



def      _A				(UpperCamelCase		:      str      ,			UpperCamelCase		:      Optional[Any]      ,			UpperCamelCase		:      Any      ,			UpperCamelCase		:      Tuple )  ->List[str]:



			'''simple docstring'''







			global f  # a global dp table for knapsack
			if f[i][j] < 0:
						if j < wt[i - 1]:
									lowerCamelCase__ :      Any								=		mf_knapsack(i - 1      ,			UpperCamelCase      ,			UpperCamelCase      ,			UpperCamelCase )
						else:
									lowerCamelCase__ :      Optional[int]								=		max(
									    mf_knapsack(i - 1      ,			UpperCamelCase      ,			UpperCamelCase      ,			UpperCamelCase )      ,			mf_knapsack(i - 1      ,			UpperCamelCase      ,			UpperCamelCase      ,			j - wt[i - 1] ) + val[i - 1]      ,			)
						lowerCamelCase__ :      Optional[int]								=		val
			return f[i][j]






def      _A				(UpperCamelCase		:      str      ,			UpperCamelCase		:      Optional[int]      ,			UpperCamelCase		:      List[Any]      ,			UpperCamelCase		:      List[Any] )  ->List[Any]:



			'''simple docstring'''







			lowerCamelCase__ :      int								=		[[0] * (w + 1) for _ in range(n + 1 )]

			for i in range(1      ,			n + 1 ):
						for w_ in range(1      ,			w + 1 ):
									if wt[i - 1] <= w_:
												lowerCamelCase__ :      Dict								=		max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]      ,			dp[i - 1][w_] )
									else:
												lowerCamelCase__ :      List[str]								=		dp[i - 1][w_]

			return dp[n][w_], dp






def      _A				(UpperCamelCase		:      int      ,			UpperCamelCase		:      list      ,			UpperCamelCase		:      list )  ->Tuple:



			'''simple docstring'''







			if not (isinstance(UpperCamelCase      ,			(list, tuple) ) and isinstance(UpperCamelCase      ,			(list, tuple) )):
						raise ValueError(
						    """Both the weights and values vectors must be either lists or tuples""" )

			lowerCamelCase__ :      int								=		len(UpperCamelCase )
			if num_items != len(UpperCamelCase ):
						lowerCamelCase__ :      List[str]								=		(
						    """The number of weights must be the same as the number of values.\n"""
						    f"But got {num_items} weights and {len(UpperCamelCase )} values"
						)
						raise ValueError(UpperCamelCase )
			for i in range(UpperCamelCase ):
						if not isinstance(wt[i]      ,			UpperCamelCase ):
									lowerCamelCase__ :      List[Any]								=		(
									    """All weights must be integers but got weight of """
									    f"type {type(wt[i] )} at index {i}"
									)
									raise TypeError(UpperCamelCase )

			lowerCamelCase__							,lowerCamelCase__ :      List[str]								=		knapsack(UpperCamelCase      ,			UpperCamelCase      ,			UpperCamelCase      ,			UpperCamelCase )
			lowerCamelCase__ :      set								=		set()
			_construct_solution(UpperCamelCase      ,			UpperCamelCase      ,			UpperCamelCase      ,			UpperCamelCase      ,			UpperCamelCase )

			return optimal_val, example_optional_set






def      _A				(UpperCamelCase		:      list      ,			UpperCamelCase		:      list      ,			UpperCamelCase		:      int      ,			UpperCamelCase		:      int      ,			UpperCamelCase		:      set )  ->Tuple:



			'''simple docstring'''







			if i > 0 and j > 0:
						if dp[i - 1][j] == dp[i][j]:
									_construct_solution(UpperCamelCase      ,			UpperCamelCase      ,			i - 1      ,			UpperCamelCase      ,			UpperCamelCase )
						else:
									optimal_set.add(UpperCamelCase )
									_construct_solution(UpperCamelCase      ,			UpperCamelCase      ,			i - 1      ,			j - wt[i - 1]      ,			UpperCamelCase )


if __name__ == "__main__":
				_lowercase     							=						[3, 2, 4, 4]
				_lowercase     							=						[4, 3, 2, 3]
				_lowercase     							=						4
				_lowercase     							=						6
				_lowercase     							=						[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
				_lowercase							,				_lowercase     							=						knapsack(w, wt, val, n)
				print(optimal_solution)
				print(mf_knapsack(n, wt, val, w))  # switched the n and w

