
'''simple docstring'''

import math






class    A     :





 def __init__(					self			:       Optional[Any]      ,							__magic_name__			:       int      ,							__magic_name__			:       int      ,							__magic_name__			:       int      ,							__magic_name__			:       List[str]							):


    """simple docstring"""

    lowerCAmelCase__								=							x
    lowerCAmelCase__								=							y
    lowerCAmelCase__								=							step_size
    lowerCAmelCase__								=							function_to_optimize





 def 							__SCREAMING_SNAKE_CASE  (					self			:       List[str]							):


    """simple docstring"""

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





 def 							__SCREAMING_SNAKE_CASE  (					self			:       Dict							):


    """simple docstring"""

    lowerCAmelCase__								=							self.step_size
    return [
        SearchProblem(__magic_name__      ,							__magic_name__      ,							__magic_name__      ,							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			:       List[str]							):


    """simple docstring"""

    return hash(str(self							)							)





 def __eq__(					self			:       Optional[int]      ,							__magic_name__			:       Optional[Any]							):


    """simple docstring"""

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







 def __str__(					self			:       List[str]							):


    """simple docstring"""

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







def   A     (      UpperCamelCase_					:     List[Any]						,	UpperCamelCase_					:     Dict = True						,	UpperCamelCase_					:     Union[str, Any] = math.inf						,	UpperCamelCase_					:     Optional[Any] = -math.inf						,	UpperCamelCase_					:     List[Any] = math.inf						,	UpperCamelCase_					:     Any = -math.inf						,	UpperCamelCase_					:     Union[str, Any] = False						,	UpperCamelCase_					:     int = 1_00_00						,	)					->       Optional[int]:







   '''simple docstring'''



   lowerCAmelCase__								=							search_prob
   lowerCAmelCase__								=							[]  # list to store the current score at each iteration
   lowerCAmelCase__								=							0
   lowerCAmelCase__								=							False
   lowerCAmelCase__								=							set()
   while not solution_found and iterations < max_iter:
      visited.add(lowerCAmelCase__      )
      iterations += 1
      lowerCAmelCase__								=							current_state.score()
      scores.append(lowerCAmelCase__      )
      lowerCAmelCase__								=							current_state.get_neighbors()
      lowerCAmelCase__								=							-math.inf
      lowerCAmelCase__								=							math.inf
      lowerCAmelCase__								=							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
         lowerCAmelCase__								=							neighbor.score() - current_score
         if find_max:  # finding max
            # going to direction with greatest ascent
            if change > max_change and change > 0:
               lowerCAmelCase__								=							change
               lowerCAmelCase__								=							neighbor
         else:  # finding min
            # to direction with greatest descent
            if change < min_change and change < 0:
               lowerCAmelCase__								=							change
               lowerCAmelCase__								=							neighbor
      if next_state is not None:
         # we found at least one neighbor which improved the current state
         lowerCAmelCase__								=							next_state
      else:
         # since we have no neighbor that improves the solution we stop the search
         lowerCAmelCase__								=							True

   if visualization:
      from matplotlib import pyplot as plt

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

   return current_state


if __name__ == "__main__":
  import doctest

  doctest.testmod()







  def   A     (      UpperCamelCase_					:     Tuple						,	UpperCamelCase_					:     List[Any]      )					->       Optional[Any]:







     '''simple docstring'''



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

  # starting the problem with initial coordinates (3, 4)
  UpperCAmelCase__   : List[Any]					=		SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  UpperCAmelCase__   : Dict					=		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__   : Union[str, Any]					=		SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
  UpperCAmelCase__   : List[Any]					=		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     (      UpperCamelCase_					:     str						,	UpperCamelCase_					:     List[Any]      )					->       Optional[Any]:







     '''simple docstring'''



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

  UpperCAmelCase__   : Optional[Any]					=		SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  UpperCAmelCase__   : int					=		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()}"
  )







'''simple docstring'''

def   A     (      UpperCamelCase_					:     int						,	UpperCamelCase_					:     int						,	UpperCamelCase_					:     int						,	UpperCamelCase_					:     int      )					->       int:







			'''simple docstring'''



			return len_board * len_board_column * row + column







def   A     (      UpperCamelCase_					:     list[list[str]]						,	UpperCamelCase_					:     str						,	UpperCamelCase_					:     int						,	UpperCamelCase_					:     int						,	UpperCamelCase_					:     int						,	UpperCamelCase_					:     set[int]						,	)					->       bool:







			'''simple docstring'''



			if board[row][column] != word[word_index]:
						return False

			if word_index == len(UpperCamelCase_      ) - 1:
						return True

			lowerCAmelCase__								=							[(0, 1), (0, -1), (-1, 0), (1, 0)]
			lowerCAmelCase__								=							len(UpperCamelCase_      )
			lowerCAmelCase__								=							len(board[0]      )
			for direction in traverts_directions:
						lowerCAmelCase__								=							row + direction[0]
						lowerCAmelCase__								=							column + direction[1]
						if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
									continue

						lowerCAmelCase__								=							get_point_key(UpperCamelCase_						,	UpperCamelCase_						,	UpperCamelCase_						,	UpperCamelCase_      )
						if key in visited_points_set:
									continue

						visited_points_set.add(UpperCamelCase_      )
						if exits_word(UpperCamelCase_						,	UpperCamelCase_						,	UpperCamelCase_						,	UpperCamelCase_						,	word_index + 1						,	UpperCamelCase_      ):
									return True

						visited_points_set.remove(UpperCamelCase_      )

			return False







def   A     (      UpperCamelCase_					:     list[list[str]]						,	UpperCamelCase_					:     str      )					->       bool:







			'''simple docstring'''



			lowerCAmelCase__								=							(
			    "The board should be a non empty matrix of single chars strings."
			)

			lowerCAmelCase__								=							len(UpperCamelCase_      )
			if not isinstance(UpperCamelCase_						,	UpperCamelCase_      ) or len(UpperCamelCase_      ) == 0:
						raise ValueError(UpperCamelCase_      )

			for row in board:
						if not isinstance(UpperCamelCase_						,	UpperCamelCase_      ) or len(UpperCamelCase_      ) == 0:
									raise ValueError(UpperCamelCase_      )

						for item in row:
									if not isinstance(UpperCamelCase_						,	UpperCamelCase_      ) or len(UpperCamelCase_      ) != 1:
												raise ValueError(UpperCamelCase_      )

    # Validate word
			if not isinstance(UpperCamelCase_						,	UpperCamelCase_      ) or len(UpperCamelCase_      ) == 0:
						raise ValueError(
						    "The word parameter should be a string of length greater than 0."      )

			lowerCAmelCase__								=							len(board[0]      )
			for i in range(UpperCamelCase_      ):
						for j in range(UpperCamelCase_      ):
									if exits_word(
									    UpperCamelCase_						,	UpperCamelCase_						,	UpperCamelCase_						,	UpperCamelCase_						,	0						,	{get_point_key(UpperCamelCase_						,	UpperCamelCase_						,	UpperCamelCase_						,	UpperCamelCase_      )}      ):
												return True

			return False


if __name__ == "__main__":
		import doctest

		doctest.testmod()





