






def   snake_case (UpperCAmelCase__  )	->    None:
  UpperCamelCase_: Union[str, 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   snake_case (UpperCAmelCase__  )	->    list[list[int]]:

  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   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__  )	->    list[int]:
  UpperCamelCase_: Dict   				=    [-1] * (current_row_idx + 1)
  # first and last elements of current row are equal to 1
  UpperCamelCase_				,UpperCamelCase_: Optional[Any]   				=    1, 1
  for current_col_idx in range(1     ,   UpperCAmelCase__  ):
    calculate_current_element(
        UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__  )
  return current_row

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__     ,   )	->    None:
  UpperCamelCase_: Union[str, Any]   				=    triangle[current_row_idx - 1][current_col_idx - 1]
  UpperCamelCase_: Optional[int]   				=    triangle[current_row_idx - 1][current_col_idx]
  UpperCamelCase_: Tuple   				=    above_to_left_elt + above_to_right_elt

def   snake_case (UpperCAmelCase__  )	->    list[list[int]]:

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

  return result

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

  def benchmark_a_function(UpperCAmelCase__     ,   UpperCAmelCase__  ) -> None:
    UpperCamelCase_: Tuple   				=    F'''{func.__name__}({value})'''
    UpperCamelCase_: Tuple   				=    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(UpperCAmelCase__     ,   UpperCAmelCase__  )
    print()


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   benchmark()







import datetime
import platform
import subprocess
from typing import Optional, Tuple, Union

import numpy as np

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__  )	->    np.array:
  UpperCamelCase_: Dict   				=    F'''{sampling_rate}'''
  UpperCamelCase_: Any   				=    '1'
  UpperCamelCase_: Any   				=    'f32le'
  UpperCamelCase_: Union[str, Any]   				=    [
      'ffmpeg',
      '-i',
      'pipe:0',
      '-ac',
      ac,
      '-ar',
      ar,
      '-f',
      format_for_conversion,
      '-hide_banner',
      '-loglevel',
      'quiet',
      'pipe:1',
  ]

  try:
    with subprocess.Popen(UpperCAmelCase__     ,   stdin=subprocess.PIPE     ,   stdout=subprocess.PIPE  ) as ffmpeg_process:
      UpperCamelCase_: Optional[Any]   				=    ffmpeg_process.communicate(UpperCAmelCase__  )
  except FileNotFoundError as error:
    raise ValueError('ffmpeg was not found but is required to load audio files from filename'  ) from error
  UpperCamelCase_: Union[str, Any]   				=    output_stream[0]
  UpperCamelCase_: List[str]   				=    np.frombuffer(UpperCAmelCase__     ,   np.floataa  )
  if audio.shape[0] == 0:
    raise ValueError('Malformed soundfile'  )
  return audio

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__ = "f32le"     ,   )	->    Tuple:
  UpperCamelCase_: Any   				=    F'''{sampling_rate}'''
  UpperCamelCase_: Union[str, Any]   				=    '1'
  if format_for_conversion == "s16le":
    UpperCamelCase_: Optional[Any]   				=    2
  elif format_for_conversion == "f32le":
    UpperCamelCase_: Any   				=    4
  else:
    raise ValueError(F'''Unhandled format `{format_for_conversion}`. Please use `s16le` or `f32le`'''  )

  UpperCamelCase_: int   				=    platform.system()
  if system == "Linux":
    UpperCamelCase_: Tuple   				=    'alsa'
    UpperCamelCase_: List[str]   				=    'default'
  elif system == "Darwin":
    UpperCamelCase_: int   				=    'avfoundation'
    UpperCamelCase_: Union[str, Any]   				=    ':0'
  elif system == "Windows":
    UpperCamelCase_: Tuple   				=    'dshow'
    UpperCamelCase_: Dict   				=    'default'

  UpperCamelCase_: Any   				=    [
      'ffmpeg',
      '-f',
      format_,
      '-i',
      input_,
      '-ac',
      ac,
      '-ar',
      ar,
      '-f',
      format_for_conversion,
      '-fflags',
      'nobuffer',
      '-hide_banner',
      '-loglevel',
      'quiet',
      'pipe:1',
  ]
  UpperCamelCase_: Tuple   				=    int(round(sampling_rate * chunk_length_s  )  ) * size_of_sample
  UpperCamelCase_: Optional[int]   				=    _ffmpeg_stream(UpperCAmelCase__     ,   UpperCAmelCase__  )
  for item in iterator:
    yield item

