






def    __lowerCAmelCase   (    __snake_case       ,			__snake_case       ,			__snake_case       ,			__snake_case							):
     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   (    __snake_case       ,			__snake_case       ,			__snake_case       ,			__snake_case							):
     __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   (    __snake_case       ,			__snake_case       ,			__snake_case							):


     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   (    __snake_case       ,			__snake_case       ,			__snake_case       ,			__snake_case       ,			__snake_case							):


     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__":
 lowerCamelCase      :       str    =						[3, 2, 4, 4]
 lowerCamelCase      :       Tuple    =						[4, 3, 2, 3]
 lowerCamelCase      :       Any    =						4
 lowerCamelCase      :       int    =						6
 lowerCamelCase      :       List[Any]    =						[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
 lowerCamelCase   ,       lowerCamelCase      :       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
 lowerCamelCase   ,       lowerCamelCase      :       int    =						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



