


import cmath
import math

def      __lowercase					( snake_case,  snake_case,  snake_case,  snake_case ):







				"""simple docstring"""






				__magic_name__		:Dict        =      math.radians(__lowercase )
				__magic_name__		:Optional[int]        =      math.radians(__lowercase )

				# Convert voltage and current to rectangular form
				__magic_name__		:Optional[Any]        =      cmath.rect(__lowercase,  __lowercase )
				__magic_name__		:List[str]        =      cmath.rect(__lowercase,  __lowercase )

				# Calculate apparent power
				return voltage_rect * current_rect


if __name__ == "__main__":
					import doctest

					doctest.testmod()














def      __lowercase					( snake_case,  snake_case,  snake_case,  snake_case ):







				"""simple docstring"""






				global f  # a global dp table for knapsack
				if f[i][j] < 0:
								if j < wt[i - 1]:
												__magic_name__		:Dict        =      mf_knapsack(i - 1,  snake_case,  snake_case,  snake_case )
								else:
												__magic_name__		:Optional[Any]        =      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],  )
								__magic_name__		:List[Any]        =      val
				return f[i][j]

def      __lowercase					( snake_case,  snake_case,  snake_case,  snake_case ):







				"""simple docstring"""






				__magic_name__		: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_:
																__magic_name__		:List[str]        =      max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]],  dp[i - 1][w_] )
												else:
																__magic_name__		:Optional[int]        =      dp[i - 1][w_]

				return dp[n][w_], dp

def      __lowercase					( snake_case,  snake_case,  snake_case ):







				"""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''' )

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

				__magic_name__     ,				__magic_name__		:Tuple        =      knapsack(snake_case,  snake_case,  snake_case,  snake_case )
				__magic_name__		:set        =      set()
				_construct_solution(snake_case,  snake_case,  snake_case,  snake_case,  snake_case )

				return optimal_val, example_optional_set

def      __lowercase					( snake_case,  snake_case,  snake_case,  snake_case,  snake_case ):







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






