code: 
  
  
  
  
  """simple docstring"""
  
  import math
  class 			lowerCamelCase__    :
  
  
  			def __init__(     self				, SCREAMING_SNAKE_CASE				, SCREAMING_SNAKE_CASE				, SCREAMING_SNAKE_CASE				, SCREAMING_SNAKE_CASE							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						int								=				x
  					snake_case		:						Any								=				y
  					snake_case		:						List[str]								=				step_size
  					snake_case		:						Dict								=				function_to_optimize
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					return self.function(self.x				, self.y							)
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						List[str]								=				self.step_size
  					return [
  					    SearchProblem(SCREAMING_SNAKE_CASE				, SCREAMING_SNAKE_CASE				, SCREAMING_SNAKE_CASE				, 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							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					return hash(str(self							)							)
  
  
  			def __eq__(     self				, SCREAMING_SNAKE_CASE							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					if isinstance(SCREAMING_SNAKE_CASE				, SCREAMING_SNAKE_CASE							):
  							return hash(str(self							)							) == hash(str(SCREAMING_SNAKE_CASE							)							)
  					return False
  
  
  
  			def __str__(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					return F'''x: {self.x} y: {self.y}'''
  
  
  
  
  
  
  
  def   UpperCamelCase__     (		lowercase__  :     Any       ,     lowercase__  :     bool = True       ,     lowercase__  :     float = math.inf       ,     lowercase__  :     float = -math.inf       ,     lowercase__  :     float = math.inf       ,     lowercase__  :     float = -math.inf       ,     lowercase__  :     bool = False       ,     lowercase__  :     int = 1_0000       ,     ):
  		snake_case		:						List[str]								=				search_prob
  		snake_case		:						Tuple								=				[]  # list to store the current score at each iteration
  		snake_case		:						Union[str, Any]								=				0
  		snake_case		:						Dict								=				False
  		snake_case		:						Dict								=				set()
  		while not solution_found and iterations < max_iter:
  				visited.add(lowercase__   )
  				iterations += 1
  				snake_case		:						List[str]								=				current_state.score()
  				scores.append(lowercase__   )
  				snake_case		:						Any								=				current_state.get_neighbors()
  				snake_case		:						str								=				-math.inf
  				snake_case		:						int								=				math.inf
  				snake_case		:						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
  						snake_case		:						List[Any]								=				neighbor.score() - current_score
  						if find_max:  # finding max
  								# going to direction with greatest ascent
  								if change > max_change and change > 0:
  										snake_case		:						Union[str, Any]								=				change
  										snake_case		:						List[Any]								=				neighbor
  						else:  # finding min
  								# to direction with greatest descent
  								if change < min_change and change < 0:
  										snake_case		:						str								=				change
  										snake_case		:						Tuple								=				neighbor
  				if next_state is not None:
  						# we found at least one neighbor which improved the current state
  						snake_case		:						List[Any]								=				next_state
  				else:
  						# since we have no neighbor that improves the solution we stop the search
  						snake_case		:						Union[str, Any]								=				True
  
  		if visualization:
  				from matplotlib import pyplot as plt
  
  				plt.plot(range(lowercase__   )       ,     lowercase__   )
  				plt.xlabel("Iterations"   )
  				plt.ylabel("Function values"   )
  				plt.show()
  
  		return current_state
  
  
  if __name__ == "__main__":
  							import doctest
  
  							doctest.testmod()
  
  
  
  							def   UpperCamelCase__     (		lowercase__  :     Any       ,     lowercase__  :     Union[str, Any]   ):
  									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   UpperCamelCase__     (		lowercase__  :     Optional[Any]       ,     lowercase__  :     Tuple   ):
  									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()}'
  							)
  
  
style_context: 
  
  
  
  
  """simple docstring"""
  
  import unittest
  
  import numpy as np
  import PIL
  import torch
  
  from diffusers.image_processor import VaeImageProcessor
  class 			lowerCamelCase__    (  unittest.TestCase			):
  
  
  			@property
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						int								=				1
  					snake_case		:						Dict								=				3
  					snake_case		:						int								=				8
  					snake_case		:						int								=				8
  
  					snake_case		:						List[str]								=				torch.rand((batch_size, num_channels, height, width)							)
  
  					return sample
  
  
  			def 							lowerCamelCase_				(     self				, SCREAMING_SNAKE_CASE							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					if isinstance(image[0]				, PIL.Image.Image							):
  							return np.stack([np.array(SCREAMING_SNAKE_CASE							) for i in image]				, axis=0							)
  					elif isinstance(SCREAMING_SNAKE_CASE				, torch.Tensor							):
  							return image.cpu().numpy().transpose(0				, 2				, 3				, 1							)
  					return image
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						Optional[int]								=				VaeImageProcessor(do_resize=SCREAMING_SNAKE_CASE				, do_normalize=SCREAMING_SNAKE_CASE							)
  
