
"""simple docstring"""


import math







class 		lowerCamelCase__					:





			'''simple docstring'''



			def __init__(							self     ,     __UpperCAmelCase     ,     __UpperCAmelCase     ,     __UpperCAmelCase     ,     __UpperCAmelCase  ) ->     Dict:
				_lowerCAmelCase								=x
				_lowerCAmelCase								=y
				_lowerCAmelCase								=step_size
				_lowerCAmelCase								=function_to_optimize



			def 					_lowerCAmelCase		(							self  ) ->     int:
				return self.function(self.x     ,     self.y  )



			def 					_lowerCAmelCase		(							self  ) ->     int:
				_lowerCAmelCase								=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]:
				return hash(str(self  )  )



			def __eq__(							self     ,     __UpperCAmelCase  ) ->     Any:
				if isinstance(__UpperCAmelCase     ,     __UpperCAmelCase  ):
					return hash(str(self  )  ) == hash(str(__UpperCAmelCase  )  )
				return False



			def __str__(							self  ) ->     Optional[int]:
				return f'''x: {self.x} y: {self.y}'''







def     _lowerCamelCase(__UpperCamelCase    , __UpperCamelCase = True    , __UpperCamelCase = math.inf    , __UpperCamelCase = -math.inf    , __UpperCamelCase = math.inf    , __UpperCamelCase = -math.inf    , __UpperCamelCase = False    , __UpperCamelCase = 10000    , )				-> SearchProblem:
	_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(__UpperCamelCase       )
		iterations += 1
		_lowerCAmelCase								=current_state.score()
		scores.append(__UpperCamelCase       )
		_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(__UpperCamelCase       )    , __UpperCamelCase       )
		plt.xlabel("""Iterations"""       )
		plt.ylabel("""Function values"""       )
		plt.show()

	return current_state


if __name__ == "__main__":
			import doctest

			doctest.testmod()



			def     _lowerCamelCase(__UpperCamelCase    , __UpperCamelCase       )				-> Tuple:
				return (x**2) + (y**2)

			# starting the problem with initial coordinates (3, 4)
			__A       						=       SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
			__A       						=       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)
			__A       						=       SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
			__A       						=       hill_climbing(
			    prob, find_max=False, max_x=100, 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     _lowerCamelCase(__UpperCamelCase    , __UpperCamelCase       )				-> Optional[Any]:
				return (3 * x**2) - (6 * y)

			__A       						=       SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
			__A       						=       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     _lowerCamelCase(__UpperCamelCase = 4000000       )				-> int:
	_lowerCAmelCase								=1
	_lowerCAmelCase								=2
	_lowerCAmelCase								=0
	while j <= n:
		if j % 2 == 0:
			total += j
		_lowerCAmelCase						,							_lowerCAmelCase								=j, i + j

	return total


if __name__ == "__main__":
			print(F"""{solution() = }""")



