"""simple docstring"""







from typing import Any

import numpy as np


class      _lowercase						:

				def __init__(       self    :      Dict    ,      _lowercase    :      np.ndarray    ,      _lowercase    :      int       ):


										'''simple docstring'''
										# Check if RHS is negative
										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     A	(       *_lowercase    :      int       ):


										'''simple docstring'''
										if len(_lowercase       ) != 3:
																raise ValueError("""Must provide n_vars, n_slack, and n_art_vars"""       )

										if not all(x >= 0 and isinstance(_lowercase    ,      _lowercase       ) 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     A	(       self    :      int    ,      _lowercase    :      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(_lowercase    ,      _lowercase    ,      out=_lowercase    ,      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(_lowercase       ) + self.n_stages
										return row_idx, col_idx

				def     A	(       self    :      Any    ,      _lowercase    :      np.ndarray    ,      _lowercase    :      int    ,      _lowercase    :      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     A	(       self    :      Tuple    ,      _lowercase    :      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(_lowercase    ,      _lowercase    ,      axis=1       )

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

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

				def     A	(       self    :      Union[str, Any]       ):


										'''simple docstring'''
										# Stop simplex algorithm from cycling.
										for _ in range(1_0_0       ):
																# 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    ,      _lowercase    ,      _lowercase       )
										return {}

				def     A	(       self    :      Any    ,      _lowercase    :      np.ndarray    ,      _lowercase    :      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(_lowercase    ,      0       )
										return output_dict


if __name__ == "__main__":
						import doctest

						doctest.testmod()


"""simple docstring"""







from __future__ import annotations


def 					a__ (						UpperCAmelCase__    :     int     )->		list[int]:
						assert (
						    isinstance(UpperCAmelCase__						,     UpperCAmelCase__     ) and mask > 0
						), f'mask needs to be positive integer, your input {mask}'
						UpperCAmelCase__   		=						[]
						UpperCAmelCase__   		=						mask

						while submask:
												all_submasks.append(UpperCAmelCase__     )
												UpperCAmelCase__   		=						(submask - 1) & mask

						return all_submasks


if __name__ == "__main__":
						import doctest

						doctest.testmod()

