)}")
						print(F"The minimum edit distance is: {solver.min_dist_bottom_up(Sa, Sa)}")
						print()
						print("""*************** End of Testing Edit Distance DP Algorithm ***************""")

'''simple docstring'''







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



def 			_a		(	_SCREAMING_SNAKE_CASE		:   int  ):

						# A local function to see if a dot lands in the circle.
						def is_in_circle(_SCREAMING_SNAKE_CASE		:   float	,			_SCREAMING_SNAKE_CASE		:   float  ) -> bool:
												_SCREAMING_SNAKE_CASE				= 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
						_SCREAMING_SNAKE_CASE				= 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.
						_SCREAMING_SNAKE_CASE				= 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		:   int	,			_SCREAMING_SNAKE_CASE		:   Callable[[float], float]	,			_SCREAMING_SNAKE_CASE		:   float = 0.0	,			_SCREAMING_SNAKE_CASE		:   float = 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		:   int	,			_SCREAMING_SNAKE_CASE		:   float = 0.0	,			_SCREAMING_SNAKE_CASE		:   float = 1.0  ):

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

						_SCREAMING_SNAKE_CASE				= area_under_curve_estimator(
						    _SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE  )
						_SCREAMING_SNAKE_CASE				= (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		:   int  ):

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

						_SCREAMING_SNAKE_CASE				= 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()