



def      a__ (		__UpperCamelCase     ,      __UpperCamelCase     ,      __UpperCamelCase     ,      __UpperCamelCase     ,      __UpperCamelCase				):


      if index == number_of_items:
            return 0
      SCREAMING_SNAKE_CASE_          =  0
      SCREAMING_SNAKE_CASE_          =  0
      SCREAMING_SNAKE_CASE_          =  knapsack(lowerCamelCase__     ,      lowerCamelCase__     ,      lowerCamelCase__     ,      lowerCamelCase__     ,      index + 1				)
      if weights[index] <= max_weight:
            SCREAMING_SNAKE_CASE_          =  values[index] + knapsack(
                lowerCamelCase__     ,      lowerCamelCase__     ,      lowerCamelCase__     ,      max_weight - weights[index]     ,      index + 1				)
      return max(lowerCamelCase__     ,      lowerCamelCase__				)


if __name__ == "__main__":
      import doctest

      doctest.testmod()



from __future__ import annotations


def      a__ (		__UpperCamelCase				):

      # preprocessing the first row
      for i in range(1     ,      len(matrix[0]				)				):
            matrix[0][i] += matrix[0][i - 1]

      # preprocessing the first column
      for i in range(1     ,      len(__UpperCamelCase				)				):
            matrix[i][0] += matrix[i - 1][0]

      # updating the path cost for current position
      for i in range(1     ,      len(__UpperCamelCase				)				):
            for j in range(1     ,      len(matrix[0]				)				):
                  matrix[i][j] += min(matrix[i - 1][j]     ,      matrix[i][j - 1]				)

      return matrix[-1][-1]


if __name__ == "__main__":
      import doctest

      doctest.testmod()


