Problem $3(12$ points$)$: Consider the following network. With the indicated link costs, using Dijkstra's algorithm, answer the following and show your work using a table.

Figure $1$: Network topology with associated link costs.

$($a$)$ Compute the shortest path from $\backslash ($ y $\backslash )$ to all network nodes.

$($b$)$ Compute the shortest path from $\backslash ($ t $\backslash )$ to all network nodes.