





'''simple docstring'''

from __future__ import annotations




def  _a     (				lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_						):





      """simple docstring"""



      if len(lowerCAmelCase_						) == 0:
            raise ValueError('''find_min() arg is an empty sequence'''						)
      if (
          left >= len(lowerCAmelCase_						)
          or left < -len(lowerCAmelCase_						)
          or right >= len(lowerCAmelCase_						)
          or right < -len(lowerCAmelCase_						)
      ):
            raise IndexError('''list index out of range'''						)
      if left == right:
            return nums[left]
      _snake_case		:						Tuple         =  (left + right) >> 1  # the middle
      _snake_case		:						Union[str, Any]         =  find_min(lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_						)  # find min in range[left, mid]
      _snake_case		:						Union[str, Any]         =  find_min(lowerCAmelCase_      ,   mid + 1      ,   lowerCAmelCase_						)  # find min in range[mid + 1, right]

      return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
   import doctest

   doctest.testmod(verbose=True)









'''simple docstring'''

from __future__ import annotations




def  _a     (				lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_						):





      """simple docstring"""



      if counter == 0 or capacity == 0:
            return 0

      # If weight of the nth item is more than Knapsack of capacity,
      #   then this item cannot be included in the optimal solution,
      # else return the maximum of two cases:
      #   (1) nth item included
      #   (2) not included
      if weights[counter - 1] > capacity:
            return knapsack(lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   counter - 1						)
      else:
            _snake_case		:						List[str]         =  capacity - weights[counter - 1]
            _snake_case		:						Tuple         =  values[counter - 1] + knapsack(
                lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   counter - 1						)
            _snake_case		:						Any         =  knapsack(lowerCAmelCase_      ,   lowerCAmelCase_      ,   lowerCAmelCase_      ,   counter - 1						)
            return max(lowerCAmelCase_      ,   lowerCAmelCase_						)


if __name__ == "__main__":
   import doctest

   doctest.testmod()


