




"""simple docstring"""

def 					a			(    __snake_case  :					int	):



				'''simple docstring'''





				UpperCAmelCase_       :List[Any]         =   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 					a			(    __snake_case  :					int	):



				'''simple docstring'''





				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'''	)

				UpperCAmelCase_       :list[list[int]]         =   []
				for current_row_idx in range(_UpperCAmelCase	):
								UpperCAmelCase_       :str         =   populate_current_row(_UpperCAmelCase,     _UpperCAmelCase	)
								triangle.append(_UpperCAmelCase	)
				return triangle



def 					a			(    __snake_case  :					list[list[int]],     __snake_case  :					int	):



				'''simple docstring'''





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



def 					a			(    __snake_case  :					list[list[int]],     __snake_case  :					list[int],     __snake_case  :					int,     __snake_case  :					int,     ):



				'''simple docstring'''





				UpperCAmelCase_       :Tuple         =   triangle[current_row_idx - 1][current_col_idx - 1]
				UpperCAmelCase_       :Dict         =   triangle[current_row_idx - 1][current_col_idx]
				UpperCAmelCase_       :str         =   above_to_left_elt + above_to_right_elt



def 					a			(    __snake_case  :					int	):



				'''simple docstring'''





				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'''	)

				UpperCAmelCase_       :list[list[int]]         =   [[1]]

				for row_index in range(1,     _UpperCAmelCase	):
								UpperCAmelCase_       :Any         =   [0] + result[-1] + [0]
								UpperCAmelCase_       :str         =   row_index + 1
								# Calculate the number of distinct elements in a row
								UpperCAmelCase_       :Optional[Any]         =   sum(divmod(_UpperCAmelCase,     2	)	)
								UpperCAmelCase_       :Optional[int]         =   [
								    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_       :Tuple         =   row_first_half + row_second_half
								result.append(_UpperCAmelCase	)

				return result



def 					a			(    ):



				'''simple docstring'''





				from collections.abc import Callable
				from timeit import timeit

				def benchmark_a_function(__snake_case  :					Callable,     __snake_case  :					int	) -> None:
								UpperCAmelCase_       :Any         =   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(_UpperCAmelCase,     _UpperCAmelCase	)
								print()


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						benchmark()




from __future__ import annotations



def 		UpperCamelCase     (       _UpperCAmelCase  :   str ,			_UpperCAmelCase  :   list[str] | None = None  )   ->			list[list[str]]:






						'''simple docstring'''

						_lowercase       :	Dict           =   word_bank or []
						# create a table
						_lowercase       :	int           =   len(_UpperCAmelCase  ) + 1

						_lowercase       :	list[list[list[str]]]           =   []
						for _ in range(_UpperCAmelCase  ):
												table.append([]  )
						# seed value
						_lowercase       :	Optional[int]           =   [[]]  # because empty string has empty combination

						# iterate through the indices
						for i in range(_UpperCAmelCase  ):
												# condition
												if table[i] != []:
																		for word in word_bank:
																								# slice condition
																								if target[i : i + len(_UpperCAmelCase  )] == word:
																														_lowercase       :	list[list[str]]           =   [
																														    [word, *way] for way in table[i]
																														]
																														# adds the word to every combination the current position holds
																														# now,push that combination to the table[i+len(word)]
																														table[i + len(_UpperCAmelCase  )] += new_combinations

    # combinations are in reverse order so reverse for better output
						for combination in table[len(_UpperCAmelCase  )]:
												combination.reverse()

						return table[len(_UpperCAmelCase  )]


if __name__ == "__main__":
							print(all_construct("""jwajalapa""", ["""jwa""", """j""", """w""", """a""", """la""", """lapa"""]))
							print(all_construct("""rajamati""", ["""s""", """raj""", """amat""", """raja""", """ma""", """i""", """t"""]))
							print(
							    all_construct(
							        """hexagonosaurus""",
							        ["""h""", """ex""", """hex""", """ag""", """ago""", """ru""", """auru""", """rus""", """go""", """no""", """o""", """s"""],
							    )
							)




