


from __future__ import annotations






def 							__lowercase   ( __lowerCAmelCase							:				str					,    __lowerCAmelCase							:				list[str] | None = None					,    __lowerCAmelCase							:				dict[str, float] | None = None					,    __lowerCAmelCase							:				bool = False					,    ):
							a__             =     cipher_alphabet or [chr(__lowerCAmelCase   ) for i in range(9_7					,    1_2_3   )]

							# 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': 0.08_497,
														    'b': 0.01_492,
														    'c': 0.02_202,
														    'd': 0.04_253,
														    'e': 0.11_162,
														    'f': 0.02_228,
														    'g': 0.02_015,
														    'h': 0.06_094,
														    'i': 0.07_546,
														    'j': 0.00_153,
														    'k': 0.01_292,
														    'l': 0.04_025,
														    'm': 0.02_406,
														    'n': 0.06_749,
														    'o': 0.07_507,
														    'p': 0.01_929,
														    'q': 0.00_095,
														    'r': 0.07_587,
														    's': 0.06_327,
														    't': 0.09_356,
														    'u': 0.02_758,
														    'v': 0.00_978,
														    'w': 0.02_560,
														    'x': 0.00_150,
														    'y': 0.01_994,
														    'z': 0.00_077,
														}
							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(__lowerCAmelCase   )   ):
														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(
																												    __lowerCAmelCase   )
																												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(__lowerCAmelCase   )

																																			# 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(__lowerCAmelCase   )

																																			# 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(__lowerCAmelCase							:				int   ) -> tuple[float, str]:
														return chi_squared_statistic_values[key]

							a__             =     min(
							    __lowerCAmelCase					,    key=__lowerCAmelCase					,    )

							# 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 							__lowercase   ( __lowerCAmelCase							:				str					,    __lowerCAmelCase							:				str   ):

							def get_matched_characters(__lowerCAmelCase							:				str					,    __lowerCAmelCase							:				str   ) -> str:
														a__             =     []
														a__             =     min(len(_stra   )					,    len(_stra   )   ) // 2
														for i, l in enumerate(_stra   ):
																					a__             =     int(max(0					,    i - limit   )   )
																					a__             =     int(min(i + limit + 1					,    len(_stra   )   )   )
																					if l in _stra[left:right]:
																												matched.append(__lowerCAmelCase   )
																												a__             =     F'{_stra[0:_stra.index(__lowerCAmelCase   )]} {_stra[_stra.index(__lowerCAmelCase   ) + 1:]}'

														return "".join(__lowerCAmelCase   )

							# matching characters
							a__             =     get_matched_characters(__lowerCAmelCase					,    __lowerCAmelCase   )
							a__             =     get_matched_characters(__lowerCAmelCase					,    __lowerCAmelCase   )
							a__             =     len(__lowerCAmelCase   )

							# transposition
							a__             =     (
							    len([(ca, ca) for ca, ca in zip(__lowerCAmelCase					,    __lowerCAmelCase   ) if ca != ca]   ) // 2
							)

							if not match_count:
														a__             =     0.0
							else:
														a__             =     (
														    1
														    / 3
														    * (
														        match_count / len(__lowerCAmelCase   )
														        + match_count / len(__lowerCAmelCase   )
														        + (match_count - transpositions) / match_count
														    )
														)

							# common prefix up to 4 characters
							a__             =     0
							for ca, ca in zip(stra[:4]					,    stra[:4]   ):
														if ca == ca:
																					prefix_len += 1
														else:
																					break

							return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						print(jaro_winkler('''hello''', '''world'''))




