





def 			_SCREAMING_SNAKE_CASE						(     SCREAMING_SNAKE_CASE						:int       )     ->       float:
 return 10 - x * x






def 			_SCREAMING_SNAKE_CASE						(     SCREAMING_SNAKE_CASE						:Optional[int]       ,       SCREAMING_SNAKE_CASE						:str       )     ->       float:
 # Bolzano theory in order to find if there is a root between a and b
 if equation(SCREAMING_SNAKE_CASE       ) * equation(SCREAMING_SNAKE_CASE       ) >= 0:
  raise ValueError("""Wrong space!"""       )

 __lowerCAmelCase	:			Any         =  a
 while (b - a) >= 0.01:
  # Find middle point
  __lowerCAmelCase	:			Tuple         =  (a + b) / 2
  # Check if middle point is root
  if equation(SCREAMING_SNAKE_CASE       ) == 0.0:
   break
  # Decide the side to repeat the steps
  if equation(SCREAMING_SNAKE_CASE       ) * equation(SCREAMING_SNAKE_CASE       ) < 0:
   __lowerCAmelCase	:			Dict         =  c
  else:
   __lowerCAmelCase	:			List[str]         =  c
 return c


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      print(bisection(-2, 5))
      print(bisection(0, 6))






from __future__ import annotations



def  SCREAMING_SNAKE_CASE				(      snake_case						,   snake_case							)		->    list[tuple[int, int]]:
		__lowercase						,      __lowercase											=     position
		__lowercase											=     [
		    (y + 1, x + 2),
		    (y - 1, x + 2),
		    (y + 1, x - 2),
		    (y - 1, x - 2),
		    (y + 2, x + 1),
		    (y + 2, x - 1),
		    (y - 2, x + 1),
		    (y - 2, x - 1),
		]
		__lowercase											=     []

		for position in positions:
				__lowercase						,      __lowercase											=     position
				if 0 <= y_test < n and 0 <= x_test < n:
						permissible_positions.append(snake_case							)

		return permissible_positions



def  SCREAMING_SNAKE_CASE				(      snake_case							)		->    bool:
		return not any(elem == 0 for row in board for elem in row							)



def  SCREAMING_SNAKE_CASE				(      snake_case						,   snake_case						,   snake_case							)		->    bool:

		if is_complete(snake_case							):
				return True

		for position in get_valid_pos(snake_case						,   len(snake_case							)							):
				__lowercase						,      __lowercase											=     position

				if board[y][x] == 0:
						__lowercase											=     curr + 1
						if open_knight_tour_helper(snake_case						,   snake_case						,   curr + 1							):
								return True
						__lowercase											=     0

		return False



def  SCREAMING_SNAKE_CASE				(      snake_case							)		->    list[list[int]]:
		__lowercase											=     [[0 for i in range(snake_case							)] for j in range(snake_case							)]

		for i in range(snake_case							):
				for j in range(snake_case							):
						__lowercase											=     1
						if open_knight_tour_helper(snake_case						,   (i, j)						,   1							):
								return board
						__lowercase											=     0

		__lowercase											=     F"Open Kight Tour cannot be performed on a board of size {n}"
		raise ValueError(snake_case							)


if __name__ == "__main__":
		import doctest

		doctest.testmod()




