


from __future__ import annotations

from math import gcd
def     __lowerCamelCase						(			UpperCAmelCase_						:		int			,  UpperCAmelCase_						:		int = 2			,  UpperCAmelCase_						:		int = 1			,  UpperCAmelCase_						:		int = 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(UpperCAmelCase_						:		int			,  UpperCAmelCase_						:		int			,  UpperCAmelCase_						:		int						) -> int:
            return (pow(UpperCAmelCase_			,  2						) + step) % modulus

      for _ in range(UpperCAmelCase_						):
            # These track the position within the cycle detection logic.
            a						:Optional[Any]										=	seed
            a						:Optional[Any]										=	seed

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

                  # 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			,  UpperCAmelCase_						)

                  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						: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

     snake_case    :   Dict	    =					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''',
     )
     snake_case    :   List[str]	    =					parser.parse_args()

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









import numpy as np
from matplotlib import pyplot as plt
from sklearn.datasets import load_iris
from sklearn.metrics import ConfusionMatrixDisplay
from sklearn.model_selection import train_test_split
from xgboost import XGBClassifier
def     __lowerCamelCase						(			UpperCAmelCase_						:		dict						):




      """simple docstring"""





      return (data["data"], data["target"])
def     __lowerCamelCase						(			UpperCAmelCase_						:		np.ndarray			,  UpperCAmelCase_						:		np.ndarray						):




      """simple docstring"""





      a						:Optional[Any]										=	XGBClassifier()
      classifier.fit(UpperCAmelCase_			,  UpperCAmelCase_						)
      return classifier
def     __lowerCamelCase						(			):




      """simple docstring"""





      a						:List[Any]										=	load_iris()
      a							,    a						:Any										=	data_handling(UpperCAmelCase_						)
      a							,    a							,    a							,    a						:Tuple										=	train_test_split(
          UpperCAmelCase_			,  UpperCAmelCase_			,  test_size=0.25						)

      a						:List[Any]										=	iris['''target_names''']

      # Create an XGBoost Classifier from the training data
      a						:Optional[int]										=	xgboost(UpperCAmelCase_			,  UpperCAmelCase_						)

      # Display the confusion matrix of the classifier with both training and test sets
      ConfusionMatrixDisplay.from_estimator(
          UpperCAmelCase_			,  UpperCAmelCase_			,  UpperCAmelCase_			,  display_labels=UpperCAmelCase_			,  cmap='''Blues'''			,  normalize='''true'''			,  )
      plt.title('''Normalized Confusion Matrix - IRIS Dataset'''						)
      plt.show()


if __name__ == "__main__":
     import doctest

     doctest.testmod(verbose=True)
     main()





