






from __future__ import annotations
def    a__    (	A		,					A       ):
   lowercase__  ,       lowercase__  ,       lowercase__    :						Any       =			"""""", """""", """"""
   lowercase__    :						Optional[Any]       =			[]

   for character in message_part:
      tmp.append(character_to_number[character]       )

   for each in tmp:
      one += each[0]
      two += each[1]
      three += each[2]

   return one + two + three
def    a__    (	A		,					A       ):
   lowercase__  ,       lowercase__    :						Dict       =			"""""", """"""
   lowercase__    :						Tuple       =			[]

   for character in message_part:
      this_part += character_to_number[character]

   for digit in this_part:
      tmp += digit
      if len(A       ) == len(A       ):
         result.append(A       )
         lowercase__    :						Optional[int]       =			""""""

   return result[0], result[1], result[2]
def    a__    (	A		,					A       ):
   # Validate message and alphabet, set to upper and remove spaces
   lowercase__    :						Tuple       =			alphabet.replace(""" """		,					""""""       ).upper()
   lowercase__    :						Optional[int]       =			message.replace(""" """		,					""""""       ).upper()

   # Check length and characters
   if len(A       ) != 27:
      raise KeyError("""Length of alphabet has to be 27."""       )
   for each in message:
      if each not in alphabet:
         raise ValueError("""Each message character has to be included in alphabet!"""       )

    # Generate dictionares
   lowercase__    :						Optional[int]       =			(
       """111""",
       """112""",
       """113""",
       """121""",
       """122""",
       """123""",
       """131""",
       """132""",
       """133""",
       """211""",
       """212""",
       """213""",
       """221""",
       """222""",
       """223""",
       """231""",
       """232""",
       """233""",
       """311""",
       """312""",
       """313""",
       """321""",
       """322""",
       """323""",
       """331""",
       """332""",
       """333""",
   )
   lowercase__    :						Union[str, Any]       =			{}
   lowercase__    :						int       =			{}
   for letter, number in zip(A		,					A       ):
      lowercase__    :						Dict       =			number
      lowercase__    :						Any       =			letter

   return message, alphabet, character_to_number, number_to_character
def    a__    (	A		,					A = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."		,					A = 5       ):
   lowercase__  ,       lowercase__  ,       lowercase__  ,       lowercase__    :						str       =			__prepare(
       A		,					A       )
   lowercase__  ,       lowercase__    :						Tuple       =			"""""", """"""

   for i in range(0		,					len(A       ) + 1		,					A       ):
      encrypted_numeric += __encrypt_part(
          message[i : i + period]		,					A       )

   for i in range(0		,					len(A       )		,					3       ):
      encrypted += number_to_character[encrypted_numeric[i : i + 3]]

   return encrypted
def    a__    (	A		,					A = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."		,					A = 5       ):
   lowercase__  ,       lowercase__  ,       lowercase__  ,       lowercase__    :						int       =			__prepare(
       A		,					A       )
   lowercase__    :						int       =			[]
   lowercase__    :						List[str]       =			""""""

   for i in range(0		,					len(A       ) + 1		,					A       ):
      lowercase__  ,       lowercase__  ,       lowercase__    :						Dict       =			__decrypt_part(message[i : i + period]		,					A       )

      for j in range(0		,					len(A       )       ):
         decrypted_numeric.append(a[j] + b[j] + c[j]       )

   for each in decrypted_numeric:
      decrypted += number_to_character[each]

   return decrypted


if __name__ == "__main__":
 a 			=							'DEFEND THE EAST WALL OF THE CASTLE.'
 a 			=							encrypt_message(msg, 'EPSDUCVWYM.ZLKXNBTFGORIJHAQ')
 a 			=							decrypt_message(encrypted, 'EPSDUCVWYM.ZLKXNBTFGORIJHAQ')
 print(F'Encrypted: {encrypted}\nDecrypted: {decrypted}')










from typing import Any

import numpy as np
class 							__snake_case:



 def __init__(						self : str			,		UpperCAmelCase__ : np.ndarray			,		UpperCAmelCase__ : int						):

