$($b$)$ Apply the Dijkstra's algorithm to find the shortest path tree and the forwarding table for node $3$ in the network shown in Fig.Q$3.$ The number besides each link represents the cost of the link. You should clearly show the details in each iteration when deriving the answer. No marks will be given for an answer without any steps.

$($c$)$ Suppose now the distance vector algorithm is used to build up the routing table of all routers for the network shown in Fig.Q$3.$ Write down the initial distance vector of node $4.$ Also determine the forwarding table of node $11$ after it receives the initial distance vectors from all its neighbors. Given that the forwarding table has the following entries:

$\backslash$table$[[$Destination$,$Next Hop,Cost$]]$

$(8$ marks$)$