"""simple docstring"""


from typing import Any

import numpy as np






class        __UpperCAmelCase						:

				def __init__(				self     ,			_lowerCamelCase     ,			_lowerCamelCase				):
										# Check if RHS is negative
										if np.any(tableau[:, -1]     ,			where=tableau[:, -1] < 0				):
																raise ValueError("RHS must be > 0"				)

										lowerCamelCase__ =tableau
										lowerCamelCase__ ,				lowerCamelCase__ =tableau.shape

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

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

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

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

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

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

										lowerCamelCase__ =[""]

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

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

				@staticmethod
				def 		_a     (				*_lowerCamelCase				):
										if len(_lowerCamelCase				) != 3:
																raise ValueError("Must provide n_vars, n_slack, and n_art_vars"				)

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

										# decision | slack | artificial
										lowerCamelCase__ =["x", "s", "a"]
										lowerCamelCase__ =[]
										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     ,			_lowerCamelCase				):
										lowerCamelCase__ =self.objectives[-1]

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

										# RHS
										lowerCamelCase__ =tableau[s, -1]

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

										# Array filled with nans
										lowerCamelCase__ =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__ =np.divide(_lowerCamelCase     ,			_lowerCamelCase     ,			out=_lowerCamelCase     ,			where=divisor > 0				)

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

				def 		_a     (				self     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase				):
										lowerCamelCase__ =tableau[row_idx].copy()

										lowerCamelCase__ =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__ =piv_row
										return tableau

				def 		_a     (				self     ,			_lowerCamelCase				):
										self.objectives.pop()

										if not self.objectives:
																return tableau

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

										# Delete the artificial variable columns
										lowerCamelCase__ =np.delete(_lowerCamelCase     ,			_lowerCamelCase     ,			axis=1				)

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

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

				def 		_a     (				self				):
										# 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:
																						lowerCamelCase__ =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__ =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__ =self.change_stage(self.tableau				)
																else:
																						lowerCamelCase__ =self.pivot(self.tableau     ,			_lowerCamelCase     ,			_lowerCamelCase				)
										return {}






				def 		_a     (				self     ,			_lowerCamelCase     ,			_lowerCamelCase				):
										lowerCamelCase__ ={"P": abs(tableau[0, -1]				)}

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

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

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


if __name__ == "__main__":
	import doctest

	doctest.testmod()



"""simple docstring"""


from __future__ import annotations





def       lowerCamelCase_			( __lowerCAmelCase    )							-> int | float:




						'''simple docstring'''



						lowerCamelCase__ =sorted(__lowerCAmelCase    )
						lowerCamelCase__ =len(__lowerCAmelCase    )
						lowerCamelCase__ =length >> 1
						return (
						    (sorted_list[mid_index] + sorted_list[mid_index - 1]) / 2
						    if length % 2 == 0
						    else sorted_list[mid_index]
						)





def       lowerCamelCase_			( )							-> Tuple:




						'''simple docstring'''



						import doctest

						doctest.testmod()


if __name__ == "__main__":
	main()


