





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






def 					SCREAMING_SNAKE_CASE__				(							UpperCamelCase__:				Optional[Any]       , UpperCamelCase__:				Any       , UpperCamelCase__:				str       , UpperCamelCase__:				int     ):
		SCREAMING_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_:
								SCREAMING_SNAKE_CASE__								=   max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]       , dp[i - 1][w_]     )
						else:
								SCREAMING_SNAKE_CASE__								=   dp[i - 1][w_]

		return dp[n][w_], dp






def 					SCREAMING_SNAKE_CASE__				(							UpperCamelCase__:				int       , UpperCamelCase__:				list       , UpperCamelCase__:				list     ):
		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"""     )

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

		SCREAMING_SNAKE_CASE__						,    SCREAMING_SNAKE_CASE__								=   knapsack(UpperCamelCase__       , UpperCamelCase__       , UpperCamelCase__       , UpperCamelCase__     )
		SCREAMING_SNAKE_CASE__								=   set()
		_construct_solution(UpperCamelCase__       , UpperCamelCase__       , UpperCamelCase__       , UpperCamelCase__       , UpperCamelCase__     )

		return optimal_val, example_optional_set






def 					SCREAMING_SNAKE_CASE__				(							UpperCamelCase__:				list       , UpperCamelCase__:				list       , UpperCamelCase__:				int       , UpperCamelCase__:				int       , UpperCamelCase__:				set     ):
		# 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(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__":
	_lowerCamelCase 					=      [3, 2, 4, 4]
	_lowerCamelCase 					=      [4, 3, 2, 3]
	_lowerCamelCase 					=      4
	_lowerCamelCase 					=      6
	_lowerCamelCase 					=      [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
	_lowerCamelCase					,							_lowerCamelCase 					=      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 					=      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_flax_available, is_torch_available


_lowerCamelCase 					=      {'configuration_speech_encoder_decoder': ['SpeechEncoderDecoderConfig']}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	_lowerCamelCase 					=      ['SpeechEncoderDecoderModel']

try:
	if not is_flax_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	_lowerCamelCase 					=      ['FlaxSpeechEncoderDecoderModel']

if TYPE_CHECKING:
	from .configuration_speech_encoder_decoder import SpeechEncoderDecoderConfig

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_speech_encoder_decoder import SpeechEncoderDecoderModel

	try:
		if not is_flax_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_flax_speech_encoder_decoder import FlaxSpeechEncoderDecoderModel

else:
	import sys

	_lowerCamelCase 					=      _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)