



def 	UpperCAmelCase   (						_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase    ):
			global f  # a global dp table for knapsack
			if f[i][j] < 0:
						if j < wt[i - 1]:
									A							:					int              =						mf_knapsack(i - 1 ,    _lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase    )
						else:
									A							:					Any              =						max(
									    mf_knapsack(i - 1 ,    _lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase    ) ,    mf_knapsack(i - 1 ,    _lowerCamelCase ,    _lowerCamelCase ,    j - wt[i - 1]    ) + val[i - 1] ,    )
						A							:					List[Any]              =						val
			return f[i][j]




def 	UpperCAmelCase   (						_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase    ):
			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							:					Union[str, Any]              =						max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]] ,    dp[i - 1][w_]    )
									else:
												A							:					Any              =						dp[i - 1][w_]

			return dp[n][w_], dp




def 	UpperCAmelCase   (						_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase    ):
			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							:					List[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							:					str              =						(
									    "All weights must be integers but got weight of "
									    f"""type {type(wt[i]    )} at index {i}"""
									)
									raise TypeError(_lowerCamelCase    )

			A       , A							:					Optional[Any]              =						knapsack(_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase    )
			A							:					set              =						set()
			_construct_solution(_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase    )

			return optimal_val, example_optional_set




def 	UpperCAmelCase   (						_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase    ):
			# 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__":
							__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)




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__SCREAMING_SNAKE_CASE           =  {
    """configuration_instructblip""": [
        """INSTRUCTBLIP_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """InstructBlipConfig""",
        """InstructBlipQFormerConfig""",
        """InstructBlipVisionConfig""",
    ],
    """processing_instructblip""": ["""InstructBlipProcessor"""],
}

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__SCREAMING_SNAKE_CASE           =  [
							    """INSTRUCTBLIP_PRETRAINED_MODEL_ARCHIVE_LIST""",
							    """InstructBlipQFormerModel""",
							    """InstructBlipPreTrainedModel""",
							    """InstructBlipForConditionalGeneration""",
							    """InstructBlipVisionModel""",
							]

if TYPE_CHECKING:
							from .configuration_instructblip import (
							    INSTRUCTBLIP_PRETRAINED_CONFIG_ARCHIVE_MAP,
							    InstructBlipConfig,
							    InstructBlipQFormerConfig,
							    InstructBlipVisionConfig,
							)
							from .processing_instructblip import InstructBlipProcessor

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_instructblip import (
														    INSTRUCTBLIP_PRETRAINED_MODEL_ARCHIVE_LIST,
														    InstructBlipForConditionalGeneration,
														    InstructBlipPreTrainedModel,
														    InstructBlipQFormerModel,
														    InstructBlipVisionModel,
														)

else:
							import sys

							__SCREAMING_SNAKE_CASE           =  _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)