A complete answer consists of three parts: a description of the algorithm, a proof of correctness, and a running time analysis No complicated code: English is the best way to express an algorithm combined with some simple pseudocode when needed. You are not writing a computer program so avoid unnecessary details in your algorithms. Fun with Algorithms. Recall that Fibonacci numbers form a sequence Fn where Fo = 0, F1 = 1, and Fn = Fn-1 + Fn-2. The standard algorithm for finding the n-th Fibonacci number takes O(n) time. The goal of this question is to design a significantly faster algorithm for this problem. (a) Prove by induction that for all n > 1: [Fn+1 F Fn Fn-1 (b) Use the first part to design an algorithm that finds Fn in O(log n) time