"""simple docstring"""
def 				lowerCAmelCase__      (     _UpperCamelCase    :			int	,     _UpperCamelCase    :			int	,     _UpperCamelCase    :			Optional[int]	,     _UpperCamelCase    :			Union[str, Any]   )   ->			Optional[int]:





						"""simple docstring"""






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





def 				lowerCAmelCase__      (     _UpperCamelCase    :			List[str]	,     _UpperCamelCase    :			int	,     _UpperCamelCase    :			int	,     _UpperCamelCase    :			List[str]   )   ->			str:





						"""simple docstring"""






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

						return dp[n][w_], dp





def 				lowerCAmelCase__      (     _UpperCamelCase    :			int	,     _UpperCamelCase    :			list	,     _UpperCamelCase    :			list   )   ->			List[Any]:





						"""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'   )

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

						snake_case   ,snake_case        =     knapsack(_UpperCamelCase	,     _UpperCamelCase	,     _UpperCamelCase	,     _UpperCamelCase   )
						snake_case        =     set()
						_construct_solution(_UpperCamelCase	,     _UpperCamelCase	,     _UpperCamelCase	,     _UpperCamelCase	,     _UpperCamelCase   )

						return optimal_val, example_optional_set





def 				lowerCAmelCase__      (     _UpperCamelCase    :			list	,     _UpperCamelCase    :			list	,     _UpperCamelCase    :			int	,     _UpperCamelCase    :			int	,     _UpperCamelCase    :			set   )   ->			Union[str, Any]:





						"""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__":
					SCREAMING_SNAKE_CASE__   =					[3, 2, 4, 4]
					SCREAMING_SNAKE_CASE__   =					[4, 3, 2, 3]
					SCREAMING_SNAKE_CASE__   =					4
					SCREAMING_SNAKE_CASE__   =					6
					SCREAMING_SNAKE_CASE__   =					[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
					SCREAMING_SNAKE_CASE__  ,    SCREAMING_SNAKE_CASE__   =					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
					SCREAMING_SNAKE_CASE__  ,    SCREAMING_SNAKE_CASE__   =					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)



"""simple docstring"""
from ..utils import DummyObject, requires_backends



class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Dict     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Optional[Any]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Optional[Any]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Union[str, Any]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Optional[int]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Dict     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Union[str, Any]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Union[str, Any]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Optional[int]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Any     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Union[str, Any]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      List[Any]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      str     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Tuple     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Union[str, Any]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Union[str, Any]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      str     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Tuple     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Any     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Tuple     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Tuple     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      int     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Any     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Optional[int]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      int     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Dict     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Any     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Union[str, Any]     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      str     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Dict     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )





class 					lowerCAmelCase_      (     metaclass=lowerCAmelCase   ):



				"""simple docstring"""
				_lowerCAmelCase       :      Tuple     					=  ["""sentencepiece"""]

				def __init__(			self						,      *lowerCAmelCase						,      **lowerCAmelCase      ):






										"""simple docstring"""

										requires_backends(self						,      ['sentencepiece']      )


