Question

Students are discussing variations of algorithms to find Fibonacci numbers, like fib(6). What is the best possible time complexity that they can get for this algorithm?(1 point)
Responses

O(logn)
upper O left parenthesis log n right parenthesis

O(n2)
upper O left parenthesis n squared right parenthesis

O(1)
upper O left parenthesis 1 right parenthesis

O(n)

Answer 1

The best possible time complexity for calculating Fibonacci numbers using the most efficient algorithm is \( O(\log n) \).

This can be achieved using matrix exponentiation, which allows us to compute Fibonacci numbers in logarithmic time with respect to the input `n`.

So, the correct response is:

**O(log n)**