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)

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)

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 17PE

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