





def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:int  )   ->    None:
  _lowercase						    =			generate_pascal_triangle(snake_case__  )
  for row_idx in range(snake_case__  ):
    # 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 				SCREAMING_SNAKE_CASE__							(	snake_case__	:int  )   ->    list[list[int]]:

  if not isinstance(snake_case__      ,				snake_case__  ):
    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'  )

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

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:list[list[int]]      ,				snake_case__	:int  )   ->    list[int]:
  _lowercase						    =			[-1] * (current_row_idx + 1)
  # first and last elements of current row are equal to 1
  _lowercase    ,		_lowercase						    =			1, 1
  for current_col_idx in range(1      ,				snake_case__  ):
    calculate_current_element(
        snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__  )
  return current_row

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:list[list[int]]      ,				snake_case__	:list[int]      ,				snake_case__	:int      ,				snake_case__	:int      ,				)   ->    None:
  _lowercase						    =			triangle[current_row_idx - 1][current_col_idx - 1]
  _lowercase						    =			triangle[current_row_idx - 1][current_col_idx]
  _lowercase						    =			above_to_left_elt + above_to_right_elt

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:int  )   ->    list[list[int]]:

  if not isinstance(snake_case__      ,				snake_case__  ):
    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'  )

  _lowercase						    =			[[1]]

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

  return result

def 				SCREAMING_SNAKE_CASE__							(	)   ->    None:
  from collections.abc import Callable
  from timeit import timeit

  def benchmark_a_function(snake_case__	:Callable      ,				snake_case__	:int  ) -> None:
    _lowercase						    =			F"""{func.__name__}({value})"""
    _lowercase						    =			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(snake_case__      ,				snake_case__  )
    print()


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      benchmark()





'''simple docstring'''





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCamelCase_		:     List[Any]          =		{
    '''configuration_git''': ['''GIT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''GitConfig''', '''GitVisionConfig'''],
    '''processing_git''': ['''GitProcessor'''],
}

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCamelCase_		:     Optional[Any]          =		[
       '''GIT_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''GitForCausalLM''',
       '''GitModel''',
       '''GitPreTrainedModel''',
       '''GitVisionModel''',
   ]

if TYPE_CHECKING:
   from .configuration_git import GIT_PRETRAINED_CONFIG_ARCHIVE_MAP, GitConfig, GitVisionConfig
   from .processing_git import GitProcessor

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_git import (
          GIT_PRETRAINED_MODEL_ARCHIVE_LIST,
          GitForCausalLM,
          GitModel,
          GitPreTrainedModel,
          GitVisionModel,
      )

else:
   import sys

   UpperCamelCase_		:     List[Any]          =		_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)


