$3$A$)$ Consider the following network. With the indicated link costs, use Dijkstra$$s shortest$-$path algorithm to compute the shortest path from x to all network nodes. Show how the algorithm works by computing the table.

$($i$)$ D$($v$)$: cost of the least$-$cost path from the source node to destination v as of this iteration of the algorithm.

$($ii$)$ p$($v$)$: previous node $($neighbor of v$)$ along the current least$-$cost path from the source to v$.$

$($iii$)$ N$\_$ : subset of nodes; v is in N$\_$ if the least$-$cost path from the source to v is definitively known.

Table $4\mathrm{.}3*$ Running the link$-$state algorithm on the network in Figure $4\mathrm{.}27$