



"""simple docstring"""







import random
import sys

import numpy as np
from matplotlib import pyplot as plt
from matplotlib.colors import ListedColormap

lowercase__		:				Tuple          =	"""Usage of script: script_name <size_of_canvas:int>"""

lowercase__		:				Any          =	[0] * 1_0_0 + [1] * 1_0
random.shuffle(choice)

def 				UpperCamelCase_    (    lowerCAmelCase__      :				Optional[Any]						)						->   list[list[bool]]:

  """simple docstring"""




  lowerCAmelCase_   :				Dict								= [[False for i in range(_lowerCAmelCase						)] for j in range(_lowerCAmelCase						)]
  return canvas

def 				UpperCamelCase_    (    lowerCAmelCase__      :				List[str]						)						->   None:

  """simple docstring"""




  for i, row in enumerate(_lowerCAmelCase						):
    for j, _ in enumerate(_lowerCAmelCase						):
      lowerCAmelCase_   :				Optional[int]								= bool(random.getrandbits(1						)						)

def 				UpperCamelCase_    (    lowerCAmelCase__      :				Optional[Any]						)						->   list[list[bool]]:

  """simple docstring"""




  lowerCAmelCase_   :				Dict								= np.array(_lowerCAmelCase						)
  lowerCAmelCase_   :				Dict								= np.array(create_canvas(current_canvas.shape[0]						)						)
  for r, row in enumerate(_lowerCAmelCase						):
    for c, pt in enumerate(_lowerCAmelCase						):
      lowerCAmelCase_   :				int								= __judge_point(
          _lowerCAmelCase    ,   current_canvas[r - 1 : r + 2, c - 1 : c + 2]						)

  lowerCAmelCase_   :				List[Any]								= next_gen_canvas
  del next_gen_canvas  # cleaning memory as we move on.
  lowerCAmelCase_   :				list[list[bool]]								= current_canvas.tolist()
  return return_canvas

def 				UpperCamelCase_    (    lowerCAmelCase__      :				Tuple    ,   lowerCAmelCase__      :				int						)						->   bool:

  """simple docstring"""




  lowerCAmelCase_   :				Dict								= 0
  lowerCAmelCase_   :				int								= 0
  # finding dead or alive neighbours count.
  for i in neighbours:
    for status in i:
      if status:
        alive += 1
      else:
        dead += 1

    # handling duplicate entry for focus pt.
  if pt:
    alive -= 1
  else:
    dead -= 1

  # running the rules of game here.
  lowerCAmelCase_   :				int								= pt
  if pt:
    if alive < 2:
      lowerCAmelCase_   :				Tuple								= False
    elif alive == 2 or alive == 3:
      lowerCAmelCase_   :				int								= True
    elif alive > 3:
      lowerCAmelCase_   :				Dict								= False
  else:
    if alive == 3:
      lowerCAmelCase_   :				Optional[Any]								= True

  return state


if __name__ == "__main__":
     if len(sys.argv) != 2:
          raise Exception(usage_doc)

     lowercase__		:				Tuple          =	int(sys.argv[1])
     # main working structure of this module.
     lowercase__		:				Any          =	create_canvas(canvas_size)
     seed(c)
     lowercase__    ,     lowercase__		:				Optional[int]          =	plt.subplots()
     fig.show()
     lowercase__		:				List[str]          =	ListedColormap(["""w""", """k"""])
     try:
          while True:
               lowercase__		:				Tuple          =	run(c)
               ax.matshow(c, cmap=cmap)
               fig.canvas.draw()
               ax.cla()
     except KeyboardInterrupt:
          # do nothing.
          pass










'''simple docstring'''





from __future__ import annotations

import math
from collections.abc import Callable

def        a_     (							_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase       ,_lowerCAmelCase = 100       ,)      ->      float:
  __lowerCamelCase       :       Dict           = x_start
  __lowerCamelCase       :       int           = fnc(_lowerCAmelCase       )
  __lowerCamelCase       :       Dict           = 0.0

  for _ in range(_lowerCAmelCase       ):
    # Approximates curve as a sequence of linear lines and sums their length
    __lowerCamelCase       :       List[str]           = (x_end - x_start) / steps + xa
    __lowerCamelCase       :       List[Any]           = fnc(_lowerCAmelCase       )
    length += math.hypot(xa - xa       ,fxa - fxa       )

    # Increment step
    __lowerCamelCase       :       Any           = xa
    __lowerCamelCase       :       Tuple           = fxa

  return length


if __name__ == "__main__":

   def        a_     (							_lowerCAmelCase       )      ->      Dict:
     return math.sin(10 * x       )

   print('f(x) = sin(10 * x)')
   print('The length of the curve from x = -10 to x = 10 is:')
   _UpperCamelCase											=						10
   while i <= 100000:
      print(f'''With {i} steps: {line_length(f, -10, 10, i)}''')
      i *= 10