				# testing the dynamic programming problem with example
				# the optimal subset for the above example are items 3 and 4
				_lowercase							,				_lowercase     							=						knapsack_with_example_solution(w, wt, val)
				assert optimal_solution == 8
				assert optimal_subset == {3, 4}
				print('''optimal_value = ''', optimal_solution)
				print('''An optimal subset corresponding to the optimal value''', optimal_subset)








from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import center_crop, normalize, rescale, resize, to_channel_dimension_format
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
				import PIL


_lowercase     							=						logging.get_logger(__name__)
class 				__A					( A_      ):
			UpperCamelCase					:Union[str, Any]     =			['''pixel_values''']





			def __init__(self							,    __magic_name__ = True							,    __magic_name__ = None							,    __magic_name__ = PIL.Image.BICUBIC							,    __magic_name__ = True							,    __magic_name__ = None							,    __magic_name__ = 1 / 255							,    __magic_name__ = True							,    __magic_name__ = True							,    __magic_name__ = None							,    __magic_name__ = None							,    **__magic_name__							,    ):
						super().__init__(**__magic_name__				)
						lowerCamelCase__ :      str								=		size if size is not None else {"""height""": 256, """width""": 256}
						lowerCamelCase__ :      Optional[int]								=		get_size_dict(__magic_name__				)
						lowerCamelCase__ :      Any								=		crop_size if crop_size is not None else {"""height""": 224, """width""": 224}
						lowerCamelCase__ :      Optional[int]								=		get_size_dict(__magic_name__							,    param_name="""crop_size"""				)

						lowerCamelCase__ :      str								=		do_resize
						lowerCamelCase__ :      Any								=		size
						lowerCamelCase__ :      Tuple								=		resample
						lowerCamelCase__ :      Union[str, Any]								=		do_center_crop
						lowerCamelCase__ :      List[str]								=		crop_size
						lowerCamelCase__ :      int								=		do_rescale
						lowerCamelCase__ :      Any								=		rescale_factor
						lowerCamelCase__ :      Dict								=		do_normalize
						lowerCamelCase__ :      Dict								=		image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
						lowerCamelCase__ :      int								=		image_std if image_std is not None else IMAGENET_STANDARD_STD





			def        _snake_case    (self							,    __magic_name__							,    __magic_name__							,    __magic_name__ = PIL.Image.BICUBIC							,    __magic_name__ = None							,    **__magic_name__							,    ):
						lowerCamelCase__ :      Optional[int]								=		get_size_dict(__magic_name__				)
						if "height" not in size or "width" not in size:
									raise ValueError(f"The size dictionary must have keys 'height' and 'width'. Got {size.keys()}"				)
						return resize(
						    __magic_name__							,    size=(size["""height"""], size["""width"""])							,    resample=__magic_name__							,    data_format=__magic_name__							,    **__magic_name__				)





			def        _snake_case    (self							,    __magic_name__							,    __magic_name__							,    __magic_name__ = None							,    **__magic_name__							,    ):
						lowerCamelCase__ :      Tuple								=		get_size_dict(__magic_name__				)
						if "height" not in size or "width" not in size:
									raise ValueError(f"The size dictionary must have keys 'height' and 'width'. Got {size.keys()}"				)
						return center_crop(__magic_name__							,    size=(size["""height"""], size["""width"""])							,    data_format=__magic_name__							,    **__magic_name__				)





			def        _snake_case    (self							,    __magic_name__							,    __magic_name__							,    __magic_name__ = None							,    **__magic_name__							,    ):
						return rescale(__magic_name__							,    scale=__magic_name__							,    data_format=__magic_name__							,    **__magic_name__				)





