If F $=\{$b$,$ c$,$ g$\}$ then we need to report $\{$a$,$ b$,$ c$,$ d$,$ g$\}$: $\{$b$,$ c$,$ g$\}$ are initially on fire

and together set d on fire, and in turn $\{$b$,$ c$,$ d$\}$ set a on fire as well. Note that

e and f don$$t catch fire, since fewer than $3$ of their neighbours are on fire. If

F $=\{$d$,$e$,$ f $\},$ we report $\{$d$,$e$,$ f $,$ g$\}$ since $\{$d$,$e$,$ f $\}$ make g catch fire and no other

vertex has $3$ burning neighbours after that.

Design an algorithm that given an initial set of burning vertices F$,$ computes

all burning vertices of V$.$ For full marks, your algorithm should run in O$($n $+$ m$)$

time. Remember to:

a$)$ describe your algorithm in plain English,

b$)$ argue its correctness, and

c$)$ analyze its time complexity