




from typing import Any

import numpy as np






class 					__lowerCAmelCase				:







			def __init__( self					:    Tuple					,					snake_case__					:    np.ndarray					,					snake_case__					:    int   ):




									"""simple docstring"""


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

									_UpperCAmelCase									=  tableau
									_UpperCAmelCase							,				_UpperCAmelCase									=  tableau.shape

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

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

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

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

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

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

									_UpperCAmelCase									=  [""]

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

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







			@staticmethod
			def UpperCamelCase    ( *snake_case__					:    int   ):




									"""simple docstring"""


									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
									_UpperCAmelCase									=  ["x", "s", "a"]
									_UpperCAmelCase									=  []
									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[int]					,					snake_case__					:    np.ndarray   ):




									"""simple docstring"""


									_UpperCAmelCase									=  self.objectives[-1]

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

									# RHS
									_UpperCAmelCase									=  tableau[s, -1]

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

									# Array filled with nans
									_UpperCAmelCase									=  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
									_UpperCAmelCase									=  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
									_UpperCAmelCase									=  np.nanargmin(snake_case__   ) + self.n_stages
									return row_idx, col_idx







			def UpperCamelCase    ( self					:    Optional[Any]					,					snake_case__					:    np.ndarray					,					snake_case__					:    int					,					snake_case__					:    int   ):




									"""simple docstring"""


									_UpperCAmelCase									=  tableau[row_idx].copy()

									_UpperCAmelCase									=  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
									_UpperCAmelCase									=  piv_row
									return tableau







			def UpperCamelCase    ( self					:    Optional[int]					,					snake_case__					:    np.ndarray   ):




									"""simple docstring"""


									self.objectives.pop()

									if not self.objectives:
															return tableau

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

									# Delete the artificial variable columns
									_UpperCAmelCase									=  np.delete(snake_case__					,					snake_case__					,					axis=1   )

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

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







			def UpperCamelCase    ( self					:    Dict   ):




									"""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:
																					_UpperCAmelCase									=  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   )

															_UpperCAmelCase							,				_UpperCAmelCase									=  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
																					_UpperCAmelCase									=  self.change_stage(self.tableau   )
															else:
																					_UpperCAmelCase									=  self.pivot(self.tableau					,					snake_case__					,					snake_case__   )
									return {}







			def UpperCamelCase    ( self					:    List[Any]					,					snake_case__					:    np.ndarray					,					snake_case__					:    list[str]   ):




									"""simple docstring"""


									_UpperCAmelCase									=  {"P": abs(tableau[0, -1]   )}

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

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

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










def 							__SCREAMING_SNAKE_CASE						(    snake_case_ = 99_8001		):

						'''simple docstring'''


						for number in range(n - 1			,					9999			,					-1		):
												_UpperCAmelCase									=  str(snake_case_		)

												# checks whether 'str_number' is a palindrome.
												if str_number == str_number[::-1]:
																		_UpperCAmelCase									=  999

																		# if 'number' is a product of two 3-digit numbers
																		# then number is the answer otherwise fetch next number.
																		while divisor != 99:
																								if (number % divisor == 0) and (len(str(number // divisor		)		) == 3.0):
																														return number
																								divisor -= 1
						raise ValueError("That number is larger than our acceptable range."		)


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




