Theoretical analysis involves understanding the time complexity of the algorithms and predicting how their runtime should behave as the input size increases. By comparing empirical runtime data with theoretical analysis, one can determine if the observed runtime growth aligns with the expected behavior based on the algorithm's theoretical time complexity. This comparison helps validate the theoretical analysis and provides insights into the practical performance of the algorithms.

Instructions

Implement an Exponential Fibonacci Algorithm in Java in R

$******************************************$

public class Fibonacci $\{$

$/**$

public static long calculateFibonacciNumber$($int n$)\{$

$//$To Do

$\}$

public static void main$($String$[]$ args$)\{$

int n $=$ Integer.parseInt$($args$[0])$;

System.out.println$($calculatesFibonacciNumber$($n$))$;

$\}$

$\}$

$*************************$

$1-$ Use the Java code template above to implement the exponential Fibonacci algorithm shown below. Name the Java file ExponentialFibonacci.java.

function fib$1($n$)$

if n$=0$: return $0$

if n$=1$: return $1$

return fib$1($n$-1)+$ fib$1($n$-2)$

$2-$ Test your Java Fibonacci program with n $=0,1,2,3,4,5,6,7,8,9.$ You may have to come with large integer numbers to see the effect on the algorithm runtime.