$2)[15$ points$]$ Given the following router network graph $\backslash ($ G$=($V$,$ E$)\backslash ),$ as shown below

$($i$)$ Apply Bellman and Ford's algorithm $($a$.$k$.$a$.$ the distance vector algorithm$)$ to find a single source shortest tree rooted at node $\backslash ($ u $\backslash ).(5$ points$)$

$($ii$)$ Apply Dijkstra's algorithm $($a$.$k$.$a$.$ the link state routing algorithm$)$ to find a single source shortest tree rooted at node $\backslash ($ u $\backslash ).(5$ points$)$

$($iii$)$ If the weight assigned to each edge in graph $\backslash ($ G$($V$,$ E$)\backslash )$ is allowed to be negative, then do the two mentioned algorithms for finding a single source shortest still work? If not, give a counter$-$example to demonstrate why the mentioned algorithm does not work. $(5$ points

$3)\backslash ([\backslash$mathbf$\{10\}\backslash )$ points $\backslash (]\backslash )$ Suppose we want to estimate the number of hosts in a subnet behind its one$-$hop