Question $3$

Algorithm A is expressed in the flowchart below:

$($a$)$ Consider input values $x=5,e=0\mathrm{.}5.$ Use the flowchart to determine what $A$

outputs. Show your working.

$($b$)$ What is the purpose of $A?$

$($c$)$ Express $A$ as recursive pseudocode.

$($d$)$ By considering inputs $x=2^n,$ where $n$ is an integer larger than $1,$ and $e=1,$

argue that the time complexity of $A$ is linear in $n.$