Starting Out with Java: From Control Structures through Data Structures (4th Edition) (What's New in Computer Science)
Starting Out with Java: From Control Structures through Data Structures (4th Edition) (What's New in Computer Science)
4th Edition
ISBN: 9780134787961
Author: Tony Gaddis, Godfrey Muganda
Publisher: PEARSON
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Chapter 16, Problem 9PC

Efficient Computation of Fibonacci Numbers

Modify the application in Code Listing 16-18 by replacing the recursive method for computing Fibonacci terms with an iterative version and try to make it as efficient as possible. Modify the application so it outputs the elapsed time in both seconds and milliseconds. Finally, run the application and generate output showing the rime required to compute the terms of the sequence in positions 45, 46, 47, 48, 49, and 50. Comment on the results.

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1. Write a recursive method expFive(n) to compute y=5^n. For instance, if n is 0, y is 1. If n is 3, then y is 125. If n is 4, then y is 625. The recursive method cannot have loops. Then write a testing program to call the recursive method. If you run your program, the results should look like this: > run RecExpTest Enter a number: 3 125 >run RecExpTest Enter a number: 3125 2. For two integers m and n, their GCD(Greatest Common Divisor) can be computed by a recursive function. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Once m is 0, the function returns n. Once n is 0, the function returns m. If neither is 0, the function can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n. Although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. Meaning your code needs to follow the given algorithm. Then…
Fibonacci numbers are a sequence of integers, starting with 1, where the value of each number is the sum of the two previous numbers, e.g. 1, 1, 2, 3, 5, 8, etc. Write a function called fibonacci that takes a parameter, n, which contains an integer value, and have it return the nth Fibonacci number. (There are two ways to do this: one with recursion, and one without.)
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Starting Out with Java: From Control Structures through Data Structures (4th Edition) (What's New in Computer Science)

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