
from random import randint
from tempfile import TemporaryFile

import numpy as np


def 							a__					(							snake_case       ,			snake_case       ,			snake_case							):





  """simple docstring"""
  __SCREAMING_SNAKE_CASE      :	Dict					=		0
  if start < end:
    __SCREAMING_SNAKE_CASE      :	List[Any]					=		randint(lowerCAmelCase_       ,			lowerCAmelCase_							)
    __SCREAMING_SNAKE_CASE      :	List[Any]					=		a[end]
    __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		a[pivot]
    __SCREAMING_SNAKE_CASE      :	Dict					=		temp

    __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE      :	Tuple					=		_in_place_partition(lowerCAmelCase_       ,			lowerCAmelCase_       ,			lowerCAmelCase_							)
    count += _in_place_quick_sort(lowerCAmelCase_       ,			lowerCAmelCase_       ,			p - 1							)
    count += _in_place_quick_sort(lowerCAmelCase_       ,			p + 1       ,			lowerCAmelCase_							)
  return count


def 							a__					(							snake_case       ,			snake_case       ,			snake_case							):





  """simple docstring"""
  __SCREAMING_SNAKE_CASE      :	int					=		0
  __SCREAMING_SNAKE_CASE      :	int					=		randint(lowerCAmelCase_       ,			lowerCAmelCase_							)
  __SCREAMING_SNAKE_CASE      :	Any					=		a[end]
  __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		a[pivot]
  __SCREAMING_SNAKE_CASE      :	str					=		temp
  __SCREAMING_SNAKE_CASE      :	Dict					=		start - 1
  for index in range(lowerCAmelCase_       ,			lowerCAmelCase_							):
    count += 1
    if a[index] < a[end]:  # check if current val is less than pivot value
      __SCREAMING_SNAKE_CASE      :	Any					=		new_pivot_index + 1
      __SCREAMING_SNAKE_CASE      :	List[str]					=		a[new_pivot_index]
      __SCREAMING_SNAKE_CASE      :	Optional[int]					=		a[index]
      __SCREAMING_SNAKE_CASE      :	Union[str, Any]					=		temp

  __SCREAMING_SNAKE_CASE      :	Dict					=		a[new_pivot_index + 1]
  __SCREAMING_SNAKE_CASE      :	int					=		a[end]
  __SCREAMING_SNAKE_CASE      :	str					=		temp
  return new_pivot_index + 1, count


lowercase_ 				=			TemporaryFile()
lowercase_ 				=			100  # 1000 elements are to be sorted


lowercase_ 				=			0, 1  # mean and standard deviation
lowercase_ 				=			np.random.normal(mu, sigma, p)
np.save(outfile, X)
print("""The array is""")
print(X)


outfile.seek(0)  # using the same array
lowercase_ 				=			np.load(outfile)
lowercase_ 				=			len(M) - 1
lowercase_ 				=			_in_place_quick_sort(M, 0, r)

print(
    """No of Comparisons for 100 elements selected from a standard normal distribution"""
    """is :"""
)


print(z)




from __future__ import annotations

from math import gcd



def       _lowerCAmelCase    (				lowerCAmelCase_				:int		,    lowerCAmelCase_				:int = 2		,    lowerCAmelCase_				:int = 1		,    lowerCAmelCase_				:int = 3		,    )->int | None:
   '''simple docstring'''






   if num < 2:
      raise ValueError("The input value cannot be less than 2"				)

   # Because of the relationship between ``f(f(x))`` and ``f(x)``, this
   # algorithm struggles to find factors that are divisible by two.
   # As a workaround, we specifically check for two and even inputs.
   #   See: https://math.stackexchange.com/a/2856214/165820
   if num > 2 and num % 2 == 0:
      return 2

   # Pollard's Rho algorithm requires a function that returns pseudorandom
   # values between 0 <= X < ``num``.  It doesn't need to be random in the
   # sense that the output value is cryptographically secure or difficult
   # to calculate, it only needs to be random in the sense that all output
   # values should be equally likely to appear.
   # For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
   # However, the success of Pollard's algorithm isn't guaranteed and is
   # determined in part by the initial seed and the chosen random function.
   # To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
   # where ``C`` is a value that we can modify between each attempt.
   def rand_fn(lowerCAmelCase_				:int		,    lowerCAmelCase_				:int		,    lowerCAmelCase_				:int				) -> int:
      return (pow(lowerCAmelCase_		,    2				) + step) % modulus

   for _ in range(lowerCAmelCase_				):
      # These track the position within the cycle detection logic.
      snake_case_            =       seed
      snake_case_            =       seed

      while True:
         # At each iteration, the tortoise moves one step and the hare moves two.
         snake_case_            =       rand_fn(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_				)
         snake_case_            =       rand_fn(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_				)
         snake_case_            =       rand_fn(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_				)

         # At some point both the tortoise and the hare will enter a cycle whose
         # length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
         # the tortoise and hare will end up on the same value modulo ``p``.
         # We can detect when this happens because the position difference between
         # the tortoise and the hare will share a common divisor with ``num``.
         snake_case_            =       gcd(hare - tortoise		,    lowerCAmelCase_				)

         if divisor == 1:
            # No common divisor yet, just keep searching.
            continue
         else:
            # We found a common divisor!
            if divisor == num:
               # Unfortunately, the divisor is ``num`` itself and is useless.
               break
            else:
               # The divisor is a nontrivial factor of ``num``!
               return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
      snake_case_            =       hare

      # The new step value for the random function can just be incremented.
      # At first the results will be similar to what the old function would
      # have produced, but the value will quickly diverge after a bit.
      step += 1

   # We haven't found a divisor within the requested number of attempts.
   # We were unlucky or ``num`` itself is actually prime.
   return None


if __name__ == "__main__":
   import argparse

   SCREAMING_SNAKE_CASE						:Union[str, Any]			=  argparse.ArgumentParser()
   parser.add_argument(
       '''num''',
       type=int,
       help='''The value to find a divisor of''',
   )
   parser.add_argument(
       '''--attempts''',
       type=int,
       default=3,
       help='''The number of attempts before giving up''',
   )
   SCREAMING_SNAKE_CASE						:List[str]			=  parser.parse_args()

   SCREAMING_SNAKE_CASE						:List[Any]			=  pollard_rho(args.num, attempts=args.attempts)
   if divisor is None:
      print(F'''{args.num} is probably prime''')
   else:
      SCREAMING_SNAKE_CASE						:List[str]			=  args.num // divisor
      print(F'''{args.num} = {divisor} * {quotient}''')




