C++ languageQuestion #6 parts A and B. Please help me. Study the Fibonacci number sequence in the following forms: (1) iterative (sequential), (2) recursive, (3)and closed form solution.1) Examine the theoretical measure of time complexity of each.a) Using theory compare the number of operations and time taken to compute Fibonacci numbersrecursively versus that needed to compute them iteratively.b) How many prime Fibonacci numbers are there, and how many can you find?c) Find the smallest Fibonacci number > 1,000,000d) Find the smallest Fibonacci number > 1,000,000,0002) Implement each Fibonacci form (1, 2, and 3 see above) in the C++ language (C++ 17).Write four functions:a) An iterative function that accepts a non-negative integer n and returns the nth Fibonacci number.b) A recursive function that inputs a non-negative integer n and returns the nth Fibonacci number.c) An improved recursive function that employs dynamic programming to improve the efficiency.d) The closed form of the Fibonacci sequence (be sure to reference the golden ratio)3) Using your software, compute a set of Fibonacci numbers employing the four techniques (c.f. 2, above);for example, use n: {10, 15, 40, 41, 42, 50, 60, 100, 500, 600}.a) Measure the time for each computation-send the results to a file.* Recommend using the Chrono library from C++b) Make certain you have "sufficient" data for convincing results.4) Import your data (from 3) to excel for easy graphing5) Compare the theoretical curves of Big-O with the empirical results.a) Try running on machines with [significantly] different speeds.b) Compare methods to answer the find an answer to question 1.c, above.6) There are other recursive functions such as the Lucas Sequence, how can you apply what you havelearned to it?a) Iteratively computationb) Recursive computationc) Recursive computation with dynamic programming.

Given: The Fibonacci number sequence is in the following forms: Iterative (sequential) Recursive…

Answered: 6) There are other recursive functions…

6) There are other recursive functions such as the Lucas Sequence, how can you apply what you have learned to it? a) Iteratively computation b) Recursive computation

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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Concept explainers

Declaring and Defining the function

A set of statements, which performs a particular task is called a function. The program gains modularity by using function. The application is quite easy to understand, read, and edit when they are created with functions. The developer/programmer creates a function and uses main() to call the function. Once the function gets executed, the control is transferred to the main program.

Question

C++ language

Question #6 parts A and B. Please help me.

Study the Fibonacci number sequence in the following forms: (1) iterative (sequential), (2) recursive, (3)
and closed form solution.
1) Examine the theoretical measure of time complexity of each.
a) Using theory compare the number of operations and time taken to compute Fibonacci numbers
recursively versus that needed to compute them iteratively.
b) How many prime Fibonacci numbers are there, and how many can you find?
c) Find the smallest Fibonacci number > 1,000,000
d) Find the smallest Fibonacci number > 1,000,000,000
2) Implement each Fibonacci form (1, 2, and 3 see above) in the C++ language (C++ 17).
Write four functions:
a) An iterative function that accepts a non-negative integer n and returns the nth Fibonacci number.
b) A recursive function that inputs a non-negative integer n and returns the nth Fibonacci number.
c) An improved recursive function that employs dynamic programming to improve the efficiency.
d) The closed form of the Fibonacci sequence (be sure to reference the golden ratio)
3) Using your software, compute a set of Fibonacci numbers employing the four techniques (c.f. 2, above);
for example, use n: {10, 15, 40, 41, 42, 50, 60, 100, 500, 600}.
a) Measure the time for each computation-send the results to a file.
* Recommend using the Chrono library from C++
b) Make certain you have "sufficient" data for convincing results.
4) Import your data (from 3) to excel for easy graphing
5) Compare the theoretical curves of Big-O with the empirical results.
a) Try running on machines with [significantly] different speeds.
b) Compare methods to answer the find an answer to question 1.c, above.
6) There are other recursive functions such as the Lucas Sequence, how can you apply what you have
learned to it?
a) Iteratively computation
b) Recursive computation
c) Recursive computation with dynamic programming.

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