




from typing import Any

import numpy as np







class 		__UpperCAmelCase:





     """simple docstring"""



     def __init__(   self			:							Optional[int]    ,					A			:							np.ndarray    ,					A			:							int     )      ->      None:






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

         a__  			=							tableau
         a__			,		a__  			=							tableau.shape

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

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

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

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

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

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

         a__  			=							[""""""]

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

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

     @staticmethod
     def 					__SCREAMING_SNAKE_CASE		(   *A			:							int     )      ->      list[str]:






         """simple docstring"""
         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
         a__  			=							["""x""", """s""", """a"""]
         a__  			=							[]
         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			:							int    ,					A			:							np.ndarray     )      ->      tuple[Any, Any]:






         """simple docstring"""
         a__  			=							self.objectives[-1]

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

         # RHS
         a__  			=							tableau[s, -1]

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

         # Array filled with nans
         a__  			=							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
         a__  			=							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
         a__  			=							np.nanargmin(A     ) + self.n_stages
         return row_idx, col_idx

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Union[str, Any]    ,					A			:							np.ndarray    ,					A			:							int    ,					A			:							int     )      ->      np.ndarray:






         """simple docstring"""
         a__  			=							tableau[row_idx].copy()

         a__  			=							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
         a__  			=							piv_row
         return tableau

     def 					__SCREAMING_SNAKE_CASE		(   self			:							List[str]    ,					A			:							np.ndarray     )      ->      np.ndarray:






         """simple docstring"""
         self.objectives.pop()

         if not self.objectives:
             return tableau

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

         # Delete the artificial variable columns
         a__  			=							np.delete(A    ,					A    ,					axis=1     )

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

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

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Tuple     )      ->      dict[Any, Any]:






         """simple docstring"""
         # 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:
                 a__  			=							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     )

             a__			,		a__  			=							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
                 a__  			=							self.change_stage(self.tableau     )
             else:
                 a__  			=							self.pivot(self.tableau    ,					A    ,					A     )
         return {}






     def 					__SCREAMING_SNAKE_CASE		(   self			:							Any    ,					A			:							np.ndarray    ,					A			:							list[str]     )      ->      dict[str, float]:






         """simple docstring"""
         a__  			=							{"""P""": abs(tableau[0, -1]     )}

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

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

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












from __future__ import annotations

import random







class 		__UpperCAmelCase:





     """simple docstring"""



     __UpperCAmelCase						:			Optional[int]							=     6

     def __init__(   self			:							int     )      ->      Optional[Any]:






         """simple docstring"""
         a__  			=							list(range(1    ,					Dice.NUM_SIDES + 1     )     )






     def 					__SCREAMING_SNAKE_CASE		(   self			:							Union[str, Any]     )      ->      List[str]:






         """simple docstring"""
         return random.choice(self.sides     )






def 							__lowerCAmelCase			(UpperCAmelCase_ ,     UpperCAmelCase_ = 2		):
    a__  			=							[Dice() for i in range(UpperCAmelCase_		)]
    a__  			=							[0] * (len(UpperCAmelCase_		) * Dice.NUM_SIDES + 1)
    for _ in range(UpperCAmelCase_		):
        count_of_sum[sum(dice.roll() for dice in dices		)] += 1
    a__  			=							[round((count * 100) / num_throws ,     2		) for count in count_of_sum]
    return probability[num_dice:]  # remove probability of sums that never appear


if __name__ == "__main__":
 import doctest

 doctest.testmod()






