

from collections import Counter
from timeit import timeit

def       a__					(		UpperCAmelCase							:      str = ""    ,			)  ->						bool:
  return sum(c % 2 for c in Counter(input_str.replace(''' '''    ,			''''''      ).lower()      ).values()      ) < 2

def       a__					(		UpperCAmelCase							:      str = ""      )  ->						bool:
  if len(UpperCAmelCase      ) == 0:
    return True
  UpperCAmelCase	:							Tuple						=			input_str.replace(''' '''    ,			''''''      ).lower()
  # character_freq_dict: Stores the frequency of every character in the input string
  UpperCAmelCase	:							dict[str, int]						=			{}

  for character in lower_case_input_str:
    UpperCAmelCase	:							Any						=			character_freq_dict.get(UpperCAmelCase    ,			0      ) + 1
  UpperCAmelCase	:							int						=			0

  for character_count in character_freq_dict.values():
    if character_count % 2:
      odd_char += 1
  if odd_char > 1:
    return False
  return True

def       a__					(		UpperCAmelCase							:      str = ""      )  ->						None:
  print('''\nFor string = '''    ,			UpperCAmelCase    ,			''':'''      )
  print(
      '''> can_string_be_rearranged_as_palindrome_counter()'''    ,			'''\tans ='''    ,			can_string_be_rearranged_as_palindrome_counter(UpperCAmelCase      )    ,			'''\ttime ='''    ,			timeit(
          '''z.can_string_be_rearranged_as_palindrome_counter(z.check_str)'''    ,			setup='''import __main__ as z'''    ,			)    ,			'''seconds'''    ,			)
  print(
      '''> can_string_be_rearranged_as_palindrome()'''    ,			'''\tans ='''    ,			can_string_be_rearranged_as_palindrome(UpperCAmelCase      )    ,			'''\ttime ='''    ,			timeit(
          '''z.can_string_be_rearranged_as_palindrome(z.check_str)'''    ,			setup='''import __main__ as z'''    ,			)    ,			'''seconds'''    ,			)


if __name__ == "__main__":
     _lowerCamelCase    :       Union[str, Any]        =							input(
         "Enter string to determine if it can be rearranged as a palindrome or not: "
     ).strip()
     benchmark(check_str)
     _lowerCamelCase    :       Any        =							can_string_be_rearranged_as_palindrome_counter(check_str)
     print(f"""{check_str} can {"" if status else "not "}be rearranged as a palindrome""")








from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean

def       a__					(		UpperCAmelCase							:      int      )  ->						Dict:

  # A local function to see if a dot lands in the circle.
  def is_in_circle(UpperCAmelCase							:      float    ,			UpperCAmelCase							:      float      ) -> bool:
    UpperCAmelCase	:							Dict						=			sqrt((x**2) + (y**2)      )
    # Our circle has a radius of 1, so a distance
    # greater than 1 would land outside the circle.
    return distance_from_centre <= 1

  # The proportion of guesses that landed in the circle
  UpperCAmelCase	:							List[str]						=			mean(
      int(is_in_circle(uniform(-1.0    ,			1.0      )    ,			uniform(-1.0    ,			1.0      )      )      )
      for _ in range(UpperCAmelCase      )      )
  # The ratio of the area for circle to square is pi/4.
  UpperCAmelCase	:							int						=			proportion * 4
  print(f'''The estimated value of pi is {pi_estimate}'''      )
  print(f'''The numpy value of pi is {pi}'''      )
  print(f'''The total error is {abs(pi - pi_estimate      )}'''      )

def       a__					(		UpperCAmelCase							:      int    ,			UpperCAmelCase							:      Callable[[float], float]    ,			UpperCAmelCase							:      float = 0.0    ,			UpperCAmelCase							:      float = 1.0    ,			)  ->						float:
  return mean(
      function_to_integrate(uniform(UpperCAmelCase    ,			UpperCAmelCase      )      ) for _ in range(UpperCAmelCase      )      ) * (max_value - min_value)

def       a__					(		UpperCAmelCase							:      int    ,			UpperCAmelCase							:      float = 0.0    ,			UpperCAmelCase							:      float = 1.0      )  ->						None:

  def identity_function(UpperCAmelCase							:      float      ) -> float:
    return x

  UpperCAmelCase	:							int						=			area_under_curve_estimator(
      UpperCAmelCase    ,			UpperCAmelCase    ,			UpperCAmelCase    ,			UpperCAmelCase      )
  UpperCAmelCase	:							Tuple						=			(max_value * max_value - min_value * min_value) / 2

  print('''******************'''      )
  print(f'''Estimating area under y=x where x varies from {min_value} to {max_value}'''      )
  print(f'''Estimated value is {estimated_value}'''      )
  print(f'''Expected value is {expected_value}'''      )
  print(f'''Total error is {abs(estimated_value - expected_value      )}'''      )
  print('''******************'''      )

def       a__					(		UpperCAmelCase							:      int      )  ->						None:

  def function_to_integrate(UpperCAmelCase							:      float      ) -> float:
    return sqrt(4.0 - x * x      )

  UpperCAmelCase	:							Optional[int]						=			area_under_curve_estimator(
      UpperCAmelCase    ,			UpperCAmelCase    ,			0.0    ,			2.0      )

  print('''******************'''      )
  print('''Estimating pi using area_under_curve_estimator'''      )
  print(f'''Estimated value is {estimated_value}'''      )
  print(f'''Expected value is {pi}'''      )
  print(f'''Total error is {abs(estimated_value - pi      )}'''      )
  print('''******************'''      )


if __name__ == "__main__":
     import doctest

     doctest.testmod()





