code: 
  
  
  from typing import Any
  
  import numpy as np
  
  
  
  
  
  class __snake_case		:
  
  
  
  
  
  
  
     """simple docstring"""
  
  
  
  
     def __init__(		self							:List[str]				,  UpperCamelCase__							:Union[str, Any]				,  UpperCamelCase__							:Any       ):
            # Check if RHS is negative
            if np.any(tableau[:, -1]				,  where=tableau[:, -1] < 0       ):
                   raise ValueError("RHS must be > 0"       )
  
            _a          =				tableau
            _a   , _a          =				tableau.shape
  
            # Number of decision variables x1, x2, x3...
            _a          =				n_vars
  
            # Number of artificial variables to be minimised
            _a          =				len(np.where(tableau[self.n_vars : -1] == -1       )[0]       )
  
            # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
            _a          =				(self.n_art_vars > 0) + 1
  
            # Number of slack variables added to make inequalities into equalities
            _a          =				self.n_rows - self.n_stages
  
            # Objectives for each stage
            _a          =				["max"]
  
            # In two stage simplex, first minimise then maximise
            if self.n_art_vars:
                   self.objectives.append("min"       )
  
            _a          =				[""]
  
            # Index of current pivot row and column
            _a          =				None
            _a          =				None
  
            # Does objective row only contain (non)-negative values?
            _a          =				False
  
  
  
  
     @staticmethod
     def SCREAMING_SNAKE_CASE_      (		*UpperCamelCase__							:str       ):
            if len(__snake_case       ) != 3:
                   raise ValueError("Must provide n_vars, n_slack, and n_art_vars"       )
  
            if not all(x >= 0 and isinstance(__snake_case				,  __snake_case       ) for x in args       ):
                   raise ValueError("All arguments must be non-negative integers"       )
  
            # decision | slack | artificial
            _a          =				["x", "s", "a"]
            _a          =				[]
            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 SCREAMING_SNAKE_CASE_      (		self							:Optional[Any]				,  UpperCamelCase__							:int       ):
            _a          =				self.objectives[-1]
  
            # Find entries of highest magnitude in objective rows
            _a          =				(objective == "min") - (objective == "max")
            _a          =				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:
                   _a          =				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
            _a          =				slice(self.n_stages				,  self.n_rows       )
  
            # RHS
            _a          =				tableau[s, -1]
  
            # Elements of pivot column within slice
            _a          =				tableau[s, col_idx]
  
            # Array filled with nans
            _a          =				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
            _a          =				np.divide(__snake_case				,  __snake_case				,  out=__snake_case				,  where=divisor > 0       )
  
            # Arg of minimum quotient excluding the nan values. n_stages is added
            # to compensate for earlier exclusion of objective columns
            _a          =				np.nanargmin(__snake_case       ) + self.n_stages
            return row_idx, col_idx
  
  
  
  
     def SCREAMING_SNAKE_CASE_      (		self							:Optional[int]				,  UpperCamelCase__							:List[Any]				,  UpperCamelCase__							:List[str]				,  UpperCamelCase__							:Tuple       ):
            _a          =				tableau[row_idx].copy()
  
            _a          =				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
            _a          =				piv_row
            return tableau
  
  
  
  
     def SCREAMING_SNAKE_CASE_      (		self							:Any				,  UpperCamelCase__							:List[str]       ):
            self.objectives.pop()
  
            if not self.objectives:
                   return tableau
  
            # Slice containing ids for artificial columns
            _a          =				slice(-self.n_art_vars - 1				,  -1       )
  
            # Delete the artificial variable columns
            _a          =				np.delete(__snake_case				,  __snake_case				,  axis=1       )
  
            # Delete the objective row of the first stage
            _a          =				np.delete(__snake_case				,  0				,  axis=0       )
  
            _a          =				1
            self.n_rows -= 1
            _a          =				0
            _a          =				False
            return tableau
  
  
  
  
     def SCREAMING_SNAKE_CASE_      (		self							:Tuple       ):
            # Stop simplex algorithm from cycling.
            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:
                          _a          =				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       )
  
                   _a   , _a          =				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
                          _a          =				self.change_stage(self.tableau       )
                   else:
                          _a          =				self.pivot(self.tableau				,  __snake_case				,  __snake_case       )
            return {}
  
  
  
  
     def SCREAMING_SNAKE_CASE_      (		self							:Any				,  UpperCamelCase__							:int				,  UpperCamelCase__							:Tuple       ):
            _a          =				{"P": abs(tableau[0, -1]       )}
  
            for i in range(self.n_vars       ):
                   # Gives ids of nonzero entries in the ith column
                   _a          =				np.nonzero(tableau[:, i]       )
                   _a          =				len(nonzero[0]       )
  
                   # First entry in the nonzero ids
                   _a          =				nonzero[0][0]
                   _a          =				tableau[nonzero_rowidx, i]
  
                   # If there is only one nonzero value in column, which is one
                   if n_nonzero == nonzero_val == 1:
                          _a          =				tableau[nonzero_rowidx, -1]
                          _a          =				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(__snake_case				,  0       )
            return output_dict
  
  
  if __name__ == "__main__":
     import doctest
  
     doctest.testmod()
  
style_context: 
  
  
  """simple docstring"""
  
  
  
  
  from __future__ import annotations
  
  from collections.abc import Iterator
  from typing import Any
  
  
  
  
  
  class __snake_case		:
  
  
  
  
  
  
  
     """simple docstring"""
  
  
  
  
     def __init__(		self							:List[Any]				,  UpperCamelCase__							:Any       ):
            _a          =				data
            _a          =				None
  
  
  
  
     def __str__(		self							:Any       ):
            return f'{self.data}'
  
  
  
  
  
  
  class __snake_case		:
  
  
  
  
  
  
  
     """simple docstring"""
  
  
  
  
     def __init__(		self							:Any       ):
            _a          =				None
            _a          =				None
  
  
  
  
     def __iter__(		self							:List[str]       ):
            _a          =				self.front
            while node:
                   yield node.data
                   _a          =				node.next
  
  
  
  
     def __len__(		self							:List[str]       ):
            return len(tuple(iter(self       )       )       )
  
  
  
  
     def __str__(		self							:Union[str, Any]       ):
            return " <- ".join(str(UpperCamelCase__       ) for item in self       )
  
  
  
  
     def SCREAMING_SNAKE_CASE_      (		self							:Any       ):
            return len(self       ) == 0
  
  
  
  
     def SCREAMING_SNAKE_CASE_      (		self							:List[str]				,  UpperCamelCase__							:Any       ):
            _a          =				Node(UpperCamelCase__       )
            if self.is_empty():
                   _a          =				_a          =				node
            else:
                   assert isinstance(self.rear				,  UpperCamelCase__       )
                   _a          =				node
                   _a          =				node
  
  
  
  
     def SCREAMING_SNAKE_CASE_      (		self							:Tuple       ):
            if self.is_empty():
                   raise IndexError("dequeue from empty queue"       )
            assert isinstance(self.front				,  UpperCamelCase__       )
            _a          =				self.front
            _a          =				self.front.next
            if self.front is None:
                   _a          =				None
            return node.data
  
  
  
  
     def SCREAMING_SNAKE_CASE_      (		self							:int       ):
            _a          =				_a          =				None
  
  
  if __name__ == "__main__":
     from doctest import testmod
  
     testmod()
  