

from typing import Any

import numpy as np



class     lowercase_       :



      def __init__(     self :							List[str]     ,   A__ :							np.ndarray     ,   A__ :							int						)       ->	int:
        # Check if RHS is negative
        if np.any(tableau[:, -1]     ,   where=tableau[:, -1] < 0						):
          raise ValueError('''RHS must be > 0'''						)

        _snake_case		=				tableau
        _snake_case		=				tableau.shape

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

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

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

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

        # Objectives for each stage
        _snake_case		=				["max"]

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

        _snake_case		=				[""]

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

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



      @staticmethod
      def 		UpperCamelCase_						(     *A__ :							int						)       ->	List[str]:
        if len(_A						) != 3:
          raise ValueError('''Must provide n_vars, n_slack, and n_art_vars'''						)

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

        # decision | slack | artificial
        _snake_case		=				["x", "s", "a"]
        _snake_case		=				[]
        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 :							Optional[Any]     ,   A__ :							np.ndarray						)       ->	Optional[Any]:
        _snake_case		=				self.objectives[-1]

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

        # RHS
        _snake_case		=				tableau[s, -1]

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

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

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



      def 		UpperCamelCase_						(     self :							Union[str, Any]     ,   A__ :							np.ndarray     ,   A__ :							int     ,   A__ :							int						)       ->	int:
        _snake_case		=				tableau[row_idx].copy()

        _snake_case		=				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
        _snake_case		=				piv_row
        return tableau



      def 		UpperCamelCase_						(     self :							List[Any]     ,   A__ :							np.ndarray						)       ->	str:
        self.objectives.pop()

        if not self.objectives:
          return tableau

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

        # Delete the artificial variable columns
        _snake_case		=				np.delete(_A     ,   _A     ,   axis=1						)

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

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



      def 		UpperCamelCase_						(     self :							Dict						)       ->	List[Any]:
        # 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:
            _snake_case		=				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						)

          _snake_case		=				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
            _snake_case		=				self.change_stage(self.tableau						)
          else:
            _snake_case		=				self.pivot(self.tableau     ,   _A     ,   _A						)
        return {}







      def 		UpperCamelCase_						(     self :							Any     ,   A__ :							np.ndarray     ,   A__ :							list[str]						)       ->	Any:
        _snake_case		=				{"P": abs(tableau[0, -1]						)}

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

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

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


if __name__ == "__main__":
 import doctest

 doctest.testmod()






def 						snake_case__							(       __lowercase							)		->		int:







						"""simple docstring"""

						A__						:				Any         =			0
						for plain_chr in plain_text:
												A__						:				List[str]         =			(
												    ord(__lowercase							) + (hash_value << 6) + (hash_value << 1_6) - hash_value
												)
						return hash_value