



"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					Dict			):
					"""simple docstring"""
					lowerCamelCase__	:	List[Any]				=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   snake_case__     (	__lowerCamelCase       :					Dict			):
					"""simple docstring"""

					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'''			)

					lowerCamelCase__	:	Optional[int]				=[]
					for current_row_idx in range(__A			):
										lowerCamelCase__	:	Any				=populate_current_row(__A							,	__A			)
										triangle.append(__A			)
					return triangle






def   snake_case__     (	__lowerCamelCase       :					Tuple							,	__lowerCamelCase       :					Optional[int]			):
					"""simple docstring"""
					lowerCamelCase__	:	str				=[-1] * (current_row_idx + 1)
					# first and last elements of current row are equal to 1
					lowerCamelCase__			,     lowerCamelCase__	:	int				=1, 1
					for current_col_idx in range(1							,	__A			):
										calculate_current_element(
										    __A							,	__A							,	__A							,	__A			)
					return current_row






def   snake_case__     (	__lowerCamelCase       :					Union[str, Any]							,	__lowerCamelCase       :					Any							,	__lowerCamelCase       :					int							,	__lowerCamelCase       :					List[Any]							,	):
					"""simple docstring"""
					lowerCamelCase__	:	Tuple				=triangle[current_row_idx - 1][current_col_idx - 1]
					lowerCamelCase__	:	List[Any]				=triangle[current_row_idx - 1][current_col_idx]
					lowerCamelCase__	:	List[Any]				=above_to_left_elt + above_to_right_elt






def   snake_case__     (	__lowerCamelCase       :					Dict			):
					"""simple docstring"""

					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'''			)

					lowerCamelCase__	:	Dict				=[[1]]

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

					return result






def   snake_case__     (	):
					"""simple docstring"""
					from collections.abc import Callable
					from timeit import timeit

					def benchmark_a_function(__lowerCamelCase       :					Optional[Any]							,	__lowerCamelCase       :					Optional[int]			) -> None:
										lowerCamelCase__	:	Dict				=f'''{func.__name__}({value})'''
										lowerCamelCase__	:	Union[str, 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(__A							,	__A			)
										print()


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		benchmark()









"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					list							,	__lowerCamelCase       :					list							,	__lowerCamelCase       :					int							,	__lowerCamelCase       :					int							,	__lowerCamelCase       :					int			):
			"""simple docstring"""
			if index == number_of_items:
						return 0
			lowerCamelCase__	:	Optional[int]				=0
			lowerCamelCase__	:	Union[str, Any]				=0
			lowerCamelCase__	:	List[str]				=knapsack(__lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase							,	index + 1			)
			if weights[index] <= max_weight:
						lowerCamelCase__	:	Dict				=values[index] + knapsack(
						    __lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase							,	max_weight - weights[index]							,	index + 1			)
			return max(__lowerCamelCase							,	__lowerCamelCase			)


if __name__ == "__main__":
		import doctest

		doctest.testmod()




