What is the time complexity of the nested loops below? Assume n is a power of $2.$ i $=$ n; while $($i $>=1)\{$ j $=$ i; while $($ j n $)\{//$ Needs T $(1)$ j $=2*$ j; $\}$ i $=?$ i$/2?$; $\}$Consider the following algorithm:

int add$\_$them $($int $n,$ int $A[])$

$\{$

index $i,j,k$;

$j=0$;

for $(i=1$;$,in$;$i++)$

$j=j+A[i]$

$k=1$;

for $(i=1$;$,in$;$i++)$

$k=k+k$

return $j+k$;

$\}$

$($a$)$ If $n=5$ and the array A contains $2,5,3,7,$ and $8,$ what is the

output?

$($b$)$ What is the time complexity $T(n)$ of the algorithm?

$($c$)$ Try to improve the efficiency of the algorithm.