
def   lowerCamelCase__							(							__lowerCAmelCase    :    Dict       ,				__lowerCAmelCase    :    List[str]       ,				__lowerCAmelCase    :    Optional[Any]       ,				__lowerCAmelCase    :    Any							):




			"""simple docstring"""


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






def   lowerCamelCase__							(							__lowerCAmelCase    :    int       ,				__lowerCAmelCase    :    Optional[Any]       ,				__lowerCAmelCase    :    Any       ,				__lowerCAmelCase    :    Any							):




			"""simple docstring"""


			lowerCAmelCase_         =      [[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_         =      max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]       ,				dp[i - 1][w_]							)
									else:
												lowerCAmelCase_         =      dp[i - 1][w_]

			return dp[n][w_], dp






def   lowerCamelCase__							(							__lowerCAmelCase    :    int       ,				__lowerCAmelCase    :    list       ,				__lowerCAmelCase    :    list							):




			"""simple docstring"""


			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"							)

			lowerCAmelCase_         =      len(__lowerCAmelCase							)
			if num_items != len(__lowerCAmelCase							):
						lowerCAmelCase_         =      (
						    "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							):
									lowerCAmelCase_         =      (
									    "All weights must be integers but got weight of "
									    F"""type {type(wt[i]							)} at index {i}"""
									)
									raise TypeError(__lowerCAmelCase							)

			lowerCAmelCase_      ,    lowerCAmelCase_         =      knapsack(__lowerCAmelCase       ,				__lowerCAmelCase       ,				__lowerCAmelCase       ,				__lowerCAmelCase							)
			lowerCAmelCase_         =      set()
			_construct_solution(__lowerCAmelCase       ,				__lowerCAmelCase       ,				__lowerCAmelCase       ,				__lowerCAmelCase       ,				__lowerCAmelCase							)

			return optimal_val, example_optional_set






def   lowerCamelCase__							(							__lowerCAmelCase    :    list       ,				__lowerCAmelCase    :    list       ,				__lowerCAmelCase    :    int       ,				__lowerCAmelCase    :    int       ,				__lowerCAmelCase    :    set							):




			"""simple docstring"""


			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__":
			_A  =	[3, 2, 4, 4]
			_A  =	[4, 3, 2, 3]
			_A  =	4
			_A  =	6
			_A  =	[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
			_A, _A  =	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, _A  =	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 dataclasses import dataclass
from enum import Enum
from typing import List, Optional, Union

import numpy as np
import PIL
from PIL import Image

from ...utils import BaseOutput, is_torch_available, is_transformers_available





@dataclass
class       _lowerCAmelCase   (      __a			):
				_lowercase     						=42
				_lowercase     						=42


if is_transformers_available() and is_torch_available():
			from .pipeline_semantic_stable_diffusion import SemanticStableDiffusionPipeline



