for $($int $i=0$; $i$ array. Iength; $i++)1$

for $($int $j=1$; $j$ array. Iength; $j++)$

for $($int $k=0$; $k$ array. length; $k+=j$

array$[i]=$array$[j]+$array$[k]$

$\}.$

$1$

$1$

Let $R(N)$ be the worst$-$case running time of this code, where $N$ is the length of the array. We want to find an $f(N)$ such that $R(N)inO(f(N)).$ Write a summation that could be used to calculate an $f(N).$

a$){\displaystyle \underset{i=0}{\overset{N-1}{}}}{\displaystyle \underset{j=1}{\overset{N-1}{}}}{\displaystyle \underset{k=0}{\overset{N-1}{}}}1$

b$){\displaystyle \underset{i=0}{\overset{N-1}{}}}{\displaystyle \underset{j=1}{\overset{N-1}{}}}{\displaystyle \underset{k=1}{\overset{\frac{N}{1}}{}}}$

c$){\displaystyle \underset{i=0}{\overset{N-1}{}}}{\displaystyle \underset{j=1}{\overset{N-1}{}}}j$

d$){\displaystyle \underset{i=0}{\overset{N-1}{}}}{\displaystyle \underset{j=1}{\overset{N-1}{}}}i+j$

e$){\displaystyle \underset{i=0}{\overset{N-1}{}}}{\displaystyle \underset{j=1}{\overset{N-1}{}}}i**j$

f$){\displaystyle \underset{i=0}{\overset{N-1}{}}}{\displaystyle \underset{j=1}{\overset{N-1}{}}}\frac{1}{j}$

g$){\displaystyle \underset{i=0}{\overset{N-1}{}}}{\displaystyle \underset{j=1}{\overset{N-1}{}}}{\displaystyle \underset{k=0}{\overset{N-1}{}}}k+j$

h$)({\displaystyle \underset{i=0}{\overset{N-1}{}}}1)+({\displaystyle \underset{j=1}{\overset{N-1}{}}}1)+({\displaystyle \underset{k=0}{\overset{N-1}{}}}1)$