




'''simple docstring'''







def 		snake_case_							(_a			:							int  ):
    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 		snake_case_							(_a			:							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'''  )

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





def 		snake_case_							(_a			:							list[list[int]]					,     _a			:							int  ):
    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 		snake_case_							(_a			:							list[list[int]]					,     _a			:							list[int]					,     _a			:							int					,     _a			:							int					,     ):
    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 		snake_case_							(_a			:							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'''  )

    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 		snake_case_							():
    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(1_5  ):  # (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 typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


A									={
    'configuration_table_transformer': [
        'TABLE_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'TableTransformerConfig',
        'TableTransformerOnnxConfig',
    ]
}

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   A									=[
       'TABLE_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
       'TableTransformerForObjectDetection',
       'TableTransformerModel',
       'TableTransformerPreTrainedModel',
   ]


if TYPE_CHECKING:
   from .configuration_table_transformer import (
       TABLE_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
       TableTransformerConfig,
       TableTransformerOnnxConfig,
   )

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_table_transformer import (
          TABLE_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          TableTransformerForObjectDetection,
          TableTransformerModel,
          TableTransformerPreTrainedModel,
      )

else:
   import sys

   A									=_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




