Computational complexity of Fibonacci Sequence

Question

I understand Big-O notation, but I don\'t know how to calculate it for many functions. In particular, I\'ve been trying to figure out the computational complexity of the nai

Answer 1

Just ask yourself how many statements need to execute for F(n) to complete.

For F(1), the answer is 1 (the first part of the conditional).

For F(n), the answer is F(n-1) + F(n-2).

So what function satisfies these rules? Try aⁿ (a > 1):

aⁿ == a^(n-1) + a^(n-2)

Divide through by a^(n-2):

a² == a + 1

Solve for a and you get (1+sqrt(5))/2 = 1.6180339887, otherwise known as the golden ratio.

So it takes exponential time.