
from __future__ import annotations


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__ ,		UpperCamelCase__ = None ,		UpperCamelCase__ = None ,		UpperCamelCase__ = False ,		):
      UpperCamelCase__    :   Optional[int]					=				cipher_alphabet or [chr(UpperCamelCase__		) 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)
            UpperCamelCase__    :   Optional[Any]					=				{
                '''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
            UpperCamelCase__    :   Union[str, Any]					=				frequencies_dict

      if not case_sensitive:
            UpperCamelCase__    :   Any					=				ciphertext.lower()

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

      # cycle through all of the shifts
      for shift in range(len(UpperCamelCase__		)		):
            UpperCamelCase__    :   Optional[int]					=				''''''

            # decrypt the message with the shift
            for letter in ciphertext:
                  try:
                        # Try to index the letter in the alphabet
                        UpperCamelCase__    :   Any					=				(alphabet_letters.index(letter.lower()		) - shift) % len(
                            UpperCamelCase__		)
                        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

            UpperCamelCase__    :   Any					=				0.0

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

                              # Get the excepcted amount of times the letter should appear based
                              # on letter frequencies
                              UpperCamelCase__    :   Union[str, Any]					=				frequencies[letter] * occurrences

                              # Complete the chi squared statistic formula
                              UpperCamelCase__    :   Dict					=				((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
                              UpperCamelCase__    :   Dict					=				decrypted_with_shift.count(UpperCamelCase__		)

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

                              # Complete the chi squared statistic formula
                              UpperCamelCase__    :   Optional[Any]					=				((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
            UpperCamelCase__    :   List[Any]					=				(
                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(UpperCamelCase__		) -> tuple[float, str]:
            return chi_squared_statistic_values[key]

      UpperCamelCase__    :   int					=				min(
          UpperCamelCase__ ,		key=UpperCamelCase__ ,		)

      # Get all the data from the most likely cipher (key, decoded message)
      (
          (
          UpperCamelCase__
      )				,(
          UpperCamelCase__
      )				,
      )    :   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,
      )




import doctest
from collections import deque

import numpy as np




class 				_lowerCamelCase :





     """simple docstring"""







     def __init__(							self  )  ->   None:




           """simple docstring"""







           UpperCamelCase__    :   Tuple					=				[2, 1, 2, -1]
           UpperCamelCase__    :   Union[str, Any]					=				[1, 2, 3, 4]






     def    __SCREAMING_SNAKE_CASE			(							self  )  ->   list[float]:




           """simple docstring"""







           UpperCamelCase__    :   List[str]					=				len(self.first_signal  )
           UpperCamelCase__    :   Any					=				len(self.second_signal  )

           UpperCamelCase__    :   Dict					=				max(__SCREAMING_SNAKE_CASE						,						__SCREAMING_SNAKE_CASE  )

           # create a zero matrix of max_length x max_length
           UpperCamelCase__    :   List[Any]					=				[[0] * max_length for i in range(__SCREAMING_SNAKE_CASE  )]

           # fills the smaller signal with zeros to make both signals of same length
           if length_first_signal < length_second_signal:
                 self.first_signal += [0] * (max_length - length_first_signal)
           elif length_first_signal > length_second_signal:
                 self.second_signal += [0] * (max_length - length_second_signal)
           for i in range(__SCREAMING_SNAKE_CASE  ):
                 UpperCamelCase__    :   Optional[int]					=				deque(self.second_signal  )
                 rotated_signal.rotate(__SCREAMING_SNAKE_CASE  )
                 for j, item in enumerate(__SCREAMING_SNAKE_CASE  ):
                       matrix[i][j] += item

        # multiply the matrix with the first signal
           UpperCamelCase__    :   Optional[Any]					=				np.matmul(np.transpose(__SCREAMING_SNAKE_CASE  )						,						np.transpose(self.first_signal  )  )

           # rounding-off to two decimal places
           return [round(__SCREAMING_SNAKE_CASE						,						2  ) for i in final_signal]


if __name__ == "__main__":
    doctest.testmod()


