




def    A						(__A   :    int       )   ->      None:







     """simple docstring"""


     UpperCAmelCase_          =							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    A						(__A   :    int       )   ->      list[list[int]]:







     """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'''       )

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


def    A						(__A   :    list[list[int]]   ,				__A   :    int       )   ->      list[int]:







     """simple docstring"""


     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   ,				__A       ):
          calculate_current_element(
              __A   ,				__A   ,				__A   ,				__A       )
     return current_row


def    A						(__A   :    list[list[int]]   ,				__A   :    list[int]   ,				__A   :    int   ,				__A   :    int   ,				)   ->      None:







     """simple docstring"""


     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    A						(__A   :    int       )   ->      list[list[int]]:







     """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'''       )

     UpperCAmelCase_          =							[[1]]

     for row_index in range(1   ,				__A       ):
          UpperCAmelCase_          =							[0] + result[-1] + [0]
          UpperCAmelCase_          =							row_index + 1
          # Calculate the number of distinct elements in a row
          UpperCAmelCase_          =							sum(divmod(__A   ,				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(__A       )

     return result


def    A						()   ->      None:







     """simple docstring"""


     from collections.abc import Callable
     from timeit import timeit

     def benchmark_a_function(__A   :    Callable   ,				__A   :    int       ) -> 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(__A   ,				__A       )
          print()


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    benchmark()












from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


snake_case_ : Dict    		=       {"configuration_mbart": ["MBART_PRETRAINED_CONFIG_ARCHIVE_MAP", "MBartConfig", "MBartOnnxConfig"]}

try:
    if not is_sentencepiece_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    snake_case_ : Tuple    		=       ["MBartTokenizer"]

try:
    if not is_tokenizers_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    snake_case_ : str    		=       ["MBartTokenizerFast"]

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    snake_case_ : List[Any]    		=       [
        "MBART_PRETRAINED_MODEL_ARCHIVE_LIST",
        "MBartForCausalLM",
        "MBartForConditionalGeneration",
        "MBartForQuestionAnswering",
        "MBartForSequenceClassification",
        "MBartModel",
        "MBartPreTrainedModel",
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    snake_case_ : Any    		=       [
        "TFMBartForConditionalGeneration",
        "TFMBartModel",
        "TFMBartPreTrainedModel",
    ]

try:
    if not is_flax_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    snake_case_ : List[str]    		=       [
        "FlaxMBartForConditionalGeneration",
        "FlaxMBartForQuestionAnswering",
        "FlaxMBartForSequenceClassification",
        "FlaxMBartModel",
        "FlaxMBartPreTrainedModel",
    ]


if TYPE_CHECKING:
    from .configuration_mbart import MBART_PRETRAINED_CONFIG_ARCHIVE_MAP, MBartConfig, MBartOnnxConfig

    try:
        if not is_sentencepiece_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_mbart import MBartTokenizer

    try:
        if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_mbart_fast import MBartTokenizerFast

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_mbart import (
            MBART_PRETRAINED_MODEL_ARCHIVE_LIST,
            MBartForCausalLM,
            MBartForConditionalGeneration,
            MBartForQuestionAnswering,
            MBartForSequenceClassification,
            MBartModel,
            MBartPreTrainedModel,
        )

    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_mbart import TFMBartForConditionalGeneration, TFMBartModel, TFMBartPreTrainedModel

    try:
        if not is_flax_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_flax_mbart import (
            FlaxMBartForConditionalGeneration,
            FlaxMBartForQuestionAnswering,
            FlaxMBartForSequenceClassification,
            FlaxMBartModel,
            FlaxMBartPreTrainedModel,
        )

else:
    import sys

    snake_case_ : Any    		=       _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)






