






"""simple docstring"""







def 							lowercase					(snake_case__   : Dict      ,       snake_case__   : Optional[int]      ,       snake_case__   : Optional[Any]      ,       snake_case__   : str )     ->  Dict:


				'''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      ,       snake_case__      ,       snake_case__      ,       snake_case__ )
								else:
												lowerCAmelCase  =				max(
												    mf_knapsack(i - 1      ,       snake_case__      ,       snake_case__      ,       snake_case__ )      ,       mf_knapsack(i - 1      ,       snake_case__      ,       snake_case__      ,       j - wt[i - 1] ) + val[i - 1]      ,       )
								lowerCAmelCase  =				val
				return f[i][j]





def 							lowercase					(snake_case__   : List[str]      ,       snake_case__   : List[Any]      ,       snake_case__   : List[Any]      ,       snake_case__   : List[Any] )     ->  List[str]:


				'''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 							lowercase					(snake_case__   : int      ,       snake_case__   : list      ,       snake_case__   : list )     ->  Dict:


				'''simple docstring'''






				if not (isinstance(snake_case__      ,       (list, tuple) ) and isinstance(snake_case__      ,       (list, tuple) )):
								raise ValueError(
								    """Both the weights and values vectors must be either lists or tuples""" )

				lowerCAmelCase  =				len(snake_case__ )
				if num_items != len(snake_case__ ):
								lowerCAmelCase  =				(
								    """The number of weights must be the same as the number of values.\n"""
								    f'''But got {num_items} weights and {len(snake_case__ )} values'''
								)
								raise ValueError(snake_case__ )
				for i in range(snake_case__ ):
								if not isinstance(wt[i]      ,       snake_case__ ):
												lowerCAmelCase  =				(
												    """All weights must be integers but got weight of """
												    f'''type {type(wt[i] )} at index {i}'''
												)
												raise TypeError(snake_case__ )

				lowerCAmelCase ,						lowerCAmelCase  =				knapsack(snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__ )
				lowerCAmelCase  =				set()
				_construct_solution(snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__ )

				return optimal_val, example_optional_set





def 							lowercase					(snake_case__   : list      ,       snake_case__   : list      ,       snake_case__   : int      ,       snake_case__   : int      ,       snake_case__   : set )     ->  List[str]:


				'''simple docstring'''






				if i > 0 and j > 0:
								if dp[i - 1][j] == dp[i][j]:
												_construct_solution(snake_case__      ,       snake_case__      ,       i - 1      ,       snake_case__      ,       snake_case__ )
								else:
												optimal_set.add(snake_case__ )
												_construct_solution(snake_case__      ,       snake_case__      ,       i - 1      ,       j - wt[i - 1]      ,       snake_case__ )


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)











"""simple docstring"""







from __future__ import annotations





def 							lowercase					(snake_case__   : list[int]      ,       snake_case__   : int      ,       snake_case__   : int      ,       snake_case__   : int )     ->  None:


				'''simple docstring'''






				if (direction == 1 and array[indexa] > array[indexa]) or (
				    direction == 0 and array[indexa] < array[indexa]
				):
								lowerCAmelCase ,						lowerCAmelCase  =				array[indexa], array[indexa]





def 							lowercase					(snake_case__   : list[int]      ,       snake_case__   : int      ,       snake_case__   : int      ,       snake_case__   : int )     ->  None:


				'''simple docstring'''






				if length > 1:
								lowerCAmelCase  =				int(length / 2 )
								for i in range(snake_case__      ,       low + middle ):
												comp_and_swap(snake_case__      ,       snake_case__      ,       i + middle      ,       snake_case__ )
								bitonic_merge(snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__ )
								bitonic_merge(snake_case__      ,       low + middle      ,       snake_case__      ,       snake_case__ )





def 							lowercase					(snake_case__   : list[int]      ,       snake_case__   : int      ,       snake_case__   : int      ,       snake_case__   : int )     ->  None:


				'''simple docstring'''






				if length > 1:
								lowerCAmelCase  =				int(length / 2 )
								bitonic_sort(snake_case__      ,       snake_case__      ,       snake_case__      ,       1 )
								bitonic_sort(snake_case__      ,       low + middle      ,       snake_case__      ,       0 )
								bitonic_merge(snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__ )


if __name__ == "__main__":
		a      =							input('Enter numbers separated by a comma:\n').strip()
		a      =							[int(item.strip()) for item in user_input.split(',')]

		bitonic_sort(unsorted, 0, len(unsorted), 1)
		print('\nSorted array in ascending order is: ', end='')
		print(*unsorted, sep=', ')

		bitonic_merge(unsorted, 0, len(unsorted), 0)
		print('Sorted array in descending order is: ', end='')
		print(*unsorted, sep=', ')