			def        _snake_case    (self							,    __magic_name__							,    __magic_name__							,    __magic_name__							,    __magic_name__ = None							,    **__magic_name__							,    ):
						return normalize(__magic_name__							,    mean=__magic_name__							,    std=__magic_name__							,    data_format=__magic_name__							,    **__magic_name__				)





			def        _snake_case    (self							,    __magic_name__							,    __magic_name__ = None							,    __magic_name__ = None							,    __magic_name__=None							,    __magic_name__ = None							,    __magic_name__ = None							,    __magic_name__ = None							,    __magic_name__ = None							,    __magic_name__ = None							,    __magic_name__ = None							,    __magic_name__ = None							,    __magic_name__ = None							,    __magic_name__ = ChannelDimension.FIRST							,    **__magic_name__							,    ):
						lowerCamelCase__ :      Tuple								=		do_resize if do_resize is not None else self.do_resize
						lowerCamelCase__ :      str								=		resample if resample is not None else self.resample
						lowerCamelCase__ :      str								=		do_center_crop if do_center_crop is not None else self.do_center_crop
						lowerCamelCase__ :      Optional[int]								=		do_rescale if do_rescale is not None else self.do_rescale
						lowerCamelCase__ :      str								=		rescale_factor if rescale_factor is not None else self.rescale_factor
						lowerCamelCase__ :      Union[str, Any]								=		do_normalize if do_normalize is not None else self.do_normalize
						lowerCamelCase__ :      Tuple								=		image_mean if image_mean is not None else self.image_mean
						lowerCamelCase__ :      List[Any]								=		image_std if image_std is not None else self.image_std

						lowerCamelCase__ :      str								=		size if size is not None else self.size
						lowerCamelCase__ :      List[str]								=		get_size_dict(__magic_name__				)
						lowerCamelCase__ :      Tuple								=		crop_size if crop_size is not None else self.crop_size
						lowerCamelCase__ :      Optional[Any]								=		get_size_dict(__magic_name__							,    param_name="""crop_size"""				)

						lowerCamelCase__ :      Optional[int]								=		make_list_of_images(__magic_name__				)

						if not valid_images(__magic_name__				):
									raise ValueError(
									    """Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, """
									    """torch.Tensor, tf.Tensor or jax.ndarray."""				)

						if do_resize and size is None or resample is None:
									raise ValueError("""Size and resample must be specified if do_resize is True."""				)

						if do_center_crop and crop_size is None:
									raise ValueError("""Crop size must be specified if do_center_crop is True."""				)

						if do_rescale and rescale_factor is None:
									raise ValueError("""Rescale factor must be specified if do_rescale is True."""				)

						if do_normalize and (image_mean is None or image_std is None):
									raise ValueError("""Image mean and std must be specified if do_normalize is True."""				)

						# All transformations expect numpy arrays.
						lowerCamelCase__ :      Optional[int]								=		[to_numpy_array(__magic_name__				) for image in images]

						if do_resize:
									lowerCamelCase__ :      int								=		[self.resize(image=__magic_name__							,    size=__magic_name__							,    resample=__magic_name__				) for image in images]

						if do_center_crop:
									lowerCamelCase__ :      List[Any]								=		[self.center_crop(image=__magic_name__							,    size=__magic_name__				) for image in images]

						if do_rescale:
									lowerCamelCase__ :      Dict								=		[self.rescale(image=__magic_name__							,    scale=__magic_name__				) for image in images]

						if do_normalize:
									lowerCamelCase__ :      Optional[Any]								=		[self.normalize(image=__magic_name__							,    mean=__magic_name__							,    std=__magic_name__				) for image in images]

						lowerCamelCase__ :      List[str]								=		[to_channel_dimension_format(__magic_name__							,    __magic_name__				) for image in images]

						lowerCamelCase__ :      Dict								=		{"""pixel_values""": images}
						return BatchFeature(data=__magic_name__							,    tensor_type=__magic_name__				)



