





"""simple docstring"""


def 					lowercase__    (					lowercase_			)					->		Dict:




      """simple docstring"""

      _UpperCamelCase      :	Tuple						=       generate_pascal_triangle(__SCREAMING_SNAKE_CASE			)
      for row_idx in range(__SCREAMING_SNAKE_CASE			):
            # Print left spaces
            for _ in range(num_rows - row_idx - 1			):
                  print(end=" "			)
            # Print row values
            for col_idx in range(row_idx + 1			):
                  if col_idx != row_idx:
                        print(triangle[row_idx][col_idx]		,end=" "			)
                  else:
                        print(triangle[row_idx][col_idx]		,end=""			)
            print()




def 					lowercase__    (					lowercase_			)					->		Optional[int]:




      """simple docstring"""

      if not isinstance(__SCREAMING_SNAKE_CASE		,__SCREAMING_SNAKE_CASE			):
            raise TypeError("The input value of 'num_rows' should be 'int'"			)

      if num_rows == 0:
            return []
      elif num_rows < 0:
            raise ValueError(
                "The input value of 'num_rows' should be greater than or equal to 0"			)

      _UpperCamelCase      :	list[list[int]]						=       []
      for current_row_idx in range(__SCREAMING_SNAKE_CASE			):
            _UpperCamelCase      :	Dict						=       populate_current_row(__SCREAMING_SNAKE_CASE		,__SCREAMING_SNAKE_CASE			)
            triangle.append(__SCREAMING_SNAKE_CASE			)
      return triangle




def 					lowercase__    (					lowercase_		,lowercase_			)					->		Optional[Any]:




      """simple docstring"""

      _UpperCamelCase      :	Dict						=       [-1] * (current_row_idx + 1)
      # first and last elements of current row are equal to 1
      _UpperCamelCase      :	Union[str, Any]						=       1, 1
      for current_col_idx in range(1		,__SCREAMING_SNAKE_CASE			):
            calculate_current_element(
                __SCREAMING_SNAKE_CASE		,__SCREAMING_SNAKE_CASE		,__SCREAMING_SNAKE_CASE		,__SCREAMING_SNAKE_CASE			)
      return current_row




def 					lowercase__    (					lowercase_		,lowercase_		,lowercase_		,lowercase_		,)					->		Dict:




      """simple docstring"""

      _UpperCamelCase      :	Dict						=       triangle[current_row_idx - 1][current_col_idx - 1]
      _UpperCamelCase      :	Optional[Any]						=       triangle[current_row_idx - 1][current_col_idx]
      _UpperCamelCase      :	List[Any]						=       above_to_left_elt + above_to_right_elt




def 					lowercase__    (					lowercase_			)					->		Tuple:




      """simple docstring"""

      if not isinstance(__SCREAMING_SNAKE_CASE		,__SCREAMING_SNAKE_CASE			):
            raise TypeError("The input value of 'num_rows' should be 'int'"			)

      if num_rows == 0:
            return []
      elif num_rows < 0:
            raise ValueError(
                "The input value of 'num_rows' should be greater than or equal to 0"			)

      _UpperCamelCase      :	list[list[int]]						=       [[1]]

      for row_index in range(1		,__SCREAMING_SNAKE_CASE			):
            _UpperCamelCase      :	Any						=       [0] + result[-1] + [0]
            _UpperCamelCase      :	Dict						=       row_index + 1
            # Calculate the number of distinct elements in a row
            _UpperCamelCase      :	Any						=       sum(divmod(__SCREAMING_SNAKE_CASE		,2			)			)
            _UpperCamelCase      :	Tuple						=       [
                temp_row[i - 1] + temp_row[i] for i in range(1		,distinct_elements + 1			)
            ]
            _UpperCamelCase      :	Dict						=       row_first_half[: (row_index + 1) // 2]
            row_second_half.reverse()
            _UpperCamelCase      :	Optional[int]						=       row_first_half + row_second_half
            result.append(__SCREAMING_SNAKE_CASE			)

      return result




def 					lowercase__    (					)					->		Optional[int]:




      """simple docstring"""

      from collections.abc import Callable
      from timeit import timeit

      def benchmark_a_function(lowercase_		,lowercase_			) -> None:
            _UpperCamelCase      :	int						=       F'''{func.__name__}({value})'''
            _UpperCamelCase      :	List[Any]						=       timeit(F'''__main__.{call}'''		,setup="import __main__"			)
            # print(f"{call:38} = {func(value)} -- {timing:.4f} seconds")
            print(F'''{call:38} -- {timing:.4f} seconds'''			)

      for value in range(15			):  # (1, 7, 14):
            for func in (generate_pascal_triangle, generate_pascal_triangle_optimized):
                  benchmark_a_function(__SCREAMING_SNAKE_CASE		,__SCREAMING_SNAKE_CASE			)
            print()


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  benchmark()







"""simple docstring"""


lowerCamelCase__				  =   "\n# Installazione di Transformers\n! pip install transformers datasets\n# Per installare dalla fonte invece dell'ultima versione rilasciata, commenta il comando sopra e\n# rimuovi la modalità commento al comando seguente.\n# ! pip install git+https://github.com/huggingface/transformers.git\n"

lowerCamelCase__				  =   [{"type": "code", "content": INSTALL_CONTENT}]
lowerCamelCase__				  =   {
    "{processor_class}": "FakeProcessorClass",
    "{model_class}": "FakeModelClass",
    "{object_class}": "FakeObjectClass",
}
