'''simple docstring'''




from __future__ import annotations






def __lowerCAmelCase (							UpperCamelCase__				,  UpperCamelCase__ = None				,  UpperCamelCase__ = None				,  UpperCamelCase__ = False				,  )	->    tuple[int, float, str]:
    __lowerCamelCase		=  cipher_alphabet or [chr(UpperCamelCase__				) for i in range(97				,  1_23				)]

    # 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)
        __lowerCamelCase		=  {
            '''a''': 0.0_8_4_9_7,
            '''b''': 0.0_1_4_9_2,
            '''c''': 0.0_2_2_0_2,
            '''d''': 0.0_4_2_5_3,
            '''e''': 0.1_1_1_6_2,
            '''f''': 0.0_2_2_2_8,
            '''g''': 0.0_2_0_1_5,
            '''h''': 0.0_6_0_9_4,
            '''i''': 0.0_7_5_4_6,
            '''j''': 0.0_0_1_5_3,
            '''k''': 0.0_1_2_9_2,
            '''l''': 0.0_4_0_2_5,
            '''m''': 0.0_2_4_0_6,
            '''n''': 0.0_6_7_4_9,
            '''o''': 0.0_7_5_0_7,
            '''p''': 0.0_1_9_2_9,
            '''q''': 0.0_0_0_9_5,
            '''r''': 0.0_7_5_8_7,
            '''s''': 0.0_6_3_2_7,
            '''t''': 0.0_9_3_5_6,
            '''u''': 0.0_2_7_5_8,
            '''v''': 0.0_0_9_7_8,
            '''w''': 0.0_2_5_6_0,
            '''x''': 0.0_0_1_5_0,
            '''y''': 0.0_1_9_9_4,
            '''z''': 0.0_0_0_7_7,
        }
    else:
        # Custom frequencies dictionary
        __lowerCamelCase		=  frequencies_dict

    if not case_sensitive:
        __lowerCamelCase		=  ciphertext.lower()

    # Chi squared statistic values
    __lowerCamelCase		=  {}

    # cycle through all of the shifts
    for shift in range(len(UpperCamelCase__				)				):
        __lowerCamelCase		=  ''''''

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

        __lowerCamelCase		=  0.0

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

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

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

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

                    # Complete the chi squared statistic formula
                    __lowerCamelCase		=  ((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
        __lowerCamelCase		=  (
            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]

    __lowerCamelCase		=  min(
        UpperCamelCase__				,  key=UpperCamelCase__				,  )

    # Get all the data from the most likely cipher (key, decoded message)
    (
        (
        __lowerCamelCase
    )	,  (
        __lowerCamelCase
    )	,  
    )		=  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"""





from __future__ import annotations

from typing import Any




class 					_lowerCAmelCase  :







 """simple docstring"""







 def __init__(			self							:			Any,					UpperCAmelCase__							:			int	):
    __lowercase								=						num_of_nodes
    __lowercase								=						[]
    __lowercase								=						{}


 def 					_lowercase (			self							:			Optional[Any],					UpperCAmelCase__							:			int,					UpperCAmelCase__							:			int,					UpperCAmelCase__							:			int	):
    self.m_edges.append([u_node, v_node, weight]	)


 def 					_lowercase (			self							:			Union[str, Any],					UpperCAmelCase__							:			int	):

    if self.m_component[u_node] == u_node:
       return u_node
    return self.find_component(self.m_component[u_node]	)


 def 					_lowercase (			self							:			List[Any],					UpperCAmelCase__							:			int	):

    if self.m_component[u_node] != u_node:
       for k in self.m_component:
          __lowercase								=						self.find_component(UpperCAmelCase__	)


 def 					_lowercase (			self							:			Union[str, Any],					UpperCAmelCase__							:			list[int],					UpperCAmelCase__							:			int,					UpperCAmelCase__							:			int	):

    if component_size[u_node] <= component_size[v_node]:
       __lowercase								=						v_node
       component_size[v_node] += component_size[u_node]
       self.set_component(UpperCAmelCase__	)

    elif component_size[u_node] >= component_size[v_node]:
       __lowercase								=						self.find_component(UpperCAmelCase__	)
       component_size[u_node] += component_size[v_node]
       self.set_component(UpperCAmelCase__	)



 def 					_lowercase (			self							:			Any	):
    __lowercase								=						[]
    __lowercase								=						0

    __lowercase								=						[-1] * self.m_num_of_nodes

    # A list of components (initialized to all of the nodes)
    for node in range(self.m_num_of_nodes	):
       self.m_component.update({node: node}	)
       component_size.append(1	)

    __lowercase								=						self.m_num_of_nodes

    while num_of_components > 1:
       for edge in self.m_edges:
          __lowercase		,__lowercase		,__lowercase								=						edge

          __lowercase								=						self.m_component[u]
          __lowercase								=						self.m_component[v]

          if u_component != v_component:

             for component in (u_component, v_component):
                if (
                    minimum_weight_edge[component] == -1
                    or minimum_weight_edge[component][2] > w
                ):
                   __lowercase								=						[u, v, w]

       for edge in minimum_weight_edge:
          if isinstance(UpperCAmelCase__,					UpperCAmelCase__	):
             __lowercase		,__lowercase		,__lowercase								=						edge

             __lowercase								=						self.m_component[u]
             __lowercase								=						self.m_component[v]

             if u_component != v_component:
                mst_weight += w
                self.union(UpperCAmelCase__,					UpperCAmelCase__,					UpperCAmelCase__	)
                print(F"""Added edge [{u} - {v}]\nAdded weight: {w}\n"""	)
                num_of_components -= 1

       __lowercase								=						[-1] * self.m_num_of_nodes
    print(F"""The total weight of the minimal spanning tree is: {mst_weight}"""	)







def   _A  (  )	->						None:
   '''simple docstring'''




if __name__ == "__main__":
   import doctest

   doctest.testmod()




