
def 			UpperCamelCase					(    __lowerCamelCase     : Union[str, Any]    ):
       snake_case       :   Optional[Any]							=      generate_pascal_triangle(__lowerCamelCase    )
       for row_idx in range(__lowerCamelCase    ):
              # 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 			UpperCamelCase					(    __lowerCamelCase     : str    ):

       if not isinstance(__lowerCamelCase				,					__lowerCamelCase    ):
              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"    )

       snake_case       :   list[list[int]]							=      []
       for current_row_idx in range(__lowerCamelCase    ):
              snake_case       :   int							=      populate_current_row(__lowerCamelCase				,					__lowerCamelCase    )
              triangle.append(__lowerCamelCase    )
       return triangle


def 			UpperCamelCase					(    __lowerCamelCase     : Tuple				,					__lowerCamelCase     : Optional[int]    ):
       snake_case       :   Union[str, Any]							=      [-1] * (current_row_idx + 1)
       # first and last elements of current row are equal to 1
       snake_case       :   Tuple							=      1, 1
       for current_col_idx in range(1				,					__lowerCamelCase    ):
              calculate_current_element(
                  __lowerCamelCase				,					__lowerCamelCase				,					__lowerCamelCase				,					__lowerCamelCase    )
       return current_row


def 			UpperCamelCase					(    __lowerCamelCase     : int				,					__lowerCamelCase     : Any				,					__lowerCamelCase     : Tuple				,					__lowerCamelCase     : Optional[int]				,					):
       snake_case       :   Optional[Any]							=      triangle[current_row_idx - 1][current_col_idx - 1]
       snake_case       :   Dict							=      triangle[current_row_idx - 1][current_col_idx]
       snake_case       :   Dict							=      above_to_left_elt + above_to_right_elt


def 			UpperCamelCase					(    __lowerCamelCase     : int    ):

       if not isinstance(__lowerCamelCase				,					__lowerCamelCase    ):
              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"    )

       snake_case       :   list[list[int]]							=      [[1]]

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

       return result


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

       def benchmark_a_function(__lowerCamelCase     : List[Any]				,					__lowerCamelCase     : Optional[int]    ) -> None:
              snake_case       :   str							=      f"""{func.__name__}({value})"""
              snake_case       :   Optional[int]							=      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(__lowerCamelCase				,					__lowerCamelCase    )
              print()


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   benchmark()










"""simple docstring"""







from dataclasses import dataclass, field
from typing import TYPE_CHECKING, Any, ClassVar, Dict, List, Optional, Union

import pyarrow as pa


if TYPE_CHECKING:
							from .features import FeatureType
@dataclass
class        __A       :







		'''simple docstring'''





		lowerCAmelCase			:					List[str]
		lowerCAmelCase			:					Optional[str]   	=				None
		# Automatically constructed
		lowerCAmelCase			:					ClassVar[str]   	=				"dict"
		lowerCAmelCase			:					ClassVar[Any]   	=				None
		lowerCAmelCase			:					str   	=				field(default="Translation"     ,init=A_     ,repr=A_    )







		def __call__(	self						:  List[str]						)					->		Any:






				"""simple docstring"""



				return pa.struct({lang: pa.string() for lang in sorted(self.languages						)}						)







		def 					UpperCAmelCase    (	self						:  List[str]						)					->		Union["FeatureType", Dict[str, "FeatureType"]]:






				"""simple docstring"""



				from .features import Value

				return {k: Value('''string'''						) for k in sorted(self.languages						)}





@dataclass
class        __A       :







		'''simple docstring'''





		lowerCAmelCase			:					Optional[List]   	=				None
		lowerCAmelCase			:					Optional[int]   	=				None
		lowerCAmelCase			:					Optional[str]   	=				None
		# Automatically constructed
		lowerCAmelCase			:					ClassVar[str]   	=				"dict"
		lowerCAmelCase			:					ClassVar[Any]   	=				None
		lowerCAmelCase			:					str   	=				field(default="TranslationVariableLanguages"     ,init=A_     ,repr=A_    )







		def 					UpperCAmelCase    (	self						:  List[Any]						)					->		Optional[int]:






				"""simple docstring"""



				lowercase__   :    Optional[int]				=			sorted(set(self.languages						)						) if self.languages else None
				lowercase__   :    Dict				=			len(self.languages						) if self.languages else None







		def __call__(	self						:  List[Any]						)					->		List[Any]:






				"""simple docstring"""



				return pa.struct({'''language''': pa.list_(pa.string()						), '''translation''': pa.list_(pa.string()						)}						)







		def 					UpperCAmelCase    (	self						:  Dict			,_snake_case						:  Tuple						)					->		int:






				"""simple docstring"""



				lowercase__   :    List[Any]				=			set(self.languages						)
				if self.languages and set(_snake_case						) - lang_set:
						raise ValueError(
						    f"""Some languages in example ({", ".join(sorted(set(_snake_case						) - lang_set						)						)}) are not in valid set ({", ".join(_snake_case						)})."""						)

				# Convert dictionary into tuples, splitting out cases where there are
				# multiple translations for a single language.
				lowercase__   :    str				=			[]
				for lang, text in translation_dict.items():
						if isinstance(_snake_case			,_snake_case						):
								translation_tuples.append((lang, text)						)
						else:
								translation_tuples.extend([(lang, el) for el in text]						)

        # Ensure translations are in ascending order by language code.
				lowercase__		,			lowercase__   :    Optional[Any]				=			zip(*sorted(_snake_case						)						)

				return {"language": languages, "translation": translations}







		def 					UpperCAmelCase    (	self						:  List[Any]						)					->		Union["FeatureType", Dict[str, "FeatureType"]]:






				"""simple docstring"""



				from .features import Sequence, Value

				return {
				    "language": Sequence(Value('''string'''						)						),
				    "translation": Sequence(Value('''string'''						)						),
				}
