



from __future__ import annotations

def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			str				,     _SCREAMING_SNAKE_CASE       :			list[str] | None = None				,     _SCREAMING_SNAKE_CASE       :			dict[str, float] | None = None				,     _SCREAMING_SNAKE_CASE       :			bool = False				,     ):
				"""simple docstring"""







				__a       =		cipher_alphabet or [chr(_SCREAMING_SNAKE_CASE    ) for i in range(97				,     123    )]

				# If the argument is None or the user provided an empty dictionary
				if not frequencies_dict:
								# Frequencies of letters in the english language (how much they show up)
								__a       =		{
								    """a""": 0.0_8497,
								    """b""": 0.0_1492,
								    """c""": 0.0_2202,
								    """d""": 0.0_4253,
								    """e""": 0.1_1162,
								    """f""": 0.0_2228,
								    """g""": 0.0_2015,
								    """h""": 0.0_6094,
								    """i""": 0.0_7546,
								    """j""": 0.0_0153,
								    """k""": 0.0_1292,
								    """l""": 0.0_4025,
								    """m""": 0.0_2406,
								    """n""": 0.0_6749,
								    """o""": 0.0_7507,
								    """p""": 0.0_1929,
								    """q""": 0.0_0095,
								    """r""": 0.0_7587,
								    """s""": 0.0_6327,
								    """t""": 0.0_9356,
								    """u""": 0.0_2758,
								    """v""": 0.0_0978,
								    """w""": 0.0_2560,
								    """x""": 0.0_0150,
								    """y""": 0.0_1994,
								    """z""": 0.0_0077,
								}
				else:
								# Custom frequencies dictionary
								__a       =		frequencies_dict

				if not case_sensitive:
								__a       =		ciphertext.lower()

				# Chi squared statistic values
				__a       =		{}

				# cycle through all of the shifts
				for shift in range(len(_SCREAMING_SNAKE_CASE    )    ):
								__a       =		""""""

								# decrypt the message with the shift
								for letter in ciphertext:
												try:
																# Try to index the letter in the alphabet
																__a       =		(alphabet_letters.index(letter.lower()    ) - shift) % len(
																    _SCREAMING_SNAKE_CASE    )
																decrypted_with_shift += (
																    alphabet_letters[new_key].upper()
																    if case_sensitive and letter.isupper()
																    else alphabet_letters[new_key]
																)
												except ValueError:
																# Append the character if it isn't in the alphabet
																decrypted_with_shift += letter

								__a       =		0.0

								# Loop through each letter in the decoded message with the shift
								for letter in decrypted_with_shift:
												if case_sensitive:
																__a       =		letter.lower()
																if letter in frequencies:
																				# Get the amount of times the letter occurs in the message
																				__a       =		decrypted_with_shift.lower().count(_SCREAMING_SNAKE_CASE    )

																				# Get the excepcted amount of times the letter should appear based
																				# on letter frequencies
																				__a       =		frequencies[letter] * occurrences

																				# Complete the chi squared statistic formula
																				__a       =		((occurrences - expected) ** 2) / expected

																				# Add the margin of error to the total chi squared statistic
																				chi_squared_statistic += chi_letter_value
												else:
																if letter.lower() in frequencies:
																				# Get the amount of times the letter occurs in the message
																				__a       =		decrypted_with_shift.count(_SCREAMING_SNAKE_CASE    )

																				# Get the excepcted amount of times the letter should appear based
																				# on letter frequencies
																				__a       =		frequencies[letter] * occurrences

																				# Complete the chi squared statistic formula
																				__a       =		((occurrences - expected) ** 2) / expected

																				# Add the margin of error to the total chi squared statistic
																				chi_squared_statistic += chi_letter_value

        # Add the data to the chi_squared_statistic_values dictionary
								__a       =		(
								    chi_squared_statistic,
								    decrypted_with_shift,
								)

				# Get the most likely cipher by finding the cipher with the smallest chi squared
				# statistic
				def chi_squared_statistic_values_sorting_key(_SCREAMING_SNAKE_CASE       :			int    ) -> tuple[float, str]:
								return chi_squared_statistic_values[key]

				__a       =		min(
				    _SCREAMING_SNAKE_CASE				,     key=_SCREAMING_SNAKE_CASE				,     )

				# Get all the data from the most likely cipher (key, decoded message)
				(
				    (
				    __a
				)     ,					(
				    __a
				)     ,					
				)       =		chi_squared_statistic_values[most_likely_cipher]

				# Return the data on the most likely shift
				return (
				    most_likely_cipher,
				    most_likely_cipher_chi_squared_value,
				    decoded_most_likely_cipher,
				)





def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			Tuple				,     _SCREAMING_SNAKE_CASE       :			Tuple				,     _SCREAMING_SNAKE_CASE       :			Tuple=False    ):
				"""simple docstring"""







				if isinstance(_SCREAMING_SNAKE_CASE				,     _SCREAMING_SNAKE_CASE    ) and isinstance(_SCREAMING_SNAKE_CASE				,     _SCREAMING_SNAKE_CASE    ):
								__a       =		len(set_a.intersection(_SCREAMING_SNAKE_CASE    )    )

								if alternative_union:
												__a       =		len(_SCREAMING_SNAKE_CASE    ) + len(_SCREAMING_SNAKE_CASE    )
								else:
												__a       =		len(set_a.union(_SCREAMING_SNAKE_CASE    )    )

								return intersection / union

				if isinstance(_SCREAMING_SNAKE_CASE				,     (list, tuple)    ) and isinstance(_SCREAMING_SNAKE_CASE				,     (list, tuple)    ):
								__a       =		[element for element in set_a if element in set_b]

								if alternative_union:
												__a       =		len(_SCREAMING_SNAKE_CASE    ) + len(_SCREAMING_SNAKE_CASE    )
												return len(_SCREAMING_SNAKE_CASE    ) / union
								else:
												__a       =		set_a + [element for element in set_b if element not in set_a]
												return len(_SCREAMING_SNAKE_CASE    ) / len(_SCREAMING_SNAKE_CASE    )

								return len(_SCREAMING_SNAKE_CASE    ) / len(_SCREAMING_SNAKE_CASE    )
				return None


if __name__ == "__main__":
						lowerCamelCase__			= {"""a""", """b""", """c""", """d""", """e"""}
						lowerCamelCase__			= {"""c""", """d""", """e""", """f""", """h""", """i"""}
						print(jaccard_similarity(set_a, set_b))
