a$.$ Find the shortest path from node s$1$ to all other nodes using Dijkstra$$s algorithm. Show all steps in a table and draw the shortest$-$path tree on the graph

b$)$Now suppose the nodes had instead implemented Bellman$-$Ford distance vector algorithm. Starting from a clean state, how many update periods $($excluding the initial point$)$ does it take until the routing protocol converges? Show the content of the routing table at each node $($next hop and total cost for all destinations$)$ at each update period until the final convergence. Show the final routing table at each node using the following format:

Node s$1$ Routing Table

Destination $,$ Next Hop $,$ Cost

Node s$2$ Routing Table

$$Destination $,$ Next Hop $,$ Cost

c$)$Now suppose that after the convergence of the distance vector algorithm in part $($b$),$ the link s$1-$s$3$ fails. Starting from the converged tables, show how all routing tables change toward a new state Show all steps and calculate how many update intervals does it take until the routing tables converge.