from typing import Any

import numpy as np
class 				a_ :






 '''simple docstring'''






 def __init__(			self					:  List[str]			,    lowercase__					:  np.ndarray			,    lowercase__					:  int):







        '''simple docstring'''



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

        lowerCAmelCase__     	=					tableau
        lowerCAmelCase__     	=					tableau.shape

        # Number of decision variables x1, x2, x3...
        lowerCAmelCase__     	=					n_vars

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

        # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
        lowerCAmelCase__     	=					(self.n_art_vars > 0) + 1

        # Number of slack variables added to make inequalities into equalities
        lowerCAmelCase__     	=					self.n_rows - self.n_stages

        # Objectives for each stage
        lowerCAmelCase__     	=					['max']

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

        lowerCAmelCase__     	=					['']

        # Index of current pivot row and column
        lowerCAmelCase__     	=					None
        lowerCAmelCase__     	=					None

        # Does objective row only contain (non)-negative values?
        lowerCAmelCase__     	=					False




 @staticmethod
 def 		__snake_case						(			*lowercase__					:  int):







        '''simple docstring'''



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

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

        # decision | slack | artificial
        lowerCAmelCase__     	=					['x', 's', 'a']
        lowerCAmelCase__     	=					[]
        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 		__snake_case						(			self					:  Optional[int]			,    lowercase__					:  np.ndarray):







        '''simple docstring'''



        lowerCAmelCase__     	=					self.objectives[-1]

        # Find entries of highest magnitude in objective rows
        lowerCAmelCase__     	=					(objective == 'min') - (objective == 'max')
        lowerCAmelCase__     	=					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:
               lowerCAmelCase__     	=					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
        lowerCAmelCase__     	=					slice(self.n_stages			,    self.n_rows)

        # RHS
        lowerCAmelCase__     	=					tableau[s, -1]

        # Elements of pivot column within slice
        lowerCAmelCase__     	=					tableau[s, col_idx]

        # Array filled with nans
        lowerCAmelCase__     	=					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
        lowerCAmelCase__     	=					np.divide(lowercase__			,    lowercase__			,    out=lowercase__			,    where=divisor > 0)

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




 def 		__snake_case						(			self					:  Union[str, Any]			,    lowercase__					:  np.ndarray			,    lowercase__					:  int			,    lowercase__					:  int):







        '''simple docstring'''



        lowerCAmelCase__     	=					tableau[row_idx].copy()

        lowerCAmelCase__     	=					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
        lowerCAmelCase__     	=					piv_row
        return tableau




 def 		__snake_case						(			self					:  Union[str, Any]			,    lowercase__					:  np.ndarray):







        '''simple docstring'''



        self.objectives.pop()

        if not self.objectives:
               return tableau

        # Slice containing ids for artificial columns
        lowerCAmelCase__     	=					slice(-self.n_art_vars - 1			,    -1)

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

        # Delete the objective row of the first stage
        lowerCAmelCase__     	=					np.delete(lowercase__			,    0			,    axis=0)

        lowerCAmelCase__     	=					1
        self.n_rows -= 1
        lowerCAmelCase__     	=					0
        lowerCAmelCase__     	=					False
        return tableau




 def 		__snake_case						(			self					:  Optional[int]):







        '''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:
                      lowerCAmelCase__     	=					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)

               lowerCAmelCase__     	=					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
                      lowerCAmelCase__     	=					self.change_stage(self.tableau)
               else:
                      lowerCAmelCase__     	=					self.pivot(self.tableau			,    lowercase__			,    lowercase__)
        return {}




 def 		__snake_case						(			self					:  Dict			,    lowercase__					:  np.ndarray			,    lowercase__					:  list[str]):







        '''simple docstring'''



        lowerCAmelCase__     	=					{'P': abs(tableau[0, -1])}

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

               # First entry in the nonzero ids
               lowerCAmelCase__     	=					nonzero[0][0]
               lowerCAmelCase__     	=					tableau[nonzero_rowidx, i]

               # If there is only one nonzero value in column, which is one
               if n_nonzero == nonzero_val == 1:
                      lowerCAmelCase__     	=					tableau[nonzero_rowidx, -1]
                      lowerCAmelCase__     	=					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(lowercase__			,    0)
        return output_dict


if __name__ == "__main__":
    import doctest

    doctest.testmod()







def 			lowerCamelCase_		(					lowerCAmelCase:		list			,							lowerCAmelCase:		list )->						list:
  _snake_case      : int														=		len(lowerCAmelCase )
  _snake_case      : int														=		len(lowerCAmelCase )
  _snake_case      : int														=		(
      first_input_list_length
      if first_input_list_length > second_input_list_length
      else second_input_list_length
  )
  _snake_case      : list														=		[]
  for char_count in range(lowerCAmelCase ):
    if char_count < first_input_list_length:
      output_result_list.append(first_input_list[char_count] )
    if char_count < second_input_list_length:
      output_result_list.append(second_input_list[char_count] )

  return output_result_list


if __name__ == "__main__":
      print(alternative_list_arrange(["""A""", """B""", """C"""], [1, 2, 3, 4, 5]), end=""" """)




