




'''simple docstring'''






from __future__ import annotations






def 		UpperCamelCase__      (		__SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE = None				,      __SCREAMING_SNAKE_CASE = None				,      __SCREAMING_SNAKE_CASE = False				,      )    ->   tuple[int, float, str]:
      snake_case__       :   Tuple	      =    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)
            snake_case__       :   str	      =    {
                'a': 0.08497,
                'b': 0.01492,
                'c': 0.02202,
                'd': 0.04253,
                'e': 0.11162,
                'f': 0.02228,
                'g': 0.02015,
                'h': 0.06094,
                'i': 0.07546,
                'j': 0.00153,
                'k': 0.01292,
                'l': 0.04025,
                'm': 0.02406,
                'n': 0.06749,
                'o': 0.07507,
                'p': 0.01929,
                'q': 0.00095,
                'r': 0.07587,
                's': 0.06327,
                't': 0.09356,
                'u': 0.02758,
                'v': 0.00978,
                'w': 0.02560,
                'x': 0.00150,
                'y': 0.01994,
                'z': 0.00077,
            }
      else:
            # Custom frequencies dictionary
            snake_case__       :   str	      =    frequencies_dict

      if not case_sensitive:
            snake_case__       :   Optional[int]	      =    ciphertext.lower()

      # Chi squared statistic values
      snake_case__       :   dict[int, tuple[float, str]]	      =    {}

      # cycle through all of the shifts
      for shift in range(len(__SCREAMING_SNAKE_CASE		)		):
            snake_case__       :   Union[str, Any]	      =    ''

            # decrypt the message with the shift
            for letter in ciphertext:
                  try:
                        # Try to index the letter in the alphabet
                        snake_case__       :   Tuple	      =    (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

            snake_case__       :   List[Any]	      =    0.0

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

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

                              # Complete the chi squared statistic formula
                              snake_case__       :   List[Any]	      =    ((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
                              snake_case__       :   List[str]	      =    decrypted_with_shift.count(__SCREAMING_SNAKE_CASE		)

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

                              # Complete the chi squared statistic formula
                              snake_case__       :   int	      =    ((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
            snake_case__       :   int	      =    (
                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		) -> tuple[float, str]:
            return chi_squared_statistic_values[key]

      snake_case__       :   int	      =    min(
          __SCREAMING_SNAKE_CASE				,      key=__SCREAMING_SNAKE_CASE				,      )

      # Get all the data from the most likely cipher (key, decoded message)
      (
          (
          snake_case__
      )      ,							(
          snake_case__
      )      ,							
      )       :   Union[str, Any]	      =    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,
      )






'''simple docstring'''






import functools






def 		UpperCamelCase__      (		__SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE		)    ->   int:
      snake_case__       :   Any	      =    len(__SCREAMING_SNAKE_CASE		)
      snake_case__       :   List[str]	      =    len(__SCREAMING_SNAKE_CASE		)

      @functools.cache
      def min_distance(__SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE		) -> int:
            # if first word index is overflow - delete all from the second word
            if indexa >= len_worda:
                  return len_worda - indexa
            # if second word index is overflow - delete all from the first word
            if indexa >= len_worda:
                  return len_worda - indexa
            snake_case__       :   Union[str, Any]	      =    int(worda[indexa] != worda[indexa]		)  # current letters not identical
            return min(
                1 + min_distance(indexa + 1				,      __SCREAMING_SNAKE_CASE		)				,      1 + min_distance(__SCREAMING_SNAKE_CASE				,      indexa + 1		)				,      diff + min_distance(indexa + 1				,      indexa + 1		)				,      )

      return min_distance(0				,      0		)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
