






'''simple docstring'''







import math

from numpy import inf
from scipy.integrate import quad





def 		_UpperCAmelCase (				__A				: float   ):
				if num <= 0:
								raise ValueError('''math domain error'''   )

				return quad(__A    ,		0    ,		__A    ,		args=(__A)   )[0]





def 		_UpperCAmelCase (				__A				: float    ,		__A				: float   ):
				return math.pow(__A    ,		z - 1   ) * math.exp(-x   )


if __name__ == "__main__":
		from doctest import testmod

		testmod()












'''simple docstring'''







from __future__ import annotations





def 		_UpperCAmelCase (				__A				: str    ,		__A				: str   ):
				a_		:	int									=   get_failure_array(__A   )

				# 2) Step through text searching for pattern
				a_					,      a_		:	Any									=   0, 0  # index into text, pattern
				while i < len(__A   ):
								if pattern[j] == text[i]:
												if j == (len(__A   ) - 1):
																return True
												j += 1

								# if this is a prefix in our pattern
								# just go back far enough to continue
								elif j > 0:
												a_		:	Any									=   failure[j - 1]
												continue
								i += 1
				return False





def 		_UpperCAmelCase (				__A				: str   ):
				a_		:	Optional[Any]									=   [0]
				a_		:	Any									=   0
				a_		:	int									=   1
				while j < len(__A   ):
								if pattern[i] == pattern[j]:
												i += 1
								elif i > 0:
												a_		:	List[Any]									=   failure[i - 1]
												continue
								j += 1
								failure.append(__A   )
				return failure


if __name__ == "__main__":
		# Test 1)
		__lowerCAmelCase									=   'abc1abc12'
		__lowerCAmelCase									=   'alskfjaldsabc1abc1abc12k23adsfabcabc'
		__lowerCAmelCase									=   'alskfjaldsk23adsfabcabc'
		assert kmp(pattern, texta) and not kmp(pattern, texta)

		# Test 2)
		__lowerCAmelCase									=   'ABABX'
		__lowerCAmelCase									=   'ABABZABABYABABX'
		assert kmp(pattern, text)

		# Test 3)
		__lowerCAmelCase									=   'AAAB'
		__lowerCAmelCase									=   'ABAAAAAB'
		assert kmp(pattern, text)

		# Test 4)
		__lowerCAmelCase									=   'abcdabcy'
		__lowerCAmelCase									=   'abcxabcdabxabcdabcdabcy'
		assert kmp(pattern, text)

		# Test 5)
		__lowerCAmelCase									=   'aabaabaaa'
		assert get_failure_array(pattern) == [0, 1, 0, 1, 2, 3, 4, 5, 2]




