
"""simple docstring"""







def     __lowerCAmelCase				(_UpperCamelCase       ,  _UpperCamelCase       ,  _UpperCamelCase       ,  _UpperCamelCase       ,  _UpperCamelCase       ,  ):
	__lowerCAmelCase			:						Any									=      [redshift, radiation_density, matter_density, dark_energy]
	if any(p < 0 for p in parameters		):
		raise ValueError('All input parameters must be positive'		)

	if any(p > 1 for p in parameters[1:4]		):
		raise ValueError('Relative densities cannot be greater than one'		)
	else:
		__lowerCAmelCase			:						Any									=      1 - (matter_density + radiation_density + dark_energy)

		__lowerCAmelCase			:						Dict									=      (
		    radiation_density * (redshift + 1) ** 4
		    + matter_density * (redshift + 1) ** 3
		    + curvature * (redshift + 1) ** 2
		    + dark_energy
		)

		__lowerCAmelCase			:						Tuple									=      hubble_constant * e_a ** (1 / 2)
		return hubble


if __name__ == "__main__":
							import doctest

							# run doctest
							doctest.testmod()

							# demo LCDM approximation
							lowerCamelCase__   					=		0.3

							print(
							    hubble_parameter(
							        hubble_constant=6_8.3,
							        radiation_density=1E-4,
							        matter_density=matter_density,
							        dark_energy=1 - matter_density,
							        redshift=0,
							    )
							)





'''simple docstring'''







from __future__ import annotations





def 						snake_case_							(_a	:							Dict    ,   _a	:							str    ,   _a	:							Optional[Any]    ,   _a	:							List[str]     ):  # noqa: E741
    while r - l > 1:
        UpperCAmelCase			       =		(l + r) // 2
        if v[m] >= key:
            UpperCAmelCase			       =		m
        else:
            UpperCAmelCase			       =		m  # noqa: E741
    return r





def 						snake_case_							(_a	:							list[int]     ):
    if len(_a     ) == 0:
        return 0

    UpperCAmelCase			       =		[0] * len(_a     )
    UpperCAmelCase			       =		1

    UpperCAmelCase			       =		v[0]

    for i in range(1    ,   len(_a     )     ):
        if v[i] < tail[0]:
            UpperCAmelCase			       =		v[i]
        elif v[i] > tail[length - 1]:
            UpperCAmelCase			       =		v[i]
            length += 1
        else:
            UpperCAmelCase			       =		v[i]

    return length


if __name__ == "__main__":
   import doctest

   doctest.testmod()