    """simple docstring"""






    if np.any(tableau[:, -1]			,		where=tableau[:, -1] < 0						):
       raise ValueError("""RHS must be > 0"""						)

    lowercase__    :						List[str]       =			tableau
    lowercase__  ,       lowercase__    :						Optional[Any]       =			tableau.shape

    # Number of decision variables x1, x2, x3...
    lowercase__    :						List[str]       =			n_vars

    # Number of artificial variables to be minimised
    lowercase__    :						str       =			len(np.where(tableau[self.n_vars : -1] == -1						)[0]						)

    # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
    lowercase__    :						Optional[Any]       =			(self.n_art_vars > 0) + 1

    # Number of slack variables added to make inequalities into equalities
    lowercase__    :						Optional[int]       =			self.n_rows - self.n_stages

    # Objectives for each stage
    lowercase__    :						Any       =			["""max"""]

    # In two stage simplex, first minimise then maximise
    if self.n_art_vars:
       self.objectives.append("""min"""						)

    lowercase__    :						Union[str, Any]       =			[""""""]

    # Index of current pivot row and column
    lowercase__    :						List[str]       =			None
    lowercase__    :						List[str]       =			None

    # Does objective row only contain (non)-negative values?
    lowercase__    :						str       =			False



 @staticmethod
 def     UpperCAmelCase     (						*UpperCAmelCase__ : int						):

    """simple docstring"""






    if len(UpperCAmelCase__						) != 3:
       raise ValueError("""Must provide n_vars, n_slack, and n_art_vars"""						)

    if not all(x >= 0 and isinstance(UpperCAmelCase__			,		UpperCAmelCase__						) for x in args						):
       raise ValueError("""All arguments must be non-negative integers"""						)

    # decision | slack | artificial
    lowercase__    :						Optional[int]       =			["""x""", """s""", """a"""]
    lowercase__    :						int       =			[]
    for i in range(3						):
       for j in range(args[i]						):
          titles.append(string_starts[i] + str(j + 1						)						)
    titles.append("""RHS"""						)
    return titles



 def     UpperCAmelCase     (						self : List[str]			,		UpperCAmelCase__ : np.ndarray						):

    """simple docstring"""






    lowercase__    :						Optional[Any]       =			self.objectives[-1]

    # Find entries of highest magnitude in objective rows
    lowercase__    :						Union[str, Any]       =			(objective == """min""") - (objective == """max""")
    lowercase__    :						Optional[int]       =			np.argmax(sign * tableau[0, : self.n_vars]						)

    # Choice is only valid if below 0 for maximise, and above for minimise
    if sign * self.tableau[0, col_idx] <= 0:
       lowercase__    :						Optional[int]       =			True
       return 0, 0

    # Pivot row is chosen as having the lowest quotient when elements of
    # the pivot column divide the right-hand side

    # Slice excluding the objective rows
    lowercase__    :						Any       =			slice(self.n_stages			,		self.n_rows						)

    # RHS
    lowercase__    :						Union[str, Any]       =			tableau[s, -1]

    # Elements of pivot column within slice
    lowercase__    :						Optional[int]       =			tableau[s, col_idx]

    # Array filled with nans
    lowercase__    :						Optional[int]       =			np.full(self.n_rows - self.n_stages			,		np.nan						)

    # If element in pivot column is greater than zeron_stages, return
    # quotient or nan otherwise
    lowercase__    :						Optional[int]       =			np.divide(UpperCAmelCase__			,		UpperCAmelCase__			,		out=UpperCAmelCase__			,		where=divisor > 0						)

