


'''simple docstring'''


UpperCAmelCase_		:   List[Any]							   =		256
# Modulus to hash a string
UpperCAmelCase_		:   Any							   =		100_0003







def 			snake_case_   (  SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__     ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE :       List[str]     		=      len(A__     )
				_SCREAMING_SNAKE_CASE :       List[Any]     		=      len(A__     )
				if p_len > t_len:
								return False

				_SCREAMING_SNAKE_CASE :       Union[str, Any]     		=      0
				_SCREAMING_SNAKE_CASE :       Union[str, Any]     		=      0
				_SCREAMING_SNAKE_CASE :       Tuple     		=      1

				# Calculating the hash of pattern and substring of text
				for i in range(A__     ):
								_SCREAMING_SNAKE_CASE :       Any     		=      (ord(pattern[i]     ) + p_hash * alphabet_size) % modulus
								_SCREAMING_SNAKE_CASE :       int     		=      (ord(text[i]     ) + text_hash * alphabet_size) % modulus
								if i == p_len - 1:
												continue
								_SCREAMING_SNAKE_CASE :       List[Any]     		=      (modulus_power * alphabet_size) % modulus

				for i in range(0							,      t_len - p_len + 1     ):
								if text_hash == p_hash and text[i : i + p_len] == pattern:
												return True
								if i == t_len - p_len:
												continue
								# Calculate the https://en.wikipedia.org/wiki/Rolling_hash
								_SCREAMING_SNAKE_CASE :       Optional[int]     		=      (
								    (text_hash - ord(text[i]     ) * modulus_power) * alphabet_size
								    + ord(text[i + p_len]     )
								) % modulus
				return False







def 			snake_case_   (  ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE :       str     		=      'abc1abc12'
				_SCREAMING_SNAKE_CASE :       Optional[Any]     		=      'alskfjaldsabc1abc1abc12k23adsfabcabc'
				_SCREAMING_SNAKE_CASE :       List[Any]     		=      'alskfjaldsk23adsfabcabc'
				assert rabin_karp(A__							,      A__     ) and not rabin_karp(A__							,      A__     )

				# Test 2)
				_SCREAMING_SNAKE_CASE :       int     		=      'ABABX'
				_SCREAMING_SNAKE_CASE :       int     		=      'ABABZABABYABABX'
				assert rabin_karp(A__							,      A__     )

				# Test 3)
				_SCREAMING_SNAKE_CASE :       List[Any]     		=      'AAAB'
				_SCREAMING_SNAKE_CASE :       Optional[Any]     		=      'ABAAAAAB'
				assert rabin_karp(A__							,      A__     )

				# Test 4)
				_SCREAMING_SNAKE_CASE :       List[str]     		=      'abcdabcy'
				_SCREAMING_SNAKE_CASE :       Optional[int]     		=      'abcxabcdabxabcdabcdabcy'
				assert rabin_karp(A__							,      A__     )

				# Test 5)
				_SCREAMING_SNAKE_CASE :       Optional[Any]     		=      'Lü'
				_SCREAMING_SNAKE_CASE :       Tuple     		=      'Lüsai'
				assert rabin_karp(A__							,      A__     )
				_SCREAMING_SNAKE_CASE :       Dict     		=      'Lue'
				assert not rabin_karp(A__							,      A__     )
				print("""Success."""     )


if __name__ == "__main__":
				test_rabin_karp()











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()


