Consider the function What AmI, whose pseudocode is given below. The algorithm takes a

graph as an input and outputs either true or false. The algorithm also uses a global array $p$ that

holds a Boalean value for every vinV and a global integer variable $c.$

input : graph $G=(V,E).$

output: either true or false

function What AmI $(G)$

for vinV do $p[v]larr$ false;

clarr$0$;

for vinV do

if $p[v]=$ false then

clarrc$+1$;

subWhatAmI $(G,v)$;

if $c>2$ then

return true

return false

procedure subWhatAmI $(G,w)$

$p[w]=$ true;

for $\{w,u\}inE$ do

if $p[u]=$ false then subWhatAmI$(G,u)$

Given a graph $G,$ then the function What AmI returns true if and anly if:

$G$ is disconnected

$G$ has at most $2$ components

$G$ has more than $2$ components

all components of $G$ have more than two vertices