






"""simple docstring"""





import math







class 						_a  :





   '''simple docstring'''






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




          '''simple docstring'''




          lowercase__:							Union[str, Any]         =     x
          lowercase__:							str         =     y
          lowercase__:							Optional[Any]         =     step_size
          lowercase__:							Union[str, Any]         =     function_to_optimize





   def __lowercase							(       self)			->   int:




          '''simple docstring'''




          return self.function(self.x					, self.y)





   def __lowercase							(       self)			->   str:




          '''simple docstring'''




          lowercase__:							str         =     self.step_size
          return [
              SearchProblem(UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_					, self.function)
              for x, y in (
                  (self.x - step_size, self.y - step_size),
                  (self.x - step_size, self.y),
                  (self.x - step_size, self.y + step_size),
                  (self.x, self.y - step_size),
                  (self.x, self.y + step_size),
                  (self.x + step_size, self.y - step_size),
                  (self.x + step_size, self.y),
                  (self.x + step_size, self.y + step_size),
              )
          ]





   def __hash__(       self)			->   Optional[int]:




          '''simple docstring'''




          return hash(str(self))





   def __eq__(       self					, UpperCAmelCase_)			->   List[Any]:




          '''simple docstring'''




          if isinstance(UpperCAmelCase_					, UpperCAmelCase_):
                 return hash(str(self)) == hash(str(UpperCAmelCase_))
          return False





   def __str__(       self)			->   Dict:




          '''simple docstring'''




          return F"""x: {self.x} y: {self.y}"""







def 							A(    snake_case_		,  snake_case_ = True		,  snake_case_ = math.inf		,  snake_case_ = -math.inf		,  snake_case_ = math.inf		,  snake_case_ = -math.inf		,  snake_case_ = False		,  snake_case_ = 10000		,  ):
       """simple docstring"""





       lowercase__:							Dict         =     search_prob
       lowercase__:							Dict         =     []  # list to store the current score at each iteration
       lowercase__:							Union[str, Any]         =     0
       lowercase__:							Union[str, Any]         =     False
       lowercase__:							Union[str, Any]         =     set()
       while not solution_found and iterations < max_iter:
              visited.add(snake_case_						)
              iterations += 1
              lowercase__:							Tuple         =     current_state.score()
              scores.append(snake_case_						)
              lowercase__:							List[str]         =     current_state.get_neighbors()
              lowercase__:							Dict         =     -math.inf
              lowercase__:							List[Any]         =     math.inf
              lowercase__:							Dict         =     None  # to hold the next best neighbor
              for neighbor in neighbors:
                     if neighbor in visited:
                            continue  # do not want to visit the same state again
                     if (
                         neighbor.x > max_x
                         or neighbor.x < min_x
                         or neighbor.y > max_y
                         or neighbor.y < min_y
                     ):
                            continue  # neighbor outside our bounds
                     lowercase__:							Tuple         =     neighbor.score() - current_score
                     if find_max:  # finding max
                            # going to direction with greatest ascent
                            if change > max_change and change > 0:
                                   lowercase__:							str         =     change
                                   lowercase__:							List[str]         =     neighbor
                     else:  # finding min
                            # to direction with greatest descent
                            if change < min_change and change < 0:
                                   lowercase__:							Optional[int]         =     change
                                   lowercase__:							Tuple         =     neighbor
              if next_state is not None:
                     # we found at least one neighbor which improved the current state
                     lowercase__:							int         =     next_state
              else:
                     # since we have no neighbor that improves the solution we stop the search
                     lowercase__:							str         =     True

       if visualization:
              from matplotlib import pyplot as plt

              plt.plot(range(snake_case_						)		,  snake_case_						)
              plt.xlabel("Iterations"						)
              plt.ylabel("Function values"						)
              plt.show()

       return current_state


if __name__ == "__main__":
  import doctest

  doctest.testmod()






  def 							A(    snake_case_		,  snake_case_						):
         """simple docstring"""





         return (x**2) + (y**2)

  # starting the problem with initial coordinates (3, 4)
  UpperCamelCase					=     SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  UpperCamelCase					=     hill_climbing(prob, find_max=False)
  print(
      """The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: """
      F"{local_min.score()}"
  )

  # starting the problem with initial coordinates (12, 47)
  UpperCamelCase					=     SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
  UpperCamelCase					=     hill_climbing(
      prob, find_max=False, max_x=1_00, min_x=5, max_y=50, min_y=-5, visualization=True
  )
  print(
      """The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 """
      F"and 50 > y > - 5 found via hill climbing: {local_min.score()}"
  )






  def 							A(    snake_case_		,  snake_case_						):
         """simple docstring"""





         return (3 * x**2) - (6 * y)

  UpperCamelCase					=     SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  UpperCamelCase					=     hill_climbing(prob, find_max=True)







  print(
      """The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: """
      F"{local_min.score()}"
  )










class 			lowerCamelCase_					:





							def __init__(							self    ):
								a_     			=   [0, 1]





							def   __magic_name__      (							self			,       _SCREAMING_SNAKE_CASE    ):
								if (difference := index - (len(self.sequence    ) - 2)) >= 1:
									for _ in range(_SCREAMING_SNAKE_CASE    ):
										self.sequence.append(self.sequence[-1] + self.sequence[-2]    )
								return self.sequence[:index]







def 			__SCREAMING_SNAKE_CASE		(		)     ->	None:



	"""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=""""""     ,					)
	a_     			=   Fibonacci()

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

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

		print(fibonacci.get(UpperCamelCase	)	)


if __name__ == "__main__":
			main()