


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()




"""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()
