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(n2) upper O left parenthesis n squared right parenthesis O(1) upper O left parenthesis 1 right parenthesis O(logn) upper O left parenthesis log n right parenthesis O(n) upper O left parenthesis n right parenthesis

Answer 1

The best possible time complexity for calculating Fibonacci numbers using an efficient algorithm is O(log n). This can be achieved using matrix exponentiation or the fast doubling method.

To clarify the options provided:

• O(n²) is too slow for Fibonacci calculation.
• O(1) would imply constant time, which is not possible for computing Fibonacci for varying n.
• O(n) is better than O(n²) but still not optimal.
• O(log n) is the best option here, as it allows for efficient computation of Fibonacci numbers.

Thus, the best answer is O(log n).