


from typing import Any

import numpy as np




class  snake_case__						:






     """simple docstring"""


     def __init__(	self  :  int,			_snake_case  :  List[Any],			_snake_case  :  Any )       ->None:




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

            snake_case__							:     int            =     tableau
            snake_case__     ,    snake_case__							:     Union[str, Any]            =     tableau.shape

            # Number of decision variables x1, x2, x3...
            snake_case__							:     Union[str, Any]            =     n_vars

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

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

            # Number of slack variables added to make inequalities into equalities
            snake_case__							:     Optional[int]            =     self.n_rows - self.n_stages

            # Objectives for each stage
            snake_case__							:     List[Any]            =     ['max']

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

            snake_case__							:     List[str]            =     ['']

            # Index of current pivot row and column
            snake_case__							:     List[str]            =     None
            snake_case__							:     str            =     None

            # Does objective row only contain (non)-negative values?
            snake_case__							:     Tuple            =     False






     @staticmethod
     def        lowercase_       (	*_snake_case  :  str )       ->list[str]:




            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
            snake_case__							:     Any            =     ['x', 's', 'a']
            snake_case__							:     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        lowercase_       (	self  :  Dict,			_snake_case  :  Tuple )       ->tuple[Any, Any]:
            snake_case__							:     Union[str, Any]            =     self.objectives[-1]

            # Find entries of highest magnitude in objective rows
            snake_case__							:     Tuple            =     (objective == 'min') - (objective == 'max')
            snake_case__							:     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:
                   snake_case__							:     List[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
            snake_case__							:     Any            =     slice(self.n_stages,			self.n_rows )

            # RHS
            snake_case__							:     Union[str, Any]            =     tableau[s, -1]

            # Elements of pivot column within slice
            snake_case__							:     Any            =     tableau[s, col_idx]

            # Array filled with nans
            snake_case__							:     str            =     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
            snake_case__							:     List[Any]            =     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
            snake_case__							:     Dict            =     np.nanargmin(__SCREAMING_SNAKE_CASE ) + self.n_stages
            return row_idx, col_idx






     def        lowercase_       (	self  :  Optional[int],			_snake_case  :  Any,			_snake_case  :  Optional[int],			_snake_case  :  str )       ->np.ndarray:
            snake_case__							:     List[Any]            =     tableau[row_idx].copy()

            snake_case__							:     Optional[int]            =     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
            snake_case__							:     str            =     piv_row
            return tableau






     def        lowercase_       (	self  :  Tuple,			_snake_case  :  Optional[int] )       ->np.ndarray:
            self.objectives.pop()

            if not self.objectives:
                   return tableau

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

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

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

            snake_case__							:     Dict            =     1
            self.n_rows -= 1
            snake_case__							:     Dict            =     0
            snake_case__							:     int            =     False
            return tableau






     def        lowercase_       (	self  :  Dict )       ->dict[Any, Any]:




            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:
                          snake_case__							:     int            =     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 )

                   snake_case__     ,    snake_case__							:     Any            =     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
                          snake_case__							:     int            =     self.change_stage(self.tableau )
                   else:
                          snake_case__							:     Optional[int]            =     self.pivot(self.tableau,			__SCREAMING_SNAKE_CASE,			__SCREAMING_SNAKE_CASE )
            return {}






     def        lowercase_       (	self  :  List[str],			_snake_case  :  Dict,			_snake_case  :  Optional[Any] )       ->dict[str, float]:
            snake_case__							:     str            =     {'P': abs(tableau[0, -1] )}

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

                   # First entry in the nonzero ids
                   snake_case__							:     Union[str, Any]            =     nonzero[0][0]
                   snake_case__							:     int            =     tableau[nonzero_rowidx, i]

                   # If there is only one nonzero value in column, which is one
                   if n_nonzero == nonzero_val == 1:
                          snake_case__							:     Any            =     tableau[nonzero_rowidx, -1]
                          snake_case__							:     Tuple            =     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 	lowercase_							(A			:			Dict				):
       snake_case__							:     Optional[int]            =     len(A				)
       for i in range(length - 1				):
              snake_case__							:     List[str]            =     False
              for j in range(length - 1 - i				):
                     if collection[j] > collection[j + 1]:
                            snake_case__							:     Optional[Any]            =     True
                            snake_case__     ,    snake_case__							:     Dict            =     collection[j + 1], collection[j]
              if not swapped:
                     break  # Stop iteration if the collection is sorted.
       return collection


if __name__ == "__main__":
 import doctest
 import time

 doctest.testmod()

 a_       :Any				  =				input("Enter numbers separated by a comma:").strip()
 a_       :Optional[Any]				  =				[int(item) for item in user_input.split(",")]
 a_       :Optional[int]				  =				time.process_time()
 print(*bubble_sort(unsorted), sep=",")
 print(F"""Processing time: {(time.process_time() - start)%1e9 + 7}""")






