

"""simple docstring"""


def   _A					(	_a	:						Dict     ,   _a	:						Tuple     ,   _a	:						List[Any]     ,   _a	:						Union[str, Any]				):



      """simple docstring"""






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



def   _A					(	_a	:						Optional[Any]     ,   _a	:						Optional[int]     ,   _a	:						Union[str, Any]     ,   _a	:						List[str]				):



      """simple docstring"""






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

      return dp[n][w_], dp



def   _A					(	_a	:						int     ,   _a	:						list     ,   _a	:						list				):



      """simple docstring"""






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

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

      A  ,			A				  =		knapsack(_a     ,   _a     ,   _a     ,   _a				)
      A				  =		set()
      _construct_solution(_a     ,   _a     ,   _a     ,   _a     ,   _a				)

      return optimal_val, example_optional_set



def   _A					(	_a	:						list     ,   _a	:						list     ,   _a	:						int     ,   _a	:						int     ,   _a	:						set				):



      """simple docstring"""






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


if __name__ == "__main__":
  UpperCAmelCase													=[3, 2, 4, 4]
  UpperCAmelCase													=[4, 3, 2, 3]
  UpperCAmelCase													=4
  UpperCAmelCase													=6
  UpperCAmelCase													=[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
  UpperCAmelCase							,			UpperCAmelCase													=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
  UpperCAmelCase							,			UpperCAmelCase													=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   _A					(	_a	:						list[float]     ,   _a	:						list[float]				):



      """simple docstring"""






      A				  =		sorted(numsa + numsa				)
      A  ,			A				  =		divmod(len(_a				)     ,   2				)
      if mod == 1:
            return all_numbers[div]
      else:
            return (all_numbers[div] + all_numbers[div - 1]) / 2


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  UpperCAmelCase													=[float(x) for x in input("Enter the elements of first array: ").split()]
  UpperCAmelCase													=[float(x) for x in input("Enter the elements of second array: ").split()]
  print(f"""The median of two arrays is: {median_of_two_arrays(array_a, array_a)}""")




