Question $5.$

$[15$ marks$]$

Consider the campus map of the Hong Kong Polytechnic University shown in Figure $5-1$:

Figure $5-1$

COMP$2012$ Discrete Mathematics $($AY$2024-25$ Semester $1)$

$5($a$)$ Draw a graph $\backslash ($ G $\backslash )$ with the following information given $(5$ marks$)$:

$5($b$)$ Suppose today is the student orientation day and the whole area between Block M and VA are occupied by Academic Registry $($AR$).$ With the graph $\backslash ($ G $\backslash )$ obtained in $5($a$),$ deduce the lowest cost distances from Core Q to the all destinations. $(8$ marks$)$

$5($c$)$ Consider that you are currently at W$202$ and then you are going to take the COMP$2012$ tutorial class at QR$602.$ Assume at Block R$,$ all the stairs and elevators are under maintenance, write down the shortest path with the result obtained in $5($b$).(2$ marks$)$