



from timeit import timeit
def        lowercase_							(A : int      ):
       if number < 0:
              raise ValueError('the value of input must not be negative'      )
       snake_case__							:	Dict   	=	0
       while number:
              number &= number - 1
              result += 1
       return result
def        lowercase_							(A : int      ):
       if number < 0:
              raise ValueError('the value of input must not be negative'      )
       snake_case__							:	List[str]   	=	0
       while number:
              if number % 2 == 1:
                     result += 1
              number >>= 1
       return result
def        lowercase_							():

       def do_benchmark(A : int      ) -> None:
              snake_case__							:	Dict   	=	'import __main__ as z'
              print(F'''Benchmark when {number = }:'''      )
              print(F'''{get_set_bits_count_using_modulo_operator(A      ) = }'''      )
              snake_case__							:	int   	=	timeit('z.get_set_bits_count_using_modulo_operator(25)'		,					setup=A      )
              print(F'''timeit() runs in {timing} seconds'''      )
              print(F'''{get_set_bits_count_using_brian_kernighans_algorithm(A      ) = }'''      )
              snake_case__							:	Tuple   	=	timeit(
                  'z.get_set_bits_count_using_brian_kernighans_algorithm(25)'		,					setup=A		,					)
              print(F'''timeit() runs in {timing} seconds'''      )

       for number in (2_5, 3_7, 5_8, 0):
              do_benchmark(A      )
              print()


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 benchmark()











from math import factorial
def        lowercase_							(A : int		,					A : int		,					A : float      ):
       if successes > trials:
              raise ValueError('successes must be lower or equal to trials'      )
       if trials < 0 or successes < 0:
              raise ValueError('the function is defined for non-negative integers'      )
       if not isinstance(A		,					A      ) or not isinstance(A		,					A      ):
              raise ValueError('the function is defined for non-negative integers'      )
       if not 0 < prob < 1:
              raise ValueError('prob has to be in range of 1 - 0'      )
       snake_case__							:	List[Any]   	=	(prob**successes) * ((1 - prob) ** (trials - successes))
       # Calculate the binomial coefficient: n! / k!(n-k)!
       snake_case__							:	List[str]   	=	float(factorial(A      )      )
       coefficient /= factorial(A      ) * factorial(trials - successes      )
       return probability * coefficient


if __name__ == "__main__":
 from doctest import testmod

 testmod()
 print("Probability of 2 successes out of 4 trails")
 print("with probability of 0.75 is:", end=" ")
 print(binomial_distribution(2, 4, 0.75))






