





'''simple docstring'''







def  _lowerCamelCase				( lowercase						:      int						)	->	None:
				_a								= generate_pascal_triangle(_A						)
				for row_idx in range(_A						):
								# 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						:      int						)	->	list[list[int]]:


				if not isinstance(_A    ,							_A						):
								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"						)

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






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






def  _lowerCamelCase				( lowercase						:      list[list[int]]    ,							lowercase						:      list[int]    ,							lowercase						:      int    ,							lowercase						:      int    ,							)	->	None:
				_a								= triangle[current_row_idx - 1][current_col_idx - 1]
				_a								= triangle[current_row_idx - 1][current_col_idx]
				_a								= above_to_left_elt + above_to_right_elt






def  _lowerCamelCase				( lowercase						:      int						)	->	list[list[int]]:


				if not isinstance(_A    ,							_A						):
								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"						)

				_a								= [[1]]

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

				return result






def  _lowerCamelCase				( )	->	None:
				from collections.abc import Callable
				from timeit import timeit

				def benchmark_a_function(lowercase						:      Callable    ,							lowercase						:      int						) -> None:
								_a								= F'{func.__name__}({value})'
								_a								= 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(_A    ,							_A						)
								print()


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					benchmark()

'''simple docstring'''




from string import ascii_lowercase, ascii_uppercase






def 				snake_case__							(			_A:					str )    ->	str:

		'''simple docstring'''


		if not sentence:
				return ""
		lowerCAmelCase   					=  dict(zip(_A      ,   _A ) )
		return lower_to_upper.get(sentence[0]      ,   sentence[0] ) + sentence[1:]


if __name__ == "__main__":
						from doctest import testmod

						testmod()




