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




def    __UpperCamelCase     (				lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				str  ,   lowerCAmelCase__							:				Dict  ,   lowerCAmelCase__							:				int  ):
 __a :  str						=  [[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_:
    __a :  List[Any]						=  max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]  ,   dp[i - 1][w_]  )
   else:
    __a :  Union[str, Any]						=  dp[i - 1][w_]

 return dp[n][w_], dp




def    __UpperCamelCase     (				lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				list  ,   lowerCAmelCase__							:				list  ):
 if not (isinstance(lowerCAmelCase__  ,   (list, tuple)  ) and isinstance(lowerCAmelCase__  ,   (list, tuple)  )):
  raise ValueError(
      '''Both the weights and values vectors must be either lists or tuples'''  )

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

 __a				,       __a :  Dict						=  knapsack(lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
 __a :  set						=  set()
 _construct_solution(lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )

 return optimal_val, example_optional_set




def    __UpperCamelCase     (				lowerCAmelCase__							:				list  ,   lowerCAmelCase__							:				list  ,   lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				set  ):
 # for the current item i at a maximum weight j to be part of an optimal subset,
 # the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
 # where i - 1 means considering only the previous items at the given maximum weight
 if i > 0 and j > 0:
  if dp[i - 1][j] == dp[i][j]:
   _construct_solution(lowerCAmelCase__  ,   lowerCAmelCase__  ,   i - 1  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
  else:
   optimal_set.add(lowerCAmelCase__  )
   _construct_solution(lowerCAmelCase__  ,   lowerCAmelCase__  ,   i - 1  ,   j - wt[i - 1]  ,   lowerCAmelCase__  )


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,
    get_resize_output_image_size,
    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 		UpperCamelCase__  (       __lowercase    ):
   _SCREAMING_SNAKE_CASE      :							Optional[Any]	       =      ["pixel_values"]
   def __init__(self :					str					,				snake_case_ :					bool = True					,				snake_case_ :					Dict[str, int] = None					,				snake_case_ :					float = None					,				snake_case_ :					PILImageResampling = PILImageResampling.BILINEAR					,				snake_case_ :					bool = True					,				snake_case_ :					Union[int, float] = 1 / 2_5_5					,				snake_case_ :					bool = True					,				snake_case_ :					Optional[Union[float, List[float]]] = None					,				snake_case_ :					Optional[Union[float, List[float]]] = None					,				**snake_case_ :					Tuple					,				):
    super().__init__(**snake_case_   )
    __a :  Optional[Any]						=  size if size is not None else {'''shortest_edge''': 3_8_4}
    __a :  str						=  get_size_dict(snake_case_					,				default_to_square=snake_case_   )

    __a :  Tuple						=  do_resize
    __a :  List[str]						=  size
    # Default value set here for backwards compatibility where the value in config is None
    __a :  List[str]						=  crop_pct if crop_pct is not None else 2_2_4 / 2_5_6
    __a :  Tuple						=  resample
    __a :  Any						=  do_rescale
    __a :  Optional[Any]						=  rescale_factor
    __a :  int						=  do_normalize
    __a :  List[str]						=  image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
    __a :  Union[str, Any]						=  image_std if image_std is not None else IMAGENET_STANDARD_STD
   def       lowerCAmelCase			(self :					int					,				snake_case_ :					np.ndarray					,				snake_case_ :					Dict[str, int]					,				snake_case_ :					float					,				snake_case_ :					PILImageResampling = PILImageResampling.BICUBIC					,				snake_case_ :					Optional[Union[str, ChannelDimension]] = None					,				**snake_case_ :					str					,				):
    __a :  str						=  get_size_dict(snake_case_					,				default_to_square=snake_case_   )
    if "shortest_edge" not in size:
     raise ValueError(f"Size dictionary must contain 'shortest_edge' key. Got {size.keys()}"   )
    __a :  Any						=  size['''shortest_edge''']

