

"""simple docstring"""




from typing import Any

import numpy as np





class 				lowerCamelCase  :

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




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

      SCREAMING_SNAKE_CASE__									= tableau
      SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__									= tableau.shape

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

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

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

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

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

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

      SCREAMING_SNAKE_CASE__									= [""""""]

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

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

   @staticmethod
   def    SCREAMING_SNAKE_CASE			(   *__UpperCAmelCase			:  List[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
      SCREAMING_SNAKE_CASE__									= ["""x""", """s""", """a"""]
      SCREAMING_SNAKE_CASE__									= []
      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]      ,			__UpperCAmelCase			:  List[str]    )				->      tuple[Any, Any]:
      SCREAMING_SNAKE_CASE__									= self.objectives[-1]

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

      # RHS
      SCREAMING_SNAKE_CASE__									= tableau[s, -1]

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

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

   def    SCREAMING_SNAKE_CASE			(   self			:  Tuple      ,			__UpperCAmelCase			:  Optional[int]      ,			__UpperCAmelCase			:  Union[str, Any]      ,			__UpperCAmelCase			:  List[Any]    )				->      np.ndarray:
      SCREAMING_SNAKE_CASE__									= tableau[row_idx].copy()

      SCREAMING_SNAKE_CASE__									= 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
      SCREAMING_SNAKE_CASE__									= piv_row
      return tableau

   def    SCREAMING_SNAKE_CASE			(   self			:  List[Any]      ,			__UpperCAmelCase			:  int    )				->      np.ndarray:
      self.objectives.pop()

      if not self.objectives:
         return tableau

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

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

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

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

   def    SCREAMING_SNAKE_CASE			(   self			:  Optional[Any]    )				->      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:
            SCREAMING_SNAKE_CASE__									= 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    )

         SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__									= 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
            SCREAMING_SNAKE_CASE__									= self.change_stage(self.tableau    )
         else:
            SCREAMING_SNAKE_CASE__									= self.pivot(self.tableau      ,			__SCREAMING_SNAKE_CASE      ,			__SCREAMING_SNAKE_CASE    )
      return {}





   def    SCREAMING_SNAKE_CASE			(   self			:  str      ,			__UpperCAmelCase			:  int      ,			__UpperCAmelCase			:  int    )				->      dict[str, float]:
      SCREAMING_SNAKE_CASE__									= {"""P""": abs(tableau[0, -1]    )}

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

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

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





"""simple docstring"""




class 				lowerCamelCase  :

			def __init__(   self			:  Dict    )				->      None:
						SCREAMING_SNAKE_CASE__									= [0, 1]





			def    SCREAMING_SNAKE_CASE			(   self			:  Optional[int]      ,			__UpperCAmelCase			:  int    )				->      list:
						if (difference := index - (len(self.sequence    ) - 2)) >= 1:
									for _ in range(__UpperCAmelCase    ):
												self.sequence.append(self.sequence[-1] + self.sequence[-2]    )
						return self.sequence[:index]

def 		A    (       ):




			'''simple docstring'''


			print(
			    """Fibonacci Series Using Dynamic Programming\n"""						,			"""Enter the index of the Fibonacci number you want to calculate """						,			"""in the prompt below. (To exit enter exit or Ctrl-C)\n"""						,			sep=""""""						,			)
			SCREAMING_SNAKE_CASE__									= Fibonacci()

			while True:
						SCREAMING_SNAKE_CASE__									= input(""">> """      )
						if prompt in {"exit", "quit"}:
									break

						try:
									SCREAMING_SNAKE_CASE__									= int(snake_case__      )
						except ValueError:
									print("""Enter a number or 'exit'"""      )
									continue

						print(fibonacci.get(snake_case__      )      )


if __name__ == "__main__":
						main()


