





"""simple docstring"""





def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )						->Dict:





  """simple docstring"""


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


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )						->List[str]:





  """simple docstring"""


  __UpperCAmelCase    :						List[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_:
        __UpperCAmelCase    :						Union[str, Any]       =						max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]  ,			dp[i - 1][w_]  )
      else:
        __UpperCAmelCase    :						str       =						dp[i - 1][w_]

  return dp[n][w_], dp


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )						->Optional[Any]:





  """simple docstring"""


  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'''  )

  __UpperCAmelCase    :						Union[str, Any]       =						len(UpperCAmelCase_  )
  if num_items != len(UpperCAmelCase_  ):
    __UpperCAmelCase    :						Dict       =						(
        '''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_  ):
      __UpperCAmelCase    :						List[Any]       =						(
          '''All weights must be integers but got weight of '''
          f'''type {type(wt[i]  )} at index {i}'''
      )
      raise TypeError(UpperCAmelCase_  )

  __UpperCAmelCase       ,     __UpperCAmelCase    :						Optional[int]       =						knapsack(UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )
  __UpperCAmelCase    :						set       =						set()
  _construct_solution(UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )

  return optimal_val, example_optional_set


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )						->Tuple:





  """simple docstring"""


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





def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  )						->Tuple:





  """simple docstring"""


  return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_=0  )						->Dict:





  """simple docstring"""


  return sorted(UpperCAmelCase_  ,			key=lambda UpperCAmelCase_  : x[column]  )


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_=float('''inf'''  )  )						->str:





  """simple docstring"""


  for i in range(points_counts - 1  ):
    for j in range(i + 1  ,			UpperCAmelCase_  ):
      __UpperCAmelCase    :						List[Any]       =						euclidean_distance_sqr(points[i]  ,			points[j]  )
      if current_dis < min_dis:
        __UpperCAmelCase    :						Tuple       =						current_dis
  return min_dis


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_=float('''inf'''  )  )						->str:





  """simple docstring"""


  for i in range(min(6  ,			points_counts - 1  )  ,			UpperCAmelCase_  ):
    for j in range(max(0  ,			i - 6  )  ,			UpperCAmelCase_  ):
      __UpperCAmelCase    :						Dict       =						euclidean_distance_sqr(points[i]  ,			points[j]  )
      if current_dis < min_dis:
        __UpperCAmelCase    :						Tuple       =						current_dis
  return min_dis


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )						->Any:





  """simple docstring"""


  if points_counts <= 3:
    return dis_between_closest_pair(UpperCAmelCase_  ,			UpperCAmelCase_  )

  # recursion
  __UpperCAmelCase    :						Any       =						points_counts // 2
  __UpperCAmelCase    :						Any       =						closest_pair_of_points_sqr(
      UpperCAmelCase_  ,			points_sorted_on_y[:mid]  ,			UpperCAmelCase_  )
  __UpperCAmelCase    :						Tuple       =						closest_pair_of_points_sqr(
      UpperCAmelCase_  ,			points_sorted_on_y[mid:]  ,			points_counts - mid  )
  __UpperCAmelCase    :						List[Any]       =						min(UpperCAmelCase_  ,			UpperCAmelCase_  )
  __UpperCAmelCase    :						int       =						[]
  for point in points_sorted_on_x:
    if abs(point[0] - points_sorted_on_x[mid][0]  ) < closest_pair_dis:
      cross_strip.append(UpperCAmelCase_  )

  __UpperCAmelCase    :						Union[str, Any]       =						dis_between_closest_in_strip(
      UpperCAmelCase_  ,			len(UpperCAmelCase_  )  ,			UpperCAmelCase_  )
  return min(UpperCAmelCase_  ,			UpperCAmelCase_  )


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  )						->List[Any]:





  """simple docstring"""


  __UpperCAmelCase    :						str       =						column_based_sort(UpperCAmelCase_  ,			column=0  )
  __UpperCAmelCase    :						Any       =						column_based_sort(UpperCAmelCase_  ,			column=1  )
  return (
      closest_pair_of_points_sqr(
          UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  )
  ) ** 0.5


if __name__ == "__main__":
  lowercase__				:Optional[Any]				   =       [(2, 3), (1_2, 3_0), (4_0, 5_0), (5, 1), (1_2, 1_0), (3, 4)]
  print('Distance:', closest_pair_of_points(points, len(points)))