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__ = None     ,   UpperCAmelCase__ = None     ,   UpperCAmelCase__ = "f32le"     ,   )	->    Any:
  if stream_chunk_s is not None:
    UpperCamelCase_: List[Any]   				=    stream_chunk_s
  else:
    UpperCamelCase_: Dict   				=    chunk_length_s

  UpperCamelCase_: List[str]   				=    ffmpeg_microphone(UpperCAmelCase__     ,   UpperCAmelCase__     ,   format_for_conversion=UpperCAmelCase__  )
  if format_for_conversion == "s16le":
    UpperCamelCase_: Union[str, Any]   				=    np.intaa
    UpperCamelCase_: List[Any]   				=    2
  elif format_for_conversion == "f32le":
    UpperCamelCase_: str   				=    np.floataa
    UpperCamelCase_: Tuple   				=    4
  else:
    raise ValueError(F'''Unhandled format `{format_for_conversion}`. Please use `s16le` or `f32le`'''  )

  if stride_length_s is None:
    UpperCamelCase_: int   				=    chunk_length_s / 6
  UpperCamelCase_: Tuple   				=    int(round(sampling_rate * chunk_length_s  )  ) * size_of_sample
  if isinstance(UpperCAmelCase__     ,   (int, float)  ):
    UpperCamelCase_: Union[str, Any]   				=    [stride_length_s, stride_length_s]

  UpperCamelCase_: Any   				=    int(round(sampling_rate * stride_length_s[0]  )  ) * size_of_sample
  UpperCamelCase_: Dict   				=    int(round(sampling_rate * stride_length_s[1]  )  ) * size_of_sample
  UpperCamelCase_: Optional[int]   				=    datetime.datetime.now()
  UpperCamelCase_: Optional[int]   				=    datetime.timedelta(seconds=UpperCAmelCase__  )
  for item in chunk_bytes_iter(UpperCAmelCase__     ,   UpperCAmelCase__     ,   stride=(stride_left, stride_right)     ,   stream=UpperCAmelCase__  ):
    # Put everything back in numpy scale
    UpperCamelCase_: Tuple   				=    np.frombuffer(item['raw']     ,   dtype=UpperCAmelCase__  )
    UpperCamelCase_: Optional[int]   				=    (
        item['stride'][0] // size_of_sample,
        item['stride'][1] // size_of_sample,
    )
    UpperCamelCase_: int   				=    sampling_rate
    audio_time += delta
    if datetime.datetime.now() > audio_time + 1_0 * delta:
      # We're late !! SKIP
      continue
    yield item

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__ = False  )	->    int:
  UpperCamelCase_: str   				=    b''
  UpperCamelCase_				,UpperCamelCase_: Union[str, Any]   				=    stride
  if stride_left + stride_right >= chunk_len:
    raise ValueError(
        F'''Stride needs to be strictly smaller than chunk_len: ({stride_left}, {stride_right}) vs {chunk_len}'''  )
  UpperCamelCase_: List[str]   				=    0
  for raw in iterator:
    acc += raw
    if stream and len(UpperCAmelCase__  ) < chunk_len:
      UpperCamelCase_: Optional[Any]   				=    (_stride_left, 0)
      yield {"raw": acc[:chunk_len], "stride": stride, "partial": True}
    else:
      while len(UpperCAmelCase__  ) >= chunk_len:
        # We are flushing the accumulator
        UpperCamelCase_: int   				=    (_stride_left, stride_right)
        UpperCamelCase_: Optional[Any]   				=    {'raw': acc[:chunk_len], 'stride': stride}
        if stream:
          UpperCamelCase_: Any   				=    False
        yield item
        UpperCamelCase_: Optional[int]   				=    stride_left
        UpperCamelCase_: Optional[Any]   				=    acc[chunk_len - stride_left - stride_right :]
    # Last chunk
  if len(UpperCAmelCase__  ) > stride_left:
    UpperCamelCase_: int   				=    {'raw': acc, 'stride': (_stride_left, 0)}
    if stream:
      UpperCamelCase_: Optional[Any]   				=    False
    yield item

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__  )	->    int:
  UpperCamelCase_: Any   				=    2**2_4  # 16Mo
  try:
    with subprocess.Popen(UpperCAmelCase__     ,   stdout=subprocess.PIPE     ,   bufsize=UpperCAmelCase__  ) as ffmpeg_process:
      while True:
        UpperCamelCase_: Any   				=    ffmpeg_process.stdout.read(UpperCAmelCase__  )
        if raw == b"":
          break
        yield raw
  except FileNotFoundError as error:
    raise ValueError('ffmpeg was not found but is required to stream audio files from filename'  ) from error