Algorithm Analysis $(15$ points$)$

ALGORITHM Fun $($a$[],$ int s$,$ int e$)$

$\{$

int m $=$ s ;

for j $=$ s$+1$ to e

if $($a$[$ j $]<$ a$[$m$])$ m $=$ j ;

return m;

$\}$

ALGORITHM Process $($a$[0..$n$1],$ int n $)$

$\{$

for i $=0$ to n$2\{$

m $=$ Fun $($a $,$ i $,$ n$1)$ ;

t $=$ a$[$i $]$; a$[$ i $]=$ a$[$m$]$; a$[$m$]=$ t; $\}$

$\}$

$1.$ What are the objectives of these two functions?

$2.$ Find the number of array element comparisons T$($n$)$ done by a call of Fun $($a$,$ s$,$ e$),$ and

by a call of Process$($a$,$ n$)$ as a function of n$.$

$3.$ What are the corresponding Big$-$O complexities in terms of n$?$