"""simple docstring"""







from __future__ import annotations

from math import gcd

def _a			(		_snake_case				,	_snake_case = 2				,	_snake_case = 1				,	_snake_case = 3				,	):







      """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(_snake_case				,	_snake_case				,	_snake_case							) -> int:
            return (pow(_snake_case				,	2							) + step) % modulus

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

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

  _UpperCamelCase					      =  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""",
  )
  _UpperCamelCase					      =  parser.parse_args()

  _UpperCamelCase					      =  pollard_rho(args.num, attempts=args.attempts)
  if divisor is None:
    print(F"""{args.num} is probably prime""")
  else:
    _UpperCamelCase					      =  args.num // divisor
    print(F"""{args.num} = {divisor} * {quotient}""")











"""simple docstring"""







import pandas as pd
from matplotlib import pyplot as plt
from sklearn.linear_model import LinearRegression

# Splitting the dataset into the Training set and Test set
from sklearn.model_selection import train_test_split

# Fitting Polynomial Regression to the dataset
from sklearn.preprocessing import PolynomialFeatures

# Importing the dataset
_UpperCamelCase					      =  pd.read_csv(
    """https://s3.us-west-2.amazonaws.com/public.gamelab.fun/dataset/"""
    """position_salaries.csv"""
)
_UpperCamelCase					      =  dataset.iloc[:, 1:2].values
_UpperCamelCase					      =  dataset.iloc[:, 2].values


_UpperCamelCase      ,  _UpperCamelCase      ,  _UpperCamelCase      ,  _UpperCamelCase					      =  train_test_split(X, y, test_size=0.2, random_state=0)


_UpperCamelCase					      =  PolynomialFeatures(degree=4)
_UpperCamelCase					      =  poly_reg.fit_transform(X)
_UpperCamelCase					      =  LinearRegression()
pol_reg.fit(X_poly, y)

def _a			(		):







      """simple docstring"""






      plt.scatter(_snake_case				,	_snake_case				,	color="""red"""							)
      plt.plot(_snake_case				,	pol_reg.predict(poly_reg.fit_transform(_snake_case							)							)				,	color="""blue"""							)
      plt.title("""Truth or Bluff (Linear Regression)"""							)
      plt.xlabel("""Position level"""							)
      plt.ylabel("""Salary"""							)
      plt.show()


if __name__ == "__main__":
  viz_polymonial()

  # Predicting a new result with Polymonial Regression
  pol_reg.predict(poly_reg.fit_transform([[5.5]]))
  # output should be 132148.43750003



