

from __future__ import annotations





def    _snake_case		(snake_case_				:    int						,					snake_case_				:    list[int]						,					snake_case_				:    list[int]						,					snake_case_				:    int     )       ->		int:

  # Base Case
  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(snake_case_						,					snake_case_						,					snake_case_						,					counter - 1     )
  else:
    __UpperCAmelCase  :     Optional[Any]		=    capacity - weights[counter - 1]
    __UpperCAmelCase  :     Tuple		=    values[counter - 1] + knapsack(
        snake_case_						,					snake_case_						,					snake_case_						,					counter - 1     )
    __UpperCAmelCase  :     List[str]		=    knapsack(snake_case_						,					snake_case_						,					snake_case_						,					counter - 1     )
    return max(snake_case_						,					snake_case_     )


if __name__ == "__main__":
      import doctest

      doctest.testmod()








def    _snake_case		(snake_case_				:    int						,					snake_case_				:    int						,					snake_case_				:    int						,					snake_case_				:    int     )       ->		int:
  return len_board * len_board_column * row + column





def    _snake_case		(snake_case_				:    list[list[str]]						,					snake_case_				:    str						,					snake_case_				:    int						,					snake_case_				:    int						,					snake_case_				:    int						,					snake_case_				:    set[int]						,					)       ->		bool:

  if board[row][column] != word[word_index]:
    return False

  if word_index == len(snake_case_     ) - 1:
    return True

  __UpperCAmelCase  :     List[Any]		=    [(0, 1), (0, -1), (-1, 0), (1, 0)]
  __UpperCAmelCase  :     Dict		=    len(snake_case_     )
  __UpperCAmelCase  :     str		=    len(board[0]     )
  for direction in traverts_directions:
    __UpperCAmelCase  :     Dict		=    row + direction[0]
    __UpperCAmelCase  :     Optional[int]		=    column + direction[1]
    if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
      continue

    __UpperCAmelCase  :     str		=    get_point_key(snake_case_						,					snake_case_						,					snake_case_						,					snake_case_     )
    if key in visited_points_set:
      continue

    visited_points_set.add(snake_case_     )
    if exits_word(snake_case_						,					snake_case_						,					snake_case_						,					snake_case_						,					word_index + 1						,					snake_case_     ):
      return True

    visited_points_set.remove(snake_case_     )

  return False





def    _snake_case		(snake_case_				:    list[list[str]]						,					snake_case_				:    str     )       ->		bool:
  __UpperCAmelCase  :     str		=    (
      'The board should be a non empty matrix of single chars strings.'
  )

  __UpperCAmelCase  :     Any		=    len(snake_case_     )
  if not isinstance(snake_case_						,					snake_case_     ) or len(snake_case_     ) == 0:
    raise ValueError(snake_case_     )

  for row in board:
    if not isinstance(snake_case_						,					snake_case_     ) or len(snake_case_     ) == 0:
      raise ValueError(snake_case_     )

    for item in row:
      if not isinstance(snake_case_						,					snake_case_     ) or len(snake_case_     ) != 1:
        raise ValueError(snake_case_     )

    # Validate word
  if not isinstance(snake_case_						,					snake_case_     ) or len(snake_case_     ) == 0:
    raise ValueError(
        'The word parameter should be a string of length greater than 0.'     )

  __UpperCAmelCase  :     str		=    len(board[0]     )
  for i in range(snake_case_     ):
    for j in range(snake_case_     ):
      if exits_word(
          snake_case_						,					snake_case_						,					snake_case_						,					snake_case_						,					0						,					{get_point_key(snake_case_						,					snake_case_						,					snake_case_						,					snake_case_     )}     ):
        return True

  return False


if __name__ == "__main__":
      import doctest

      doctest.testmod()