    # Arg of minimum quotient excluding the nan values. n_stages is added
    # to compensate for earlier exclusion of objective columns
    lowercase__    :						Dict       =			np.nanargmin(UpperCAmelCase__						) + self.n_stages
    return row_idx, col_idx



 def     UpperCAmelCase     (						self : Union[str, Any]			,		UpperCAmelCase__ : np.ndarray			,		UpperCAmelCase__ : int			,		UpperCAmelCase__ : int						):

    """simple docstring"""






    lowercase__    :						int       =			tableau[row_idx].copy()

    lowercase__    :						Optional[Any]       =			piv_row[col_idx]

    # Entry becomes 1
    piv_row *= 1 / piv_val

    # Variable in pivot column becomes basic, ie the only non-zero entry
    for idx, coeff in enumerate(tableau[:, col_idx]						):
       tableau[idx] += -coeff * piv_row
    lowercase__    :						Any       =			piv_row
    return tableau



 def     UpperCAmelCase     (						self : Optional[Any]			,		UpperCAmelCase__ : np.ndarray						):

    """simple docstring"""






    self.objectives.pop()

    if not self.objectives:
       return tableau

    # Slice containing ids for artificial columns
    lowercase__    :						Optional[int]       =			slice(-self.n_art_vars - 1			,		-1						)

    # Delete the artificial variable columns
    lowercase__    :						Dict       =			np.delete(UpperCAmelCase__			,		UpperCAmelCase__			,		axis=1						)

    # Delete the objective row of the first stage
    lowercase__    :						Optional[Any]       =			np.delete(UpperCAmelCase__			,		0			,		axis=0						)

    lowercase__    :						str       =			1
    self.n_rows -= 1
    lowercase__    :						List[str]       =			0
    lowercase__    :						List[Any]       =			False
    return tableau



 def     UpperCAmelCase     (						self : Optional[Any]						):

    """simple docstring"""






    for _ in range(100						):
       # Completion of each stage removes an objective. If both stages
       # are complete, then no objectives are left
       if not self.objectives:
          lowercase__    :						List[Any]       =			self.generate_col_titles(
              self.n_vars			,		self.n_slack			,		self.n_art_vars						)

          # Find the values of each variable at optimal solution
          return self.interpret_tableau(self.tableau			,		self.col_titles						)

       lowercase__  ,       lowercase__    :						Optional[Any]       =			self.find_pivot(self.tableau						)

       # If there are no more negative values in objective row
       if self.stop_iter:
          # Delete artificial variable columns and rows. Update attributes
          lowercase__    :						Any       =			self.change_stage(self.tableau						)
       else:
          lowercase__    :						str       =			self.pivot(self.tableau			,		UpperCAmelCase__			,		UpperCAmelCase__						)
    return {}







 def     UpperCAmelCase     (						self : str			,		UpperCAmelCase__ : np.ndarray			,		UpperCAmelCase__ : list[str]						):

    """simple docstring"""






    lowercase__    :						List[str]       =			{"""P""": abs(tableau[0, -1]						)}

    for i in range(self.n_vars						):
       # Gives ids of nonzero entries in the ith column
       lowercase__    :						int       =			np.nonzero(tableau[:, i]						)
       lowercase__    :						Tuple       =			len(nonzero[0]						)

       # First entry in the nonzero ids
       lowercase__    :						int       =			nonzero[0][0]
       lowercase__    :						Tuple       =			tableau[nonzero_rowidx, i]

       # If there is only one nonzero value in column, which is one
       if n_nonzero == nonzero_val == 1:
          lowercase__    :						Tuple       =			tableau[nonzero_rowidx, -1]
          lowercase__    :						Union[str, Any]       =			rhs_val

        # Check for basic variables
    for title in col_titles:
       # Don't add RHS or slack variables to output dict
       if title[0] not in "R-s-a":
          output_dict.setdefault(UpperCAmelCase__			,		0						)
    return output_dict


if __name__ == "__main__":
 import doctest

 doctest.testmod()


