Answered: Fibonacci sequence is given by the…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Fibonacci sequence is given by the recursive relation:
F(0) = 1 and F(1) = 1
F(n) = F(n-1) + F(n-2)

Ultimately, as discussed in lecture 6, Slide 23, it can be shown that: F(n) =1/√5 ((1+√5)/2)ⁿ - 1/√5((1-√5)/2)ⁿ
The number (1+√5)/2 = 1.618 is called the Golden Ratio

Clearly F(n) = O(2ⁿ).

Write a recursive program like the one described in Lecture 5, Slide 32.

Then, perform a numeric asymtotic analysis and try to determine a more precise asymptotic estimate of time needed to calculate F(n) (e.g., use a time function).

Esentially, try to estimate/infer the tight bound, (f(n)). More details on Big O and in Lecture 5b.

Upload both the program (upload your exact cpp, java, py file - source files) and a pdf file analyzing the output of your program.

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