






def 						a    (		lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				global f  # a global dp table for knapsack
				if f[i][j] < 0:
								if j < wt[i - 1]:
												lowercase__     				=    mf_knapsack(i - 1	,     __A	,     __A	,     __A       )
								else:
												lowercase__     				=    max(
												    mf_knapsack(i - 1	,     __A	,     __A	,     __A       )	,     mf_knapsack(i - 1	,     __A	,     __A	,     j - wt[i - 1]       ) + val[i - 1]	,     )
								lowercase__     				=    val
				return f[i][j]


def 						a    (		lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				lowercase__     				=    [[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_:
																lowercase__     				=    max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]	,     dp[i - 1][w_]       )
												else:
																lowercase__     				=    dp[i - 1][w_]

				return dp[n][w_], dp


def 						a    (		lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				if not (isinstance(__A	,     (list, tuple)       ) and isinstance(__A	,     (list, tuple)       )):
								raise ValueError(
								    '''Both the weights and values vectors must be either lists or tuples'''       )

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

				lowercase__     				=    knapsack(__A	,     __A	,     __A	,     __A       )
				lowercase__     				=    set()
				_construct_solution(__A	,     __A	,     __A	,     __A	,     __A       )

				return optimal_val, example_optional_set


def 						a    (		lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				# 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(__A	,     __A	,     i - 1	,     __A	,     __A       )
								else:
												optimal_set.add(__A       )
												_construct_solution(__A	,     __A	,     i - 1	,     j - wt[i - 1]	,     __A       )


if __name__ == "__main__":
							A__			:    Any         =				[3, 2, 4, 4]
							A__			:    str         =				[4, 3, 2, 3]
							A__			:    Dict         =				4
							A__			:    str         =				6
							A__			:    List[str]         =				[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
							A__			:    Union[str, Any]         =				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
							A__			:    Optional[Any]         =				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)












import unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
							import torch

if is_vision_available():
							from PIL import Image

							from transformers import MobileNetVaImageProcessor
class    _UpperCAmelCase      ( unittest.TestCase			):

				"""simple docstring"""




				def __init__(  self		:					str,						lowerCamelCase		:					Any,						lowerCamelCase		:					Tuple=7,						lowerCamelCase		:					str=3,						lowerCamelCase		:					Tuple=18,						lowerCamelCase		:					int=30,						lowerCamelCase		:					Tuple=400,						lowerCamelCase		:					Any=True,						lowerCamelCase		:					Any=None,						lowerCamelCase		:					List[str]=True,						lowerCamelCase		:					Union[str, Any]=None,						):

								'''simple docstring'''
								lowercase__     				=    size if size is not None else {'''shortest_edge''': 20}
								lowercase__     				=    crop_size if crop_size is not None else {'''height''': 18, '''width''': 18}
								lowercase__     				=    parent
								lowercase__     				=    batch_size
								lowercase__     				=    num_channels
								lowercase__     				=    image_size
								lowercase__     				=    min_resolution
								lowercase__     				=    max_resolution
								lowercase__     				=    do_resize
								lowercase__     				=    size
								lowercase__     				=    do_center_crop
								lowercase__     				=    crop_size




				def        lowercase__     (  self		:					Any						):

								'''simple docstring'''
								return {
								    "do_resize": self.do_resize,
								    "size": self.size,
								    "do_center_crop": self.do_center_crop,
								    "crop_size": self.crop_size,
								}



@require_torch
@require_vision
class    _UpperCAmelCase      ( A__	,unittest.TestCase			):

				"""simple docstring"""




				lowercase__       							= MobileNetVaImageProcessor if is_vision_available() else None




				def        lowercase__     (  self		:					Any						):

								'''simple docstring'''
								lowercase__     				=    MobileNetVaImageProcessingTester(self						)




				@property
				def        lowercase__     (  self		:					Union[str, Any]						):

								'''simple docstring'''
								return self.image_processor_tester.prepare_image_processor_dict()




				def        lowercase__     (  self		:					Dict						):

								'''simple docstring'''
								lowercase__     				=    self.image_processing_class(**self.image_processor_dict						)
								self.assertTrue(hasattr(lowerCamelCase,						'''do_resize'''						)						)
								self.assertTrue(hasattr(lowerCamelCase,						'''size'''						)						)
								self.assertTrue(hasattr(lowerCamelCase,						'''do_center_crop'''						)						)
								self.assertTrue(hasattr(lowerCamelCase,						'''crop_size'''						)						)




				def        lowercase__     (  self		:					Any						):

