


'''simple docstring'''
from typing import Any

import numpy as np






class 		UpperCamelCase_		:





						"""simple docstring"""




						def __init__( self				:					Any	,				_lowerCamelCase				:					np.ndarray	,				_lowerCamelCase				:					int  )							->					None:
										# Check if RHS is negative
										if np.any(tableau[:, -1]	,				where=tableau[:, -1] < 0  ):
														raise ValueError("RHS must be > 0"  )

										__magic_name__	  = tableau
										__magic_name__	  = tableau.shape

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

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

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

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

										# Objectives for each stage
										__magic_name__	  = ['max']

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

										__magic_name__	  = ['']

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

										# Does objective row only contain (non)-negative values?
										__magic_name__	  = False
						@staticmethod
						def 					__A					( *_lowerCamelCase				:					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
										__magic_name__	  = ['x', 's', 'a']
										__magic_name__	  = []
										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				:					Optional[Any]	,				_lowerCamelCase				:					np.ndarray  )							->					tuple[Any, Any]:
										__magic_name__	  = self.objectives[-1]

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

										# RHS
										__magic_name__	  = tableau[s, -1]

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

										# Array filled with nans
										__magic_name__	  = 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
										__magic_name__	  = 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
										__magic_name__	  = np.nanargmin(_A  ) + self.n_stages
										return row_idx, col_idx
						def 					__A					( self				:					Tuple	,				_lowerCamelCase				:					np.ndarray	,				_lowerCamelCase				:					int	,				_lowerCamelCase				:					int  )							->					np.ndarray:
										__magic_name__	  = tableau[row_idx].copy()

										__magic_name__	  = 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
										__magic_name__	  = piv_row
										return tableau
						def 					__A					( self				:					Optional[int]	,				_lowerCamelCase				:					np.ndarray  )							->					np.ndarray:
										self.objectives.pop()

										if not self.objectives:
														return tableau

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

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

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

										__magic_name__	  = 1
										self.n_rows -= 1
										__magic_name__	  = 0
										__magic_name__	  = False
										return tableau
						def 					__A					( self				:					Dict  )							->					dict[Any, Any]:
										# Stop simplex algorithm from cycling.
										for _ in range(1_00  ):
														# Completion of each stage removes an objective. If both stages
														# are complete, then no objectives are left
														if not self.objectives:
																		__magic_name__	  = 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  )

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

						def 					__A					( self				:					Tuple	,				_lowerCamelCase				:					np.ndarray	,				_lowerCamelCase				:					list[str]  )							->					dict[str, float]:
										__magic_name__	  = {'P': abs(tableau[0, -1]  )}

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

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

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







'''simple docstring'''
from __future__ import annotations




def      __snake_case       (       lowerCamelCase_ :				list[list[int]]	,  lowerCamelCase_ :				list[list[int]]						):
				'''simple docstring'''




				assert len(lowerCamelCase_						) == len(lowerCamelCase_						)

				__magic_name__	  = len(lowerCamelCase_						)
				__magic_name__	  = list(range(lowerCamelCase_						)						)
				__magic_name__	  = [-1] * n  # who the donor has donated to
				__magic_name__	  = [-1] * n  # who the recipient has received from
				__magic_name__	  = [0] * n

				while unmatched_donors:
								__magic_name__	  = unmatched_donors[0]
								__magic_name__	  = donor_pref[donor]
								__magic_name__	  = donor_preference[num_donations[donor]]
								num_donations[donor] += 1
								__magic_name__	  = recipient_pref[recipient]
								__magic_name__	  = rec_record[recipient]

								if prev_donor != -1:
												if rec_preference.index(lowerCamelCase_						) > rec_preference.index(lowerCamelCase_						):
																__magic_name__	  = donor
																__magic_name__	  = recipient
																unmatched_donors.append(lowerCamelCase_						)
																unmatched_donors.remove(lowerCamelCase_						)
								else:
												__magic_name__	  = donor
												__magic_name__	  = recipient
												unmatched_donors.remove(lowerCamelCase_						)
				return donor_record



