
from typing import Any

import numpy as np





class 						__lowercase:


       """simple docstring"""







       def __init__(     self					:			str  ,      _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'       )

         _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 SCREAMING_SNAKE_CASE_				(     *_lowerCAmelCase					:			int       )					->   list[str]:
         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 SCREAMING_SNAKE_CASE_				(     self					:			List[str]  ,      _lowerCAmelCase					:			np.ndarray       )					->   tuple[Any, Any]:
         _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 SCREAMING_SNAKE_CASE_				(     self					:			Optional[Any]  ,      _lowerCAmelCase					:			np.ndarray  ,      _lowerCAmelCase					:			int  ,      _lowerCAmelCase					:			int       )					->   np.ndarray:
         _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 SCREAMING_SNAKE_CASE_				(     self					:			int  ,      _lowerCAmelCase					:			np.ndarray       )					->   np.ndarray:
         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 SCREAMING_SNAKE_CASE_				(     self					:			Optional[int]       )					->   dict[Any, Any]:
         # 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 SCREAMING_SNAKE_CASE_				(     self					:			Any  ,      _lowerCAmelCase					:			np.ndarray  ,      _lowerCAmelCase					:			list[str]       )					->   dict[str, float]:
         _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()


import random



def 	_a  (					__SCREAMING_SNAKE_CASE					:  str    ):






  """simple docstring"""




  def is_sorted(__SCREAMING_SNAKE_CASE					:  str    ):
    for i in range(len(__SCREAMING_SNAKE_CASE    ) - 1    ):
      if collection[i] > collection[i + 1]:
        return False
    return True

  while not is_sorted(__SCREAMING_SNAKE_CASE    ):
    random.shuffle(__SCREAMING_SNAKE_CASE    )
  return collection


if __name__ == "__main__":
       _UpperCamelCase:					Dict     =input('Enter numbers separated by a comma:\n').strip()
       _UpperCamelCase:					Optional[Any]     =[int(item) for item in user_input.split(',')]
       print(bogo_sort(unsorted))
