



"""simple docstring"""


def  _lowerCAmelCase      (   lowercase_						):
						UpperCAmelCase             = generate_pascal_triangle(lowercase_						)
						for row_idx in range(lowercase_						):
												# 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  _lowerCAmelCase      (   lowercase_						):

						if not isinstance(lowercase_		,	lowercase_						):
												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             = []
						for current_row_idx in range(lowercase_						):
												UpperCAmelCase             = populate_current_row(lowercase_		,	lowercase_						)
												triangle.append(lowercase_						)
						return triangle

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

def  _lowerCAmelCase      (   lowercase_		,	lowercase_		,	lowercase_		,	lowercase_		,	):
						UpperCAmelCase             = triangle[current_row_idx - 1][current_col_idx - 1]
						UpperCAmelCase             = triangle[current_row_idx - 1][current_col_idx]
						UpperCAmelCase             = above_to_left_elt + above_to_right_elt

def  _lowerCAmelCase      (   lowercase_						):

						if not isinstance(lowercase_		,	lowercase_						):
												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             = [[1]]

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

						return result

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

						def benchmark_a_function(lowercase_		,	lowercase_						) -> None:
												UpperCAmelCase             = F"""{func.__name__}({value})"""
												UpperCAmelCase             = 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(lowercase_		,	lowercase_						)
												print()


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				benchmark()










'''simple docstring'''





from transformers import BertTokenizerFast

from .custom_tokenization import CustomTokenizer







class     UpperCAmelCase_       (       _a	):
    """simple docstring"""







    lowercase					=		CustomTokenizer
    pass
