Instructions

In the text book, Chapter $4,$ complete exercise

R$-4\mathrm{.}1$ through R$4\mathrm{.}3$

P$-4\mathrm{.}61-$ Perform an experimental analysis that compares the relative running times of the methods shown in Code Fragment

$4\mathrm{.}12.$

R$-4\mathrm{.}1$ Graph the functions $8n,4nlogn,2n^2,n^3,$ and $2^n$ using a logarithmic scale for

the $x-$ and $y-$axes; that is$,$ if the function value $f(n)$ is $y,$ plot this as a point with

$x-$coordinate at $logn$ and $y-$coordinate at $logy.$

R$-4\mathrm{.}2$ The number of operations executed by algorithms A and $B$ is $8nlogn$ and $2n^2,$

respectively. Determine $n_0$ such that $A$ is better than $B$ for $n{n}_0.$

R$-4\mathrm{.}3$ The number of operations executed by algorithms A and $B$ is $40n^2$ and $2n^3,$ re$-$

spectively. Determine $n_0$ such that $A$ is better than $B$ for $n{n}_0.$

P$-4\mathrm{.}61$ Perform an experimental analysis that compares the relative running times of the

methods shown in Code Fragment $4\mathrm{.}12.$

$\frac{?}{?}****$ Returns the sum of the integers in given array. $*\frac{*}{?}$