
'''simple docstring'''







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A			) ->			bool:
	return not any(
	    neighbour == 1 and colored_vertices[i] == color
	    for i, neighbour in enumerate(__A			)			)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A    ,       __A			) ->			bool:

	# Base Case
	if index == len(__A			):
		return True

	# Recursive Step
	for i in range(__A			):
		if valid_coloring(graph[index]    ,       __A    ,       __A			):
			# Color current vertex
			_snake_case     		=	i
			# Validate coloring
			if util_color(__A    ,       __A    ,       __A    ,       index + 1			):
				return True
			# Backtrack
			_snake_case     		=	-1
	return False







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			list[int]:
	_snake_case     		=	[-1] * len(__A			)

	if util_color(__A    ,       __A    ,       __A    ,       0			):
		return colored_vertices

	return []



'''simple docstring'''







import math







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if (
	    not isinstance(__A    ,       (int, float)			)
	    or power_factor < -1
	    or power_factor > 1
	):
		raise ValueError('power_factor must be a valid float value between -1 and 1.'			)
	return apparent_power * power_factor







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:
	if (
	    not isinstance(__A    ,       (int, float)			)
	    or power_factor < -1
	    or power_factor > 1
	):
		raise ValueError('power_factor must be a valid float value between -1 and 1.'			)
	return apparent_power * math.sqrt(1 - power_factor**2			)


if __name__ == "__main__":
					import doctest

					doctest.testmod()

