Recursion

(A) [15 points] Write a recursive function that will calculate Fibonacci numbers using a recursive

definition. Write a short program to test it. The input of this program must be a positive integer

n; the output is the corresponding Fibonacci number F(n).

(B) [20 points] Write an iterative function to calculate Fibonacci numbers. Write a test driver for it.

The input of this program must be a positive integer n; the output is the corresponding Fibonacci

number F(n).

(C) [10 points] Write a program that will compare running time of the recursive and iterative

functions for calculating Fibonacci numbers. Call each function for the same size of input n and

find their running times. For part (E) of this project you will have to run this program multiple

times to find out how the running time of each function depends on the value of n.

(D)[35 points] NOT RELEVANT TO PREVIOUS PARTS.

In this part of the project, write a function that will implement each Fibonacci number with the

help of an integer array of size 100 (elements of this array will be digits of the Fibonacci

number). When the function is called to find F(n), it will calculate all Fibonacci numbers from

F(2) to F(n). using the basic formula F(n) = F(n-1)+F(n-2). To add two Fibonacci

numbers, the function will add elements of two arrays corresponding to F(n-1) and F(n-2)

and store their sums in the array corresponding to F(n). (You are NOT supposed to store ALL

arrays.) Write a program that will calculate Fibonacci numbers containing up to 100 digits.

Display the biggest Fibonacci number that has less than 100 digits. Make sure that your program

will display the error message when a Fibonacci number has 100 digits or more.

(E) [20 points] This part of the project is a written analysis of two algorithms of calculating

Fibonacci numbers: recursive (part A) and iterative (part B). Show the theoretical order of

growth of the running time for both algorithms. Then include experimental results based on part

(C) and explain them.

( 1 comentário ) St Louis, United States

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