  					snake_case		:						Any								=				self.dummy_sample
  					snake_case		:						Optional[Any]								=				self.to_np(SCREAMING_SNAKE_CASE							)
  
  					for output_type in ["pt", "np", "pil"]:
  							snake_case		:						Optional[Any]								=				image_processor.postprocess(
  							    image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type=SCREAMING_SNAKE_CASE				, )
  							snake_case		:						Optional[Any]								=				self.to_np(SCREAMING_SNAKE_CASE							)
  							snake_case		:						Any								=				(input_np * 255).round() if output_type == "pil" else input_np
  							assert (
  							    np.abs(in_np - out_np							).max() < 1E-6
  							), F'''decoded output does not match input for output_type {output_type}'''
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						Dict								=				VaeImageProcessor(do_resize=SCREAMING_SNAKE_CASE				, do_normalize=SCREAMING_SNAKE_CASE							)
  					snake_case		:						Tuple								=				self.dummy_sample.cpu().numpy().transpose(0				, 2				, 3				, 1							)
  
  					for output_type in ["pt", "np", "pil"]:
  							snake_case		:						Dict								=				image_processor.postprocess(image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type=SCREAMING_SNAKE_CASE							)
  
  							snake_case		:						Union[str, Any]								=				self.to_np(SCREAMING_SNAKE_CASE							)
  							snake_case		:						Tuple								=				(input_np * 255).round() if output_type == "pil" else input_np
  							assert (
  							    np.abs(in_np - out_np							).max() < 1E-6
  							), F'''decoded output does not match input for output_type {output_type}'''
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						Optional[Any]								=				VaeImageProcessor(do_resize=SCREAMING_SNAKE_CASE				, do_normalize=SCREAMING_SNAKE_CASE							)
  
  					snake_case		:						str								=				self.dummy_sample.cpu().numpy().transpose(0				, 2				, 3				, 1							)
  					snake_case		:						int								=				image_processor.numpy_to_pil(SCREAMING_SNAKE_CASE							)
  
  					for output_type in ["pt", "np", "pil"]:
  							snake_case		:						Dict								=				image_processor.postprocess(image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type=SCREAMING_SNAKE_CASE							)
  							for i, o in zip(SCREAMING_SNAKE_CASE				, SCREAMING_SNAKE_CASE							):
  									snake_case		:						Dict								=				np.array(SCREAMING_SNAKE_CASE							)
  									snake_case		:						Tuple								=				self.to_np(SCREAMING_SNAKE_CASE							) if output_type == "pil" else (self.to_np(SCREAMING_SNAKE_CASE							) * 255).round()
  									assert (
  									    np.abs(in_np - out_np							).max() < 1E-6
  									), F'''decoded output does not match input for output_type {output_type}'''
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						Tuple								=				VaeImageProcessor(do_resize=SCREAMING_SNAKE_CASE				, do_normalize=SCREAMING_SNAKE_CASE							)
  
  					snake_case		:						List[str]								=				self.dummy_sample
  					snake_case		:						Optional[int]								=				input_pt_ad.squeeze(0							)
  
  					snake_case		:						Any								=				image_processor.postprocess(
  					    image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type="np"				, )
  					snake_case		:						Union[str, Any]								=				image_processor.postprocess(
  					    image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type="np"				, )
  
  					snake_case		:						Union[str, Any]								=				self.to_np(self.dummy_sample							)
  					snake_case		:						Tuple								=				input_np_ad.squeeze(0							)
  
  					snake_case		:						str								=				image_processor.postprocess(
  					    image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type="np"				, )
  					snake_case		:						Union[str, Any]								=				image_processor.postprocess(
  					    image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type="np"				, )
  
  					assert np.abs(out_pt_ad - out_pt_ad							).max() < 1E-6
  					assert np.abs(out_np_ad - out_np_ad							).max() < 1E-6
  
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						Optional[Any]								=				VaeImageProcessor(do_resize=SCREAMING_SNAKE_CASE				, do_normalize=SCREAMING_SNAKE_CASE							)
  
  					snake_case		:						Union[str, Any]								=				self.dummy_sample
  					snake_case		:						List[str]								=				list(SCREAMING_SNAKE_CASE							)
  
  					snake_case		:						str								=				image_processor.postprocess(
  					    image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type="np"				, )
  
  					snake_case		:						Any								=				image_processor.postprocess(
  					    image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type="np"				, )
  
  					snake_case		:						Dict								=				self.to_np(self.dummy_sample							)
  					list(SCREAMING_SNAKE_CASE							)
  
  					snake_case		:						str								=				image_processor.postprocess(
  					    image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type="np"				, )
  
  					snake_case		:						Union[str, Any]								=				image_processor.postprocess(
  					    image_processor.preprocess(SCREAMING_SNAKE_CASE							)				, output_type="np"				, )
  
  					assert np.abs(out_pt_ad - out_pt_list							).max() < 1E-6
  					assert np.abs(out_np_ad - out_np_list							).max() < 1E-6
  
  