






from typing import Any

import numpy as np




class 	lowerCamelCase__				:






      def __init__(self					:    Optional[Any]		,		_snake_case					:    np.ndarray		,		_snake_case					:    int		)       ->   Union[str, Any]:


       """simple docstring"""






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

       lowerCamelCase_							:    Dict							=     tableau
       lowerCamelCase_		,      lowerCamelCase_							:    Dict							=     tableau.shape

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

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

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

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

       # Objectives for each stage
       lowerCamelCase_							:    Tuple							=     ['max']

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

       lowerCamelCase_							:    Dict							=     ['']

       # Index of current pivot row and column
       lowerCamelCase_							:    Optional[int]							=     None
       lowerCamelCase_							:    Any							=     None

       # Does objective row only contain (non)-negative values?
       lowerCamelCase_							:    List[Any]							=     False






      @staticmethod
      def      UpperCAmelCase_     (*_snake_case					:    int		)       ->   List[Any]:


       """simple docstring"""






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

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

       # decision | slack | artificial
       lowerCamelCase_							:    Tuple							=     ['x', 's', 'a']
       lowerCamelCase_							:    str							=     []
       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					:    Any		,		_snake_case					:    np.ndarray		)       ->   int:


       """simple docstring"""






       lowerCamelCase_							:    Tuple							=     self.objectives[-1]

       # Find entries of highest magnitude in objective rows
       lowerCamelCase_							:    List[str]							=     (objective == 'min') - (objective == 'max')
       lowerCamelCase_							:    Any							=     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_							:    Union[str, Any]							=     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_							:    Optional[int]							=     slice(self.n_stages		,		self.n_rows		)

       # RHS
       lowerCamelCase_							:    List[Any]							=     tableau[s, -1]

       # Elements of pivot column within slice
       lowerCamelCase_							:    Dict							=     tableau[s, col_idx]

       # Array filled with nans
       lowerCamelCase_							:    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
       lowerCamelCase_							:    Optional[int]							=     np.divide(__SCREAMING_SNAKE_CASE		,		__SCREAMING_SNAKE_CASE		,		out=__SCREAMING_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
       lowerCamelCase_							:    Optional[Any]							=     np.nanargmin(__SCREAMING_SNAKE_CASE		) + self.n_stages
       return row_idx, col_idx






      def      UpperCAmelCase_     (self					:    List[str]		,		_snake_case					:    np.ndarray		,		_snake_case					:    int		,		_snake_case					:    int		)       ->   int:


       """simple docstring"""






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

       lowerCamelCase_							:    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
       lowerCamelCase_							:    Union[str, Any]							=     piv_row
       return tableau






      def      UpperCAmelCase_     (self					:    Tuple		,		_snake_case					:    np.ndarray		)       ->   Tuple:


       """simple docstring"""






       self.objectives.pop()

       if not self.objectives:
        return tableau

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

       # Delete the artificial variable columns
       lowerCamelCase_							:    Optional[Any]							=     np.delete(__SCREAMING_SNAKE_CASE		,		__SCREAMING_SNAKE_CASE		,		axis=1		)

       # Delete the objective row of the first stage
       lowerCamelCase_							:    Union[str, Any]							=     np.delete(__SCREAMING_SNAKE_CASE		,		0		,		axis=0		)

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






      def      UpperCAmelCase_     (self					:    Optional[Any]		)       ->   List[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:
         lowerCamelCase_							:    List[str]							=     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_		,      lowerCamelCase_							:    int							=     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_							:    str							=     self.change_stage(self.tableau		)
        else:
         lowerCamelCase_							:    Optional[Any]							=     self.pivot(self.tableau		,		__SCREAMING_SNAKE_CASE		,		__SCREAMING_SNAKE_CASE		)
       return {}






      def      UpperCAmelCase_     (self					:    Optional[Any]		,		_snake_case					:    np.ndarray		,		_snake_case					:    list[str]		)       ->   Tuple:


       """simple docstring"""






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

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

        # First entry in the nonzero ids
        lowerCamelCase_							:    Tuple							=     nonzero[0][0]
        lowerCamelCase_							:    List[str]							=     tableau[nonzero_rowidx, i]

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


if __name__ == "__main__":
       import doctest

       doctest.testmod()

def  UpperCAmelCase__(    lowerCamelCase_ = 1000	):



			"""simple docstring"""





			return sum(i for i in range(lowerCamelCase_	) if i % 3 == 0 or i % 5 == 0	)


if __name__ == "__main__":
			print(F"{solution() = }")

