





'''simple docstring'''




import itertools
from dataclasses import dataclass
from typing import Optional

import pandas as pd
import pyarrow as pa

import datasets
from datasets.table import table_cast


@dataclass
class 			SCREAMING_SNAKE_CASE   (datasets.BuilderConfig							):
     lowerCAmelCase		      =	None




class 			SCREAMING_SNAKE_CASE   (datasets.ArrowBasedBuilder							):
     lowerCAmelCase		      =	PandasConfig


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          return datasets.DatasetInfo(features=self.config.features)


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase):

          '''simple docstring'''






          if not self.config.data_files:
               raise ValueError(F'At least one data file must be specified, but got data_files={self.config.data_files}')
          __A						:			str								=	dl_manager.download_and_extract(self.config.data_files)
          if isinstance(_UpperCAmelCase						,     (str, list, tuple)):
               __A						:			Optional[Any]								=	data_files
               if isinstance(_UpperCAmelCase						,     _UpperCAmelCase):
                    __A						:			Union[str, Any]								=	[files]
               # Use `dl_manager.iter_files` to skip hidden files in an extracted archive
               __A						:			str								=	[dl_manager.iter_files(_UpperCAmelCase) for file in files]
               return [datasets.SplitGenerator(name=datasets.Split.TRAIN						,     gen_kwargs={'files': files})]
          __A						:			int								=	[]
          for split_name, files in data_files.items():
               if isinstance(_UpperCAmelCase						,     _UpperCAmelCase):
                    __A						:			List[str]								=	[files]
               # Use `dl_manager.iter_files` to skip hidden files in an extracted archive
               __A						:			Union[str, Any]								=	[dl_manager.iter_files(_UpperCAmelCase) for file in files]
               splits.append(datasets.SplitGenerator(name=_UpperCAmelCase						,     gen_kwargs={'files': files}))
          return splits


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase):

          '''simple docstring'''






          if self.config.features is not None:
               # more expensive cast to support nested features with keys in a different order
               # allows str <-> int/float or str to Audio for example
               __A						:			Union[str, Any]								=	table_cast(_UpperCAmelCase						,     self.config.features.arrow_schema)
          return pa_table


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase):

          '''simple docstring'''






          for i, file in enumerate(itertools.chain.from_iterable(_UpperCAmelCase)):
               with open(_UpperCAmelCase						,     'rb') as f:
                    __A						:			Tuple								=	pa.Table.from_pandas(pd.read_pickle(_UpperCAmelCase))
                    yield i, self._cast_table(_UpperCAmelCase)






'''simple docstring'''




from __future__ import annotations

from math import gcd






def 	_lowerCAmelCase      (  __snake_case  :			int			,							__snake_case  :			int = 2			,							__snake_case  :			int = 1			,							__snake_case  :			int = 3			,							)					->					int | None:
     # A value less than 2 can cause an infinite loop in the algorithm.
     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(__snake_case  :			int			,							__snake_case  :			int			,							__snake_case  :			int      ) -> int:
          return (pow(__snake_case			,							2      ) + step) % modulus

     for _ in range(__snake_case      ):
          # These track the position within the cycle detection logic.
          __A						:			int								=	seed
          __A						:			Union[str, Any]								=	seed

          while True:
               # At each iteration, the tortoise moves one step and the hare moves two.
               __A						:			List[Any]								=	rand_fn(__snake_case			,							__snake_case			,							__snake_case      )
               __A						:			Optional[Any]								=	rand_fn(__snake_case			,							__snake_case			,							__snake_case      )
               __A						:			Any								=	rand_fn(__snake_case			,							__snake_case			,							__snake_case      )

               # 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``.
               __A						:			Optional[int]								=	gcd(hare - tortoise			,							__snake_case      )

               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.
          __A						:			Union[str, Any]								=	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

  lowercase__   :				str      =   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''',
  )
  lowercase__   :				Optional[int]      =   parser.parse_args()

  lowercase__   :				int      =   pollard_rho(args.num, attempts=args.attempts)
  if divisor is None:
    print(f"""{args.num} is probably prime""")
  else:
    lowercase__   :				List[str]      =   args.num // divisor
    print(f"""{args.num} = {divisor} * {quotient}""")