$1.$ The following network with $8$ nodes is given. The link costs are marked next to the corresponding links. $(25$pt$)$

$($a$)$ Calculate the shortest paths from all nodes to node A using Dijkstra's algorithm. To break visiting order ties, start with the node whose label letter appears earlier in the alphabet. Show your work on the figure above.

$($b$)$ Show the sink tree for A in a separate diagram.

$($c$)$ If all nodes are equally likely to send a packet to A$,$ which link has the highest potential to carry packets destined to A$?$ Why?