Complexity of the recursion: T(n) = T(n-1) + T(n-2) + C

Question

I want to understand how to arrive at the complexity of the below recurrence relation.

T(n) = T(n-1) + T(n-2) + C Given T(1) = C and

Answer 1

The complexity is related to input-size, where each call produce a binary-tree of calls

Where T(n) make 2n calls in total ..

T(n) = T(n-1) + T(n-2) + C

T(n) = O(2n-1) + O(2n-2) + O(1)

O(2n)

In the same fashion, you can generalize your recursive function, as a Fibonacci number

T(n) = F(n) + ( C * 2n)

Next you can use a direct formula instead of recursive way

Using a complex method known as Binet's Formula