    if shortest_edge < 3_8_4:
     # maintain same ratio, resizing shortest edge to shortest_edge/crop_pct
     __a :  Union[str, Any]						=  int(shortest_edge / crop_pct   )
     __a :  Tuple						=  get_resize_output_image_size(snake_case_					,				size=snake_case_					,				default_to_square=snake_case_   )
     __a :  List[str]						=  resize(image=snake_case_					,				size=snake_case_					,				resample=snake_case_					,				data_format=snake_case_					,				**snake_case_   )
     # then crop to (shortest_edge, shortest_edge)
     return center_crop(image=snake_case_					,				size=(shortest_edge, shortest_edge)					,				data_format=snake_case_					,				**snake_case_   )
    else:
     # warping (no cropping) when evaluated at 384 or larger
     return resize(
         snake_case_					,				size=(shortest_edge, shortest_edge)					,				resample=snake_case_					,				data_format=snake_case_					,				**snake_case_   )
   def       lowerCAmelCase			(self :					Optional[int]					,				snake_case_ :					np.ndarray					,				snake_case_ :					Union[int, float]					,				snake_case_ :					Optional[Union[str, ChannelDimension]] = None					,				**snake_case_ :					Union[str, Any]					,				):
    return rescale(snake_case_					,				scale=snake_case_					,				data_format=snake_case_					,				**snake_case_   )
   def       lowerCAmelCase			(self :					Union[str, Any]					,				snake_case_ :					np.ndarray					,				snake_case_ :					Union[float, List[float]]					,				snake_case_ :					Union[float, List[float]]					,				snake_case_ :					Optional[Union[str, ChannelDimension]] = None					,				**snake_case_ :					Union[str, Any]					,				):
    return normalize(snake_case_					,				mean=snake_case_					,				std=snake_case_					,				data_format=snake_case_					,				**snake_case_   )







   def       lowerCAmelCase			(self :					Dict					,				snake_case_ :					ImageInput					,				snake_case_ :					bool = None					,				snake_case_ :					Dict[str, int] = None					,				snake_case_ :					float = None					,				snake_case_ :					PILImageResampling = None					,				snake_case_ :					bool = None					,				snake_case_ :					float = None					,				snake_case_ :					bool = None					,				snake_case_ :					Optional[Union[float, List[float]]] = None					,				snake_case_ :					Optional[Union[float, List[float]]] = None					,				snake_case_ :					Optional[Union[str, TensorType]] = None					,				snake_case_ :					ChannelDimension = ChannelDimension.FIRST					,				**snake_case_ :					Dict					,				):
    __a :  List[Any]						=  do_resize if do_resize is not None else self.do_resize
    __a :  Dict						=  crop_pct if crop_pct is not None else self.crop_pct
    __a :  Tuple						=  resample if resample is not None else self.resample
    __a :  Optional[int]						=  do_rescale if do_rescale is not None else self.do_rescale
    __a :  Optional[int]						=  rescale_factor if rescale_factor is not None else self.rescale_factor
    __a :  int						=  do_normalize if do_normalize is not None else self.do_normalize
    __a :  Optional[int]						=  image_mean if image_mean is not None else self.image_mean
    __a :  Optional[int]						=  image_std if image_std is not None else self.image_std

    __a :  Dict						=  size if size is not None else self.size
    __a :  List[str]						=  get_size_dict(snake_case_					,				default_to_square=snake_case_   )

    __a :  List[str]						=  make_list_of_images(snake_case_   )

    if not valid_images(snake_case_   ):
     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_resize and size["shortest_edge"] < 3_8_4 and crop_pct is None:
     raise ValueError('''crop_pct must be specified if size < 384.'''   )

    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.
    __a :  List[Any]						=  [to_numpy_array(snake_case_   ) for image in images]

    if do_resize:
     __a :  List[str]						=  [self.resize(image=snake_case_					,				size=snake_case_					,				crop_pct=snake_case_					,				resample=snake_case_   ) for image in images]

    if do_rescale:
     __a :  List[Any]						=  [self.rescale(image=snake_case_					,				scale=snake_case_   ) for image in images]

    if do_normalize:
     __a :  Optional[int]						=  [self.normalize(image=snake_case_					,				mean=snake_case_					,				std=snake_case_   ) for image in images]

    __a :  str						=  [to_channel_dimension_format(snake_case_					,				snake_case_   ) for image in images]

    __a :  Tuple						=  {'''pixel_values''': images}
    return BatchFeature(data=snake_case_					,				tensor_type=snake_case_   )
