





def 				SCREAMING_SNAKE_CASE__							(       UpperCamelCase__:							int    ):
		SCREAMING_SNAKE_CASE__			=      generate_pascal_triangle(UpperCamelCase__    )
		for row_idx in range(UpperCamelCase__    ):
				# 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 				SCREAMING_SNAKE_CASE__							(       UpperCamelCase__:							int    ):

		if not isinstance(UpperCamelCase__					,   UpperCamelCase__    ):
				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"""    )

		SCREAMING_SNAKE_CASE__			=      []
		for current_row_idx in range(UpperCamelCase__    ):
				SCREAMING_SNAKE_CASE__			=      populate_current_row(UpperCamelCase__					,   UpperCamelCase__    )
				triangle.append(UpperCamelCase__    )
		return triangle






def 				SCREAMING_SNAKE_CASE__							(       UpperCamelCase__:							list[list[int]]					,   UpperCamelCase__:							int    ):
		SCREAMING_SNAKE_CASE__			=      [-1] * (current_row_idx + 1)
		# first and last elements of current row are equal to 1
		SCREAMING_SNAKE_CASE__	,						SCREAMING_SNAKE_CASE__			=      1, 1
		for current_col_idx in range(1					,   UpperCamelCase__    ):
				calculate_current_element(
				    UpperCamelCase__					,   UpperCamelCase__					,   UpperCamelCase__					,   UpperCamelCase__    )
		return current_row






def 				SCREAMING_SNAKE_CASE__							(       UpperCamelCase__:							list[list[int]]					,   UpperCamelCase__:							list[int]					,   UpperCamelCase__:							int					,   UpperCamelCase__:							int					,   ):
		SCREAMING_SNAKE_CASE__			=      triangle[current_row_idx - 1][current_col_idx - 1]
		SCREAMING_SNAKE_CASE__			=      triangle[current_row_idx - 1][current_col_idx]
		SCREAMING_SNAKE_CASE__			=      above_to_left_elt + above_to_right_elt






def 				SCREAMING_SNAKE_CASE__							(       UpperCamelCase__:							int    ):

		if not isinstance(UpperCamelCase__					,   UpperCamelCase__    ):
				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"""    )

		SCREAMING_SNAKE_CASE__			=      [[1]]

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

		return result






def 				SCREAMING_SNAKE_CASE__							(       ):
		from collections.abc import Callable
		from timeit import timeit

		def benchmark_a_function(UpperCamelCase__:							Callable					,   UpperCamelCase__:							int    ) -> None:
				SCREAMING_SNAKE_CASE__			=      f'''{func.__name__}({value})'''
				SCREAMING_SNAKE_CASE__			=      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(UpperCamelCase__					,   UpperCamelCase__    )
				print()


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	benchmark()






import warnings
from functools import wraps
from typing import Callable






def 				SCREAMING_SNAKE_CASE__							(       UpperCamelCase__:							Callable    ):

		@wraps(UpperCamelCase__    )
		def _inner_fn(*UpperCamelCase__:							Dict					,   **UpperCamelCase__:							Any    ):
				warnings.warn(
				    (f'''\'{fn.__name__}\' is experimental and might be subject to breaking changes in the future.''')					,   UpperCamelCase__					,   )
				return fn(*UpperCamelCase__					,   **UpperCamelCase__    )

		return _inner_fn