

'''simple docstring'''
def 	_lowerCAmelCase (						_UpperCamelCase						:					list    )				->      list:
     """simple docstring"""




     if any(not isinstance(_UpperCamelCase							,			_UpperCamelCase    ) or x < 0 for x in sequence    ):
          raise TypeError('Sequence must be list of non-negative integers'    )
     for _ in range(len(_UpperCamelCase    )    ):
          for i, (rod_upper, rod_lower) in enumerate(zip(_UpperCamelCase							,			sequence[1:]    )    ):
               if rod_upper > rod_lower:
                    sequence[i] -= rod_upper - rod_lower
                    sequence[i + 1] += rod_upper - rod_lower
     return sequence


if __name__ == "__main__":
     assert bead_sort([5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5]
     assert bead_sort([7, 9, 4, 3, 5]) == [3, 4, 5, 7, 9]



'''simple docstring'''
from math import factorial


def 	_lowerCAmelCase (						_UpperCamelCase						:					int							,			_UpperCamelCase						:					int							,			_UpperCamelCase						:					float    )				->      float:
     """simple docstring"""




     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(_UpperCamelCase							,			_UpperCamelCase    ) or not isinstance(_UpperCamelCase							,			_UpperCamelCase    ):
          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'    )
     _SCREAMING_SNAKE_CASE							   =(prob**successes) * ((1 - prob) ** (trials - successes))
     # Calculate the binomial coefficient: n! / k!(n-k)!
     _SCREAMING_SNAKE_CASE							   =float(factorial(_UpperCamelCase    )    )
     coefficient /= factorial(_UpperCamelCase    ) * 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, 0.7_5))