								'''simple docstring'''
								lowercase__     				=    self.image_processing_class.from_dict(self.image_processor_dict						)
								self.assertEqual(image_processor.size,						{'''shortest_edge''': 20}						)
								self.assertEqual(image_processor.crop_size,						{'''height''': 18, '''width''': 18}						)

								lowercase__     				=    self.image_processing_class.from_dict(self.image_processor_dict,						size=42,						crop_size=84						)
								self.assertEqual(image_processor.size,						{'''shortest_edge''': 42}						)
								self.assertEqual(image_processor.crop_size,						{'''height''': 84, '''width''': 84}						)




				def        lowercase__     (  self		:					Optional[int]						):

								'''simple docstring'''
								pass




				def        lowercase__     (  self		:					Any						):

								'''simple docstring'''
								# Initialize image_processing
								lowercase__     				=    self.image_processing_class(**self.image_processor_dict						)
								# create random PIL images
								lowercase__     				=    prepare_image_inputs(self.image_processor_tester,						equal_resolution=lowerCamelCase						)
								for image in image_inputs:
												self.assertIsInstance(lowerCamelCase,						Image.Image						)

								# Test not batched input
								lowercase__     				=    image_processing(image_inputs[0],						return_tensors='''pt'''						).pixel_values
								self.assertEqual(
								    encoded_images.shape,						(
								        1,
								        self.image_processor_tester.num_channels,
								        self.image_processor_tester.crop_size['''height'''],
								        self.image_processor_tester.crop_size['''width'''],
								    ),						)

								# Test batched
								lowercase__     				=    image_processing(lowerCamelCase,						return_tensors='''pt'''						).pixel_values
								self.assertEqual(
								    encoded_images.shape,						(
								        self.image_processor_tester.batch_size,
								        self.image_processor_tester.num_channels,
								        self.image_processor_tester.crop_size['''height'''],
								        self.image_processor_tester.crop_size['''width'''],
								    ),						)




				def        lowercase__     (  self		:					str						):

								'''simple docstring'''
								# Initialize image_processing
								lowercase__     				=    self.image_processing_class(**self.image_processor_dict						)
								# create random numpy tensors
								lowercase__     				=    prepare_image_inputs(self.image_processor_tester,						equal_resolution=lowerCamelCase,						numpify=lowerCamelCase						)
								for image in image_inputs:
												self.assertIsInstance(lowerCamelCase,						np.ndarray						)

								# Test not batched input
								lowercase__     				=    image_processing(image_inputs[0],						return_tensors='''pt'''						).pixel_values
								self.assertEqual(
								    encoded_images.shape,						(
								        1,
								        self.image_processor_tester.num_channels,
								        self.image_processor_tester.crop_size['''height'''],
								        self.image_processor_tester.crop_size['''width'''],
								    ),						)

								# Test batched
								lowercase__     				=    image_processing(lowerCamelCase,						return_tensors='''pt'''						).pixel_values
								self.assertEqual(
								    encoded_images.shape,						(
								        self.image_processor_tester.batch_size,
								        self.image_processor_tester.num_channels,
								        self.image_processor_tester.crop_size['''height'''],
								        self.image_processor_tester.crop_size['''width'''],
								    ),						)




				def        lowercase__     (  self		:					str						):

								'''simple docstring'''
								# Initialize image_processing
								lowercase__     				=    self.image_processing_class(**self.image_processor_dict						)
								# create random PyTorch tensors
								lowercase__     				=    prepare_image_inputs(self.image_processor_tester,						equal_resolution=lowerCamelCase,						torchify=lowerCamelCase						)
								for image in image_inputs:
												self.assertIsInstance(lowerCamelCase,						torch.Tensor						)

								# Test not batched input
								lowercase__     				=    image_processing(image_inputs[0],						return_tensors='''pt'''						).pixel_values
								self.assertEqual(
								    encoded_images.shape,						(
								        1,
								        self.image_processor_tester.num_channels,
								        self.image_processor_tester.crop_size['''height'''],
								        self.image_processor_tester.crop_size['''width'''],
								    ),						)

								# Test batched
								lowercase__     				=    image_processing(lowerCamelCase,						return_tensors='''pt'''						).pixel_values
								self.assertEqual(
								    encoded_images.shape,						(
								        self.image_processor_tester.batch_size,
								        self.image_processor_tester.num_channels,
								        self.image_processor_tester.crop_size['''height'''],
								        self.image_processor_tester.crop_size['''width'''],
								    ),